Education
Pythagorean Theorem Calculator
Pick which side you want to solve for, enter the two known sides, and we apply a² + b² = c² to find the third. The labeled triangle on the right shows what each side represents.
Solve for
e.g. 3
e.g. 4
Reference
Right angle at the bottom-right; c is the hypotenuse.
Side c
5
√(3² + 4²)
Examples
Legs 3 and 4 → hypotenuse
= 5
Legs 5 and 12 → hypotenuse
= 13
Hypotenuse 10, leg 6 → other leg
= 8
Legs 1 and 1 → hypotenuse
≈ 1.414 (= √2)
How it works
For any right triangle with legs a and b and hypotenuse c:
Hypotenuse · c = √(a² + b²)
Missing leg · a = √(c² − b²)
When solving for a leg, the hypotenuse must be larger than the other leg — otherwise no real triangle exists.
Frequently asked questions
In any right triangle, the square of the hypotenuse (the longest side, opposite the right angle) is equal to the sum of the squares of the two legs. Written as a² + b² = c², where c is the hypotenuse.
The hypotenuse is the side directly opposite the 90° corner. It's always the longest side in a right triangle. The other two sides are the legs and are labeled a and b.
Rearrange: if you know c and one leg (say b), then a = √(c² − b²). The hypotenuse must be longer than the other leg, otherwise the triangle is impossible — the calculator will tell you when that happens.
No. The Pythagorean theorem is specific to right triangles. For triangles without a right angle, use the Law of Cosines: c² = a² + b² − 2ab·cos(C).
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