Linear Interpolation Calculator
Linear interpolation estimates an intermediate y-value by assuming the relationship between two known points is a straight line. It is useful for table lookups and proportional estimates between measured points.
How to use this calculator
- Enter both known (x, y) points and the target x. The page flags whether the target lies between the points or outside them.
- Check the labels and units before applying the result to a real task.
- Change one input at a time when comparing scenarios.
Formula and method
y = y₀ + (x−x₀)(y₁−y₀)/(x₁−x₀)
- y = y₀ + (x−x₀)(y₁−y₀)/(x₁−x₀)
- The estimate assumes a linear relationship. When the target is outside the supplied x interval, the method extrapolates and can be unreliable.
Worked examples
Worked example
Between (0, 10) and (10, 30), estimate y when x = 4.
The fraction of the interval is 4/10; y = 10 + 0.4×(30−10) = 18.
The fraction of the interval is 4/10; y = 10 + 0.4×(30−10) = 18.
Understanding the result
Linear interpolation estimates an intermediate y-value by assuming the relationship between two known points is a straight line. It is useful for table lookups and proportional estimates between measured points.
The estimate assumes a linear relationship. When the target is outside the supplied x interval, the method extrapolates and can be unreliable.
Important notes
The estimate assumes a linear relationship. When the target is outside the supplied x interval, the method extrapolates and can be unreliable.
Displayed values are rounded for readability; retain appropriate precision when continuing a calculation.
Frequently asked questions
What is the difference between interpolation and extrapolation?
Interpolation estimates inside the known x range. Extrapolation extends the line outside that range and is usually more sensitive to a wrong linear assumption.
Must the x values be increasing?
No, but they must be different. The formula works for either endpoint order as long as x₀ and x₁ are not equal.
Does this handle a curved relationship?
No. The formula uses a straight line between two points. Curved trends need a suitable nonlinear model or more data.
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This page provides a calculation tool plus explanatory information so you can understand what the result means and when the underlying method may not fit your situation.