Math Calculators

Calculate percentages, percentage of a number, and percentage change between two values.

Convert numbers between binary, decimal, hexadecimal, and octal.

Add, subtract, multiply, and divide fractions with step-by-step simplification.

Find the Least Common Multiple and Greatest Common Divisor of any set of numbers.

Convert numbers to Roman numerals and Roman numerals back to numbers.

Check if a number is prime, and find all prime numbers up to any limit.

Calculate the mean, median, mode, and range of any set of numbers.

Simplify ratios, scale ratios, and solve ratio proportions.

Full scientific calculator with trigonometry, logarithms, exponents, and more.

Calculate the percentage increase or decrease between two values.

Calculate your Grade Point Average from course grades and credit hours.

Calculate your final grade from weighted assignments, exams, and projects.

Calculate percentage error and absolute error between observed and reference values.

Calculate population or sample standard deviation, variance, mean, sum, and count.

Calculate simple event probability from favorable outcomes and total outcomes.

Calculate the z-score of a value using its mean and standard deviation.

Calculate the area of a rectangle, circle, or triangle.

Calculate the volume of a rectangular box, cylinder, or sphere.

Find the hypotenuse of a right triangle from the two perpendicular sides.

Calculate triangle perimeter and area from three side lengths.

Calculate the slope between two points on a line.

Calculate a number raised to a positive, negative, or fractional exponent.

Calculate the square root of a non-negative number.

Calculate a logarithm for any positive value and valid base.

Round a number to a selected number of significant figures.

Calculate the score needed on a final assessment to reach a target overall grade.

Calculate density from mass and volume using density = mass ÷ volume.

Calculate percent difference between two values using their average magnitude.

Solve a quadratic equation and calculate its discriminant and real roots.

Calculate circle area, circumference, and diameter from radius.

Calculate surface area for a rectangular prism, cylinder, or sphere.

Calculate straight-line distance between two points on a coordinate plane.

Round a number to a selected number of decimal places.

Find the positive factors of a positive integer.

Convert a number to normalized scientific notation.

Convert a terminating decimal to a simplified fraction.

Convert a fraction to a decimal value.

Convert between mixed numbers, improper fractions, and decimal values.

Calculate a weighted average from values and their weights.

Find the median of a list of numbers.

Find the most frequent value or values in a data set.

Find the range, minimum, and maximum of a data set.

Calculate the quantity or cost per one unit.

Solve a simple proportion with three known values.

Calculate permutations and combinations for n items taken r at a time.

Calculate the factorial of a non-negative integer.

Calculate area, perimeter, and diagonal of a rectangle.

Calculate area and perimeter of a parallelogram.

Calculate area and perimeter of a trapezoid from its sides and height.

Calculate the volume and surface area of a sphere.

Calculate the volume and surface area of a cylinder.

Calculate the volume and surface area of a cone.

Calculate the volume and surface area of a cube.

Calculate the percentage-point difference between two percentages and the relative percentage change.

Calculate the first quartile, third quartile, and interquartile range of a numeric data set.

Calculate population or sample variance from a list of numeric observations and inspect the mean used.

Estimate the standard error of a sample mean from sample standard deviation and sample size.

Measure the average absolute distance of data values from their arithmetic mean.

Work out the score required on a final assessment to reach a target overall grade, given the current grade and final weight.

Find a requested nearest-rank percentile from a list of numeric observations.

Calculate the population coefficient of variation from a numeric data set with a positive mean.

Estimate a simple proportion margin of error from sample size, assumed proportion, and a critical z value.

Calculate the Pearson correlation coefficient for paired numeric observations and see the direction and strength of their linear association.

Fit a simple least-squares line to paired x and y data and estimate a y value for a chosen x.

Estimate a simple random-sample size for a proportion using a chosen confidence z-score, assumed proportion and margin of error.

Calculate the probability of exactly a chosen number of successes in independent trials with the same success probability.

Calculate the magnitude of a two- or three-dimensional vector from its components.

Calculate straight-line distance between two points in a two-dimensional coordinate plane.

Calculate a right triangle hypotenuse and acute angles from its two perpendicular side lengths.

Calculate pyramid volume from the base area and perpendicular height.

Calculate the area between two concentric circles from the outer and inner radii.

Calculate circular arc length and sector area from a radius and central angle in degrees.

Find the nth term and finite sum of an arithmetic sequence with a constant difference.

Calculate a term and finite sum in a mathematical geometric sequence with a constant ratio.

Calculate a real integer-degree root, with domain checks for negative values and even roots.

Calculate the real cube root of positive, zero, or negative numbers.

Find the normalized remainder from division for cycle, modular arithmetic, and number theory problems.

Calculate the geometric mean of positive values and compare it with their arithmetic mean.

Calculate the harmonic mean of positive numerical values for suitable rate and ratio problems.

Calculate a trimmed mean by removing a chosen percentage of observations from both tails.

Flag possible low and high outliers using Tukey fences based on the interquartile range.

Estimate a normal-approximation confidence interval around a sample mean from its spread and sample size.

Calculate an ellipse area from its semi-major and semi-minor axes, with a perimeter approximation.

Calculate rhombus area from the lengths of its two diagonals.

Calculate the area of a standard kite from its perpendicular diagonal lengths.

Calculate area, perimeter, and apothem for a convex regular polygon from side count and side length.

Calculate prism volume from base area and perpendicular height.

Update a prior probability with new evidence using Bayes’ theorem and supplied conditional probabilities.

Find the union, intersection and differences of two comma-separated sets, with duplicate values removed.

Add, subtract and multiply 2×2 matrices and calculate each determinant with transparent row and column inputs.

Add, subtract, multiply and divide complex numbers, and calculate their magnitudes from real and imaginary parts.

Estimate a y-value between two known points using linear interpolation and identify when the result is extrapolated.

Calculate the dot product, vector magnitudes and angle between two three-dimensional vectors.

Calculate the three-dimensional cross product vector and its magnitude using the right-hand-rule convention.

Estimate probability below, between or above two values for a normal distribution with a chosen mean and spread.

Find the midpoint and straight-line distance between two points on a Cartesian plane.

Calculate slope, y-intercept and the equation of the straight line through two distinct coordinate points.

Solve a triangle side from two side lengths and their included angle using the law of cosines.

Calculate the projection vector and scalar projection of one three-dimensional vector onto another.

Find the smaller angle between two non-zero three-dimensional vectors from their components.

Calculate population and sample covariance from two equally sized paired data series.

Calculate raw median absolute deviation and mean absolute deviation from the data median.

Compare observed category counts with expected counts and estimate the chi-square statistic, degrees of freedom and upper-tail p-value.

Compare two independent success proportions using a pooled z statistic and a two-sided normal approximation.

Calculate the probability of an event count under a Poisson model using its expected rate.

Calculate the probability that the first success occurs on a specified trial in repeated independent trials.

Combine two sample standard deviations into a pooled estimate when the equal-variance assumption is appropriate.

Calculate a weighted average from matching score and weight lists.

Express a standard deviation relative to a positive mean as a percentage.

Estimate sample size for a proportion at a chosen confidence z-score and margin of error.

Calculate the latest rolling mean and each rolling average in a numeric sequence.

Calculate the probability of an exact number of successes when drawing from a finite population without replacement.

Estimate the sample size needed to estimate a population mean for a stated standard deviation, margin of error and confidence z-score.

Calculate a Wilson score confidence interval for a proportion from observed successes and total observations.

Calculate the finite population correction factor for simple random sampling without replacement.

Compare observed and predicted numeric sequences using root mean square error, mean squared error and count of observations.

Calculate mean absolute percentage error from aligned observed and predicted values.

Calculate a paired-samples t statistic, degrees of freedom and two-sided p-value from sample summary statistics.

Compare two independent sample means with Welch’s t-test without assuming equal population variances.

Calculate Pearson’s chi-square statistic and an asymptotic p-value for a 2 by 2 contingency table.

Estimate standardized mean difference using the pooled sample standard deviation of two independent groups.

Calculate Spearman’s rank correlation from two matched numeric series, including average ranks for tied values.

Square a Pearson correlation coefficient to calculate R-squared for a simple linear relationship with an intercept.

Calculate adjusted Fisher–Pearson sample skewness from a list of numeric observations.

Calculate adjusted sample excess kurtosis to describe tail weight relative to a normal distribution.

Calculate sensitivity, specificity, predictive values and total sample count from confusion-matrix counts.

Calculate precision, recall and F1 score from true-positive, false-positive and false-negative counts.

Estimate chance-corrected agreement between two raters from a 2 by 2 agreement table.

Calculate each interior angle and the angle sum of a regular polygon from its number of sides.

Estimate ellipse circumference using Ramanujan’s approximation from the semi-major and semi-minor axes.

Estimate the standard error of a sample mean from sample standard deviation and sample size.

Calculate the first quartile, third quartile and interquartile range from an entered numeric sample.

Calculate the exact probability of a specified number of successes in a fixed number of independent trials with constant success probability.

Calculate what percentage of a defined population is represented by a sample, and see the remaining population count.

Estimate per-variant sample size for a two-sided conversion-rate A/B test using a normal approximation, baseline rate and relative minimum detectable lift.

Calculate a Wilson score confidence interval for a binomial proportion from observed successes and a chosen z multiplier.

Estimate a two-sided Fisher exact p-value for a 2×2 table of integer counts, using fixed margins.

Calculate Cohen’s kappa from observed agreement and the agreement expected by chance.

Estimate the continuity-corrected McNemar chi-square statistic and approximate p-value from discordant pairs in paired binary observations.

Calculate a Mann–Whitney U statistic and an approximate two-sided normal p-value from sample sizes and the rank sum for sample one.

Find the exact probability of a specified count and the cumulative probability up to that count under a Poisson model.

Compare an observed sample proportion with a user-specified null proportion using a normal-approximation z test.

Calculate Kendall tau-a from concordant and discordant pair counts to summarize monotonic rank association.

Estimate a predictor’s variance inflation factor from its R-squared when regressed on other predictors.

Estimate a prediction interval for one future observation from a mean, sample standard deviation, sample size and supplied critical t multiplier.

Estimate internal consistency from item count and average inter-item correlation, with assumptions made explicit.

Estimate a simple variance-components intraclass correlation from between-subject and within-subject variance.

Combine two sample standard deviations using degrees-of-freedom weighting.

Estimate the standard error of the difference between two independent sample means.

Compare an outcome risk between exposed and unexposed groups using a four-cell table.

Calculate the risk difference between two groups from event and non-event counts.

Calculate a standard-normal critical z value for a central confidence level.

Calculate Shannon entropy and effective category count from up to five nonnegative category weights.

Estimate the finite-sample Simpson diversity index from category counts.

Calculate an expected cell frequency under independence from its row, column and grand totals.

Calculate one Benjamini–Hochberg rank threshold from the number of tests, target FDR and p-value rank.

Evaluate the discriminant of a quadratic polynomial to understand the number of real roots.

Calculate the perpendicular height of a parallelogram from its area and chosen base length.

Calculate the length of a trapezoid midsegment from the two parallel base lengths.

Find the volume of a straight triangular prism from its triangle base, perpendicular height, and prism length.

Calculate just the curved outside surface area of a right circular cylinder without its end caps.

Determine a right circular cone’s slant height from its radius and perpendicular height.

Calculate the area of a minor circular segment from circle radius and its central angle.

Calculate the curved surface area of a conical frustum using its top and base radii and vertical height.

Find the radius of the incircle inside a triangle from its three side lengths.

Calculate the center-to-side perpendicular distance of a regular polygon from its side length and side count.

Approximate ellipse circumference from its semi-major and semi-minor axes using Ramanujan’s first formula.

Calculate the solid volume of a straight hollow cylinder or pipe from its outer radius, inner radius and length.

Evaluate the logarithm of a positive number using a chosen valid positive base other than one.

Calculate the scalar dot product of two two-dimensional vectors from their horizontal and vertical components.

Find the signed scalar length of one 2D vector projected onto the direction of a second nonzero vector.

Calculate the geometric mean of three positive numbers on the same meaningful numeric scale.

Torus Volume Calculator estimates cm³ using major radius to tube center (cm), tube radius (cm). A ring torus assumes major radius exceeds minor radius and a perfect circular cross-section.

Ellipsoid Volume Calculator estimates cm³ using first semi-axis (cm), second semi-axis (cm), third semi-axis (cm). Use radii, not full diameters; this applies to an ideal ellipsoid.

Regular Tetrahedron Volume Calculator estimates cm³ using edge length (cm). Only equilateral triangular faces are valid for this formula.

Spherical Cap Volume Calculator estimates cm³ using sphere radius (cm), cap height (cm). Cap height must be at most twice sphere radius.

Circular Chord Length Calculator estimates cm using circle radius (cm), central angle (degrees). The supplied angle must be in degrees; geometry assumes a perfect circle.

Polygon Diagonals Count Calculator estimates diagonals using polygon sides. Only simple polygons with at least three integer sides are covered.

Right Cone Total Surface Area Calculator estimates cm² using cone base radius (cm), vertical height (cm). Includes circular base and sloping side but assumes a perfect right cone.

Annular Sector Area Calculator estimates cm² using outer radius (cm), inner radius (cm), central angle (degrees). The inner radius must not exceed the outer radius.

Ellipse Focal Distance Calculator estimates cm using semi-major axis (cm), semi-minor axis (cm). Use semi-axes with semi-major no smaller than semi-minor.

Regular Hexagonal Prism Volume Calculator estimates cm³ using hexagon side (cm), prism height (cm). Requires regular hexagonal bases and perpendicular height.

Heron Triangle Area Calculator uses triangle side a and triangle side b to calculate unit². All three sides must obey the triangle inequality.

Triangle Circumradius from Sides Calculator uses side a and side b to calculate length units. A degenerate triangle has no finite circumcircle radius.

Parabola Vertex X Coordinate Calculator uses quadratic coefficient a and linear coefficient b to calculate x units. Requires nonzero a; the x coordinate alone does not give the vertex height.

Regular Octagon Area Calculator uses octagon side length to calculate unit². Only applies to a regular eight-sided polygon.

Rectangular Prism Diagonal Calculator uses prism length and prism width to calculate length units. Inputs must be measured along mutually perpendicular edges.

Isosceles Triangle Height Calculator uses equal side length and base length to calculate length units. The base must be shorter than twice either equal side.

Triangular Prism Surface Area Calculator uses base side a and base side b to calculate unit². Assumes a right prism with congruent triangular ends; exclude material thickness.

Hollow Sphere Volume Calculator uses outer sphere radius and inner cavity radius to calculate unit³. Uses concentric inner and outer spherical boundaries.

Circular Segment Sagitta Calculator uses circle radius and chord length to calculate length units. Sagitta is the minor segment height; it is not an arc length.

3D Scalar Triple Product Calculator uses vector a x and vector a y to calculate unit³. The signed value is determinant A dot (B cross C); absolute value gives parallelepiped volume.

2×2 Odds Ratio Calculator uses exposed with outcome and exposed without outcome to calculate odds ratio. Zero-cell corrections and confidence intervals require additional modeling.

Positive Likelihood Ratio Calculator uses sensitivity percent and specificity percent to calculate ratio. Derived from sensitivity and specificity; not an individual prediction.

Negative Likelihood Ratio Calculator uses sensitivity percent and specificity percent to calculate ratio. Derived from test characteristics, not personal diagnosis.

Balanced Accuracy Calculator uses true-positive rate percent and true-negative rate percent to calculate %. Balance across classes does not show calibration or prevalence.

Matthews Correlation Coefficient Calculator uses true positives and true negatives to calculate MCC. The coefficient is undefined if any marginal product is zero.

Jaccard Similarity Calculator uses items common to both sets and only in set a to calculate %. Empty-union conventions vary; this tool treats it as undefined.

Sørensen Dice Similarity Calculator uses shared items and only a to calculate %. Appropriate for sets, not automatically for fuzzy matching scores.

Hedges g Effect Size Calculator uses group mean difference and pooled standard deviation to calculate g. Uses a common large-sample correction with pooled SD, not a significance test.

Phi Coefficient Calculator uses cell a and cell b to calculate phi. Uses nonnegative 2×2 counts; not proof of causal association.

Weighted RMS Calculator uses first measured value and second measured value to calculate units. Use nonnegative weights and compatible physical units; this differs from arithmetic averaging.

20-sided Polygon Interior Angle uses number of polygon sides to calculate degrees. The formula assumes a simple Euclidean polygon; a regular figure has equal angles.

Regular Polygon Exterior Angle uses number of sides to calculate degrees. Applies to regular convex polygons, not general irregular polygons.

Annulus Area from Radii uses outer radius m and inner radius m to calculate m². Both circles must be concentric for an annulus interpretation.

Parabola Focal Distance from Coefficient uses absolute quadratic coefficient to calculate units. For y=ax², signed focus direction depends on coefficient sign; this is the distance.

Ellipse Latus Rectum Length uses semi-major axis and semi-minor axis to calculate units. Assumes a standard axis-aligned ellipse with minor axis not exceeding major.

Circle External Tangent Length uses distance from outside point to circle centre and circle radius to calculate units. Only applies to an external point tangent to a circle in Euclidean geometry.

IQR from First and Third Quartiles uses first quartile and third quartile to calculate units. Quartile conventions can differ for small samples; choose one consistent method.

Coefficient of Range uses maximum observation and minimum observation to calculate ratio. Only a rough relative spread statistic, sensitive to outliers.

Poisson Probability of Zero Events uses expected event count to calculate %. Assumes independent events with a constant rate over the chosen interval.

Triangle Centroid Distance on Median uses full median length to calculate units. Measured from the vertex to centroid; centroid to midpoint is one-third.

Spherical Cap Surface Area uses sphere radius metres and cap height metres to calculate m². Curved surface only; excludes the circular base.

Trapezoidal Prism Volume uses upper trapezoid base m and lower trapezoid base m to calculate m³. Bases must be parallel for the area formula to apply.

Regular Octagon Perimeter uses octagon side length metres to calculate m. Applies only to eight equal sides.

Ellipse Eccentricity uses semimajor axis a and semiminor axis b to calculate ratio. For a circle eccentricity is zero.

Circle Chord Length from Angle uses circle radius metres and central angle degrees to calculate m. Returns nonnegative chord length for the full-circle central angle range.

Triangular Number of Points uses points on each side row count to calculate points. Counts a triangular array 1 plus 2 up to n.

Rectangular Pyramid Volume uses rectangular base length m and rectangular base width m to calculate m³. Height is perpendicular to base, not slant height.

Annulus Total Boundary Length uses outer circle radius m and inner circle radius m to calculate m. Adds inside and outside edge lengths.

Polygon Interior Angle Sum uses number of polygon sides to calculate degrees. For a simple polygon without self-intersection.

Conical Frustum Lateral Area uses large radius metres and small radius metres to calculate m². Excludes the two circular end faces.

Relative Frequency Percentage uses occurrences in category and all observations to calculate %. Use the same observations in numerator and denominator.

Conditional Probability of A Given B uses observed a and b events and observed b events to calculate %. Counts must refer to a single consistent population.

Sample Proportion Standard Error uses sample proportion and sample size to calculate ratio. Normal approximation may be unreliable for very small expected counts.

Count Ratio uses numerator count and denominator count to calculate times. A rate ratio requires rates with comparable exposure times, not only counts.

Data Range from Extremes uses observed maximum and observed minimum to calculate units. Range is sensitive to outliers and ignores the rest of the distribution.

Survey Screenout Rate uses respondents screened out and respondents starting screening to calculate %. Depends on how the study defines ineligible participants.

Midrange of a Dataset uses smallest observed value and largest observed value to calculate units. Sensitive to extreme observations and not a robust central measure.

Union Probability Two Events uses p(a) percent and p(b) percent to calculate %. Events need a common probability space; overlapping probability cannot exceed either marginal.

Mean Forecast Residual Error uses sum of signed forecast minus actual residuals and number of forecasts to calculate units. Positive means overprediction using forecast minus actual; cancellations hide large errors.

Semi Interquartile Range uses third quartile value and first quartile value to calculate units. Quartile interpolation method must be consistent across samples.

Calculate circular sagitta from chord from radius, chord. The result is expressed in m. Valid for the minor arc of a circle.

Calculate regular hexagon diagonal from side. The result is expressed in m. Returns the longest vertex-to-opposite-vertex diagonal.

Calculate rectangle diagonal angle from width, height. The result is expressed in degrees. Angle is measured from the width edge.

Calculate isosceles trapezoid leg length from top, bottom, height. The result is expressed in m. Assumes a centered isosceles trapezoid and parallel bases.

Calculate sphere section area offset from radius, offset. The result is expressed in m². Offset is the distance from the sphere center to the cutting plane.

Calculate triangle excircle tangent length from a, b, c. The result is expressed in m. A tangent length uses the triangle semiperimeter and side a.

Calculate regular pentagon diagonal ratio from side, diagonal. The result is expressed in ratio. For a mathematically regular pentagon, the ratio is the golden ratio.

Calculate ellipse bounding box unused area from major radius, minor radius. The result is expressed in m². Returns the bounding rectangle area outside the inscribed ellipse.

Calculate square inscribed circle unused area from side. The result is expressed in m². Returns the square corners outside its inscribed circle.

Calculate rhombus perimeter diagonals from d1, d2. The result is expressed in m. Uses perpendicular diagonals of a rhombus.

Calculate wilson interval center from successes, trials, z. The result is expressed in ratio. Wilson center is only one part of the confidence interval.

Calculate wilson interval halfwidth from successes, trials, z. The result is expressed in ratio. Assumes independent Bernoulli trials.

Calculate geometric distribution expected trials from success probability. The result is expressed in trials. Trials are independent with a constant success probability.

Calculate normal distribution variance from sd from sd. The result is expressed in units². Population and sample standard deviations have different estimators.

Calculate cohens h standardized effect from p1, p2. The result is expressed in units. Both proportions must be between zero and one.

Calculate harmonic speed outbound return from outbound, return speed. The result is expressed in km/h. Valid when the two trip distances are equal.

Calculate normal mean interval halfwidth from sd, n, z. The result is expressed in units. Known/estimated spread and sampling assumptions determine interval validity.

Calculate f1 score from precision recall from precision, recall. The result is expressed in %. Precision and recall must refer to the same classification threshold.

Calculate population variance expected square from mean square, squared mean. The result is expressed in units². Use E[X²] minus E[X]² with consistent input units.

Calculate sample standard error from variance from variance, n. The result is expressed in units. Assumes independent observations and a compatible variance estimate.

Calculate regular polygon interior angle from Number of sides. Get the result in degrees with a worked formula and clear assumptions: Requires at least three sides for a valid polygon.

Calculate regular polygon triangulation count from Number of sides. Get the result in triangles with a worked formula and clear assumptions: Counts triangles from a single vertex in a convex polygon; at least three sides required.

Calculate spherical cap volume from height from Sphere radius m, Cap height m. Get the result in m³ with a worked formula and clear assumptions: Cap height must be between zero and twice the sphere radius.

Calculate cylinder lateral surface area from Radius m, Height m. Get the result in m² with a worked formula and clear assumptions: This excludes the two circular end faces.

Calculate cone lateral surface area from Cone radius m, Cone height m. Get the result in m² with a worked formula and clear assumptions: A straight right circular cone is assumed.

Calculate annular sector perimeter from Outer radius m, Inner radius m, Sector angle degrees. Get the result in metres with a worked formula and clear assumptions: Requires inner radius not exceeding outer radius and sector angle from 0 to 360 degrees.

Calculate ellipsoid volume from First semiaxis m, Second semiaxis m, Third semiaxis m. Get the result in m³ with a worked formula and clear assumptions: All values are semiaxes, not full diameters.

Calculate rectangular pyramid frustum volume from Lower square base side m, Upper square base side m, Vertical height m. Get the result in m³ with a worked formula and clear assumptions: Assumes parallel square faces of a straight-sided pyramid frustum.

Calculate regular polygon area from apothem from Polygon perimeter m, Apothem m. Get the result in m² with a worked formula and clear assumptions: Use the perpendicular distance from the center to a side of a regular polygon.

Calculate angle complement from Angle degrees. Get the result in degrees with a worked formula and clear assumptions: Complement exists as a nonnegative angle only for zero to ninety degrees.

Calculate frequency table relative share from Count in bin, Total observations. Get the result in % with a worked formula and clear assumptions: Use a positive total and nonnegative bin count.

Calculate histogram bin frequency density from Observations in bin, Bin width. Get the result in count per unit with a worked formula and clear assumptions: For unequal bin widths, histogram heights should represent frequency density rather than raw count.

Calculate two-category weighted score from First score, First weight, Second score, Second weight. Get the result in points with a worked formula and clear assumptions: Weights must represent nonnegative relative importance.

Calculate standard deviation from variance from Nonnegative variance. Get the result in same units as original with a worked formula and clear assumptions: The variance must be computed using a matching population/sample convention.

Calculate variance from standard deviation from Standard deviation. Get the result in squared units with a worked formula and clear assumptions: Units are squared relative to the source measurement.

Calculate normalized score within bounds from Measured score, Lower bound, Upper bound. Get the result in % with a worked formula and clear assumptions: The maximum must exceed the minimum; results outside 0–100 indicate out-of-range input.

Calculate index number relative change from Current index, Base index. Get the result in % with a worked formula and clear assumptions: The base index must be nonzero and both values use the same index definition.

Calculate event incidence per thousand from Observed events, Population at risk. Get the result in per 1,000 with a worked formula and clear assumptions: The exposure interval and population at risk must be defined consistently.

Calculate measurement resolution percentage from Instrument resolution, Measured value. Get the result in % with a worked formula and clear assumptions: Instrument accuracy and resolution are different properties.

Calculate repeated measurement time from Replicate measurements, Seconds per measurement. Get the result in minutes with a worked formula and clear assumptions: Calibration, instrument setup and breaks are excluded.

Use the Regular Polygon Circumradius to calculate m from Polygon sides, Side length m. See the underlying formula, units, a worked example, and key limitation: Valid for a regular polygon with at least three sides.

Use the Polygon Triangulation Triangle Count to calculate triangles from Simple polygon vertices. See the underlying formula, units, a worked example, and key limitation: Counts triangles in a triangulation of a simple polygon.

Use the Rhombus Side from Diagonal Lengths to calculate m from First diagonal m, Second diagonal m. See the underlying formula, units, a worked example, and key limitation: Assumes diagonals bisect each other at right angles.

Use the Trapezoid Area from Midsegment to calculate m² from Trapezoid midsegment m, Perpendicular height m. See the underlying formula, units, a worked example, and key limitation: Requires the true midsegment parallel to both bases.

Use the Regular Polygon Side Length to calculate m from Polygon perimeter m, Number of equal sides. See the underlying formula, units, a worked example, and key limitation: Requires a regular polygon with identical sides.

Use the Hollow Cylinder Material Volume to calculate m³ from Outer radius m, Inner radius m, Cylinder height m. See the underlying formula, units, a worked example, and key limitation: Requires outer radius larger than inner radius.

Use the Sphere Surface-Area-to-Volume Ratio to calculate inverse m from Sphere radius m. See the underlying formula, units, a worked example, and key limitation: For an ideal sphere only.

Use the Hemisphere Curved Surface Area to calculate m² from Hemisphere radius m. See the underlying formula, units, a worked example, and key limitation: Excludes the flat circular base.

Use the Concentric Ring Area per Width to calculate m² per m from Outer radius m, Inner radius m. See the underlying formula, units, a worked example, and key limitation: Requires a positive ring thickness.

Use the Cube Space Diagonal Length to calculate m from Cube edge length m. See the underlying formula, units, a worked example, and key limitation: Assumes all cube edges have the same length.

Use the Quartile Coefficient of Dispersion to calculate % from First quartile, Third quartile. See the underlying formula, units, a worked example, and key limitation: Use quartiles calculated consistently from the same dataset.

Use the Spearman Rank Correlation from Differences to calculate coefficient from Sum of squared rank differences, Paired ranks. See the underlying formula, units, a worked example, and key limitation: Assumes no tied ranks; ties require a corrected procedure.

Use the Geometric Mean of Two Numbers to calculate value from First positive number, Second positive number. See the underlying formula, units, a worked example, and key limitation: Both values must be positive.

Use the Harmonic Mean of Two Numbers to calculate value from First positive number, Second positive number. See the underlying formula, units, a worked example, and key limitation: Useful for averaging rates over equal distances or amounts.

Use the Relative Error Percentage to calculate % from Measured value, Reference true value. See the underlying formula, units, a worked example, and key limitation: Do not use a zero reference value.

Use the Standard Error from Sample SD to calculate value from Sample standard deviation, Sample size. See the underlying formula, units, a worked example, and key limitation: Assumes independent observations; population assumptions matter.

Use the Covariance from Correlation to calculate covariance from Correlation coefficient, Standard deviation X, Standard deviation Y. See the underlying formula, units, a worked example, and key limitation: Correlation must lie between minus one and one.

Use the Poisson Probability of At Least One Event to calculate % from Expected events. See the underlying formula, units, a worked example, and key limitation: Assumes a Poisson distribution with a fixed expectation.

Use the Geometric First-Success Probability to calculate % from Success probability per trial, Trial number of first success. See the underlying formula, units, a worked example, and key limitation: Assumes independent identical trials.

Use the Normal-Approximation Mean Error Margin to calculate value from Critical z value, Sample SD, Sample size. See the underlying formula, units, a worked example, and key limitation: Normal approximation may be poor for small skewed samples.

Calculate m for parallelogram diagonal length using Side A m, Side B m, Included angle degrees. Includes the formula, input validation, an example with real numbers, and practical limitations. Select the diagonal associated with the sum of adjacent side vectors.

Calculate cm for regular hexagon width across flats using Hexagon side length cm. Includes the formula, input validation, an example with real numbers, and practical limitations. Only valid for a regular hexagon.

Calculate cm for ellipse center-to-directrix distance using Semi-major axis cm, Semi-minor axis cm. Includes the formula, input validation, an example with real numbers, and practical limitations. Only valid for noncircular ellipses with positive eccentricity.

Calculate cm for circle sector arc length using Radius cm, Central angle degrees. Includes the formula, input validation, an example with real numbers, and practical limitations. The angle must be measured in degrees.

Calculate cm for cuboid face diagonal using Face width cm, Face height cm. Includes the formula, input validation, an example with real numbers, and practical limitations. Only the selected rectangular face is measured.

Calculate m for trapezoid midline length using Short base m, Long base m. Includes the formula, input validation, an example with real numbers, and practical limitations. Midline joins the midpoints of the two nonparallel sides.

Calculate cm³ for regular tetrahedron volume using Edge length cm. Includes the formula, input validation, an example with real numbers, and practical limitations. All six edges must be equal.

Calculate degrees for regular polygon exterior turn angle using Number of sides. Includes the formula, input validation, an example with real numbers, and practical limitations. Only valid for regular polygons with at least three sides.

Calculate cm for ellipse perimeter approximation using Semi-major axis cm, Semi-minor axis cm. Includes the formula, input validation, an example with real numbers, and practical limitations. Ramanujan's first approximation is accurate for most practical ellipses.

Calculate cm for triangle median to side a using Opposite side a cm, Other side b cm, Other side c cm. Includes the formula, input validation, an example with real numbers, and practical limitations. Sides must satisfy triangle inequality.