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Triangle Inradius Calculator

Find the radius of the incircle inside a triangle from its three side lengths. This tool uses side a, side b, side c as its stated inputs. The output is reported in length units, so it should be compared only with figures in compatible units. Only valid for nondegenerate triangles that satisfy the strict triangle inequality.

How to use this calculator

  1. Measure or look up the input for side a and check that its unit matches the field.
  2. Enter side b, side c. 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 triangle inradius

Inradius = √(s(s−a)(s−b)(s−c)) ÷ s, where s = (a+b+c)/2.

  • 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: Triangle Inradius

Consider the following example input values: Side A = 13, Side B = 14, Side C = 15.

Apply the stated relationship: Inradius = √(s(s−a)(s−b)(s−c)) ÷ s, where s = (a+b+c)/2.

Using those inputs gives approximately 4 length units.

Understanding the result

The result of the worked example is approximately 4 length units; it is an arithmetic outcome rather than a prediction of actual conditions.

Only valid for nondegenerate triangles that satisfy the strict triangle inequality.

Important notes

Only valid for nondegenerate triangles that satisfy the strict triangle inequality.

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

Frequently asked questions

What does the triangle inradius calculator measure?

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

What formula does this triangle inradius calculator use?

Inradius = √(s(s−a)(s−b)(s−c)) ÷ s, where s = (a+b+c)/2. Only valid for nondegenerate triangles that satisfy the strict triangle inequality.

Can I rely on this triangle inradius calculator for a final decision?

First check the input units and whether the underlying assumption is appropriate. Only valid for nondegenerate triangles that satisfy the strict triangle inequality. 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.