JLJosh Liljenquist

Geometry calculator

Pythagorean theorem calculator

Find one missing side of a right triangle from the other two. Enter exactly two values for legs a and b or hypotenuse c; the calculator validates that c can be the longest side and shows the substitution used.

By

Find any one sideSteps shownTriangle validation

Enter known values

Enter the known values and select Calculate.

How to use this calculator

  1. Identify the hypotenuse opposite the right angle and label it c.
  2. Enter exactly two positive side lengths.
  3. Leave the side you want to find blank.
  4. Use one consistent length unit for all entries.

Formula and method

a² + b² = c². To find c, use √(a² + b²). To find a, use √(c² − b²); to find b, use √(c² − a²).

Worked example

If a = 5 and b = 12, then c = √(25 + 144) = √169 = 13. If c = 13 and b = 12, then a = √(169 − 144) = 5.

Assumptions and result interpretation

  • The triangle is a right triangle.
  • The hypotenuse c must be longer than either leg.
  • The output uses the same generic length unit as the inputs.
  • Rounding is applied only to the displayed result.

Understanding the result

This page owns the direct missing-side job. Use the broader right-triangle calculator when angles, area, or perimeter are also needed.

Common mistakes

  • Labeling a leg as c
  • Entering three conflicting values
  • Subtracting in the wrong order when solving a leg
  • Mixing feet and inches without converting first

Methodology sources

Right triangle calculatorStair calculator

Browse all calculators.

Use this result as a calculation aid. Confirm input definitions, required precision, and any governing policy or professional standard separately.