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Hypotenuse Calculator

Calculate the hypotenuse or a missing side of a right triangle.

Choose which right-triangle side is missing.

One leg of the right triangle. Required unless solving for side a.

The other leg of the right triangle. Required unless solving for side b.

The side opposite the right angle. Required when solving for a leg.

Status: initial

Results

Awaiting calculation

Calculator guide

Introduction

The Hypotenuse Calculator uses the Pythagorean theorem to find the longest side of a right triangle from the two shorter sides.

Purpose

Use this calculator for geometry homework, construction measurements, layout checks, and right-triangle problems.

Right triangle method

Use c = sqrt(a^2 + b^2) to find the hypotenuse, or rearrange the formula to find a missing leg: a = sqrt(c^2 - b^2) or b = sqrt(c^2 - a^2).

Variable explanations

Side a

One leg of the right triangle.

Side b

The other leg of the right triangle.

Hypotenuse c

The longest side, opposite the right angle.

Area

For a right triangle, area = a x b / 2.

Perimeter

The sum of all three side lengths.

Formula guide

Find hypotenuse

c = sqrt(a^2 + b^2)

  • a and b are legs.
  • c is the hypotenuse.

Use this when both legs are known.

Find leg a

a = sqrt(c^2 - b^2)

  • b is the known leg.
  • c must be greater than b.

Use this when the hypotenuse and leg b are known.

Find leg b

b = sqrt(c^2 - a^2)

  • a is the known leg.
  • c must be greater than a.

Use this when the hypotenuse and leg a are known.

Worked examples

Classic 3-4-5 triangle

  1. a = 3 and b = 4 gives c = sqrt(9 + 16) = 5.

Missing leg

  1. c = 13 and a = 5 gives b = sqrt(169 - 25) = 12.

Diagonal distance

  1. A rectangle 6 by 8 has diagonal sqrt(36 + 64) = 10.

Common mistakes

Using it for non-right triangles

The theorem applies to right triangles only.

Treating a leg as the hypotenuse

The hypotenuse is always the longest side and opposite the right angle.

Forgetting the square root

After solving for a squared side, take the square root to get the side length.

Entering a hypotenuse shorter than a leg

A valid right triangle requires c to be greater than either leg.

FAQs

What does this Pythagorean Theorem Calculator do?
It solves a missing side of a right triangle using a^2 + b^2 = c^2.
What is the Pythagorean theorem formula?
The formula is a^2 + b^2 = c^2, where c is the hypotenuse.
What is the hypotenuse?
The hypotenuse is the longest side of a right triangle and is opposite the right angle.
Can this find a missing leg?
Yes. Choose leg a or leg b and enter the hypotenuse plus the other leg.
Can this find the hypotenuse?
Yes. Choose hypotenuse c and enter both legs.
Does this work for every triangle?
No. It applies to right triangles only.
Why must the hypotenuse be longer than a leg?
In a right triangle, the hypotenuse is the longest side.
Can I use decimals?
Yes. Decimal side lengths are supported.
What units should I use?
Use any consistent length unit. The output uses the same unit.
How is area calculated?
Area is a x b / 2 for a right triangle.
How is perimeter calculated?
Perimeter is a + b + c.
What is a 3-4-5 triangle?
It is a common right triangle where 3^2 + 4^2 = 5^2.
Can this check construction diagonals?
Yes, for rectangular right-angle layouts, the diagonal can be found as the hypotenuse.
What if my answer is not a whole number?
Many right triangles have irrational side lengths, so decimals are normal.
Does this replace a full triangle calculator?
No. It only solves right-triangle side lengths using the Pythagorean theorem.

References

Related calculators

Last updated and version history

Last updated: 2026-07-09

  • 1.0.0 (2026-07-09): Initial hypotenuse calculator page using the verified Pythagorean theorem engine.