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Regular Polygon Apothem Calculator

Calculate the center-to-side perpendicular distance of a regular polygon from its side length and side count. This tool uses polygon side length, number of sides as its stated inputs. The output is reported in length units, so it should be compared only with figures in compatible units. This formula applies only to regular polygons whose sides and angles are equal.

How to use this calculator

  1. Measure or look up the input for polygon side length and check that its unit matches the field.
  2. Enter number of sides. Change the supplied example numbers to match your own scenario.
  3. Read the calculation in length units and review the formula and limitations below before using it to make a decision.

How to calculate regular polygon apothem

Apothem = side length ÷ [2 × tan(π ÷ number of sides)].

  • The formula uses the supplied measurements directly and returns its primary result in length units. No external data or background estimates are fetched by this calculator.
  • Use consistent reporting intervals and measurement units. A different unit or different definition for one input changes the meaning of the result.

Worked examples

Worked example: Regular Polygon Apothem

Consider the following example input values: Polygon side length = 10, Number of sides = 6.

Apply the stated relationship: Apothem = side length ÷ [2 × tan(π ÷ number of sides)].

Using those inputs gives approximately 8.660254 length units.

Understanding the result

The result of the worked example is approximately 8.660254 length units; it is an arithmetic outcome rather than a prediction of actual conditions.

This formula applies only to regular polygons whose sides and angles are equal.

Important notes

This formula applies only to regular polygons whose sides and angles are equal.

This result reflects the entered values only. Validate polygon side length against a relevant measurement or primary record; rounding, timing, or inconsistent units can affect practical decisions.

Frequently asked questions

What does the regular polygon apothem calculator measure?

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

What formula does this regular polygon apothem calculator use?

Apothem = side length ÷ [2 × tan(π ÷ number of sides)]. This formula applies only to regular polygons whose sides and angles are equal.

Can I rely on this regular polygon apothem calculator for a final decision?

First check the input units and whether the underlying assumption is appropriate. This formula applies only to regular polygons whose sides and angles are equal. For regulated or safety-critical decisions, verify with appropriate authoritative guidance.

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Related explanations

Learn the method behind the number or compare the terminology before using the calculator.

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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.