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Pythagorean Theorem Calculator : Find Hypotenuse & Missing Sides (a² + b² = c²)

The Pythagorean Theorem Calculator solves for any missing side of a right triangle given the other two sides. It also computes the triangle area, perimeter, and internal angles in degrees and radians.

Interactive Calculator

100% Client-Side Engine
Pythagorean Theorem: a² + b² = c²
Leave exactly one side blank to calculate it.
Solved Unknown Side (c)
c = 5
Triangle Area
6
Perimeter
12
Acute Angles (α, β)
36.87°, 53.13°
Pythagorean Triple
Yes (Integer Triple)
Theorem Proof & Solution
Pythagorean Theorem: a² + b² = c²
Solving hypotenuse c = √(a² + b²) = √(3² + 4²) = √(25) = 5

Step-by-Step Examples

Classic 3-4-5 Right Triangle

Finding hypotenuse with legs 3 and 4.

Inputs: Leg a: 3, Leg b: 4
Result: Hypotenuse c = 5 (Area: 6, Perimeter: 12)

c = √(3² + 4²) = √(9 + 16) = √25 = 5.

How to Use This Tool

  1. Choose what to find: Hypotenuse c or Leg a/b.
  2. Enter the lengths of the two known sides.
  3. Click Calculate to see the missing side, area, perimeter, and angles.

Frequently Asked Questions

No, in Euclidean geometry the hypotenuse is always the longest side of a right triangle opposite the 90-degree angle. If c <= a or c <= b, a valid right triangle cannot be formed.

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