📐 Pythagorean Theorem Calculator
Solve the right triangle equation a² + b² = c². Enter any two sides and the calculator finds the third, plus the area and perimeter — all in your browser.
Enter two known sides to find the third, plus area and perimeter.
About the Pythagorean Theorem Calculator
This calculator applies the Pythagorean theorem a² + b² = c² to find the missing side of a right triangle from the other two sides, then computes the triangle's area and perimeter. All math runs in your browser.
Formulas
- Hypotenuse:
c = √(a² + b²) - Leg a:
a = √(c² − b²) - Leg b:
b = √(c² − a²) - Area:
(a × b) / 2 - Perimeter:
a + b + c
How to use
- Select the side to solve for: hypotenuse c, leg a, or leg b.
- Enter the two known sides in the matching fields.
- Click Calculate. The missing side, area and perimeter appear below.
Frequently asked questions
Why does solving for a leg require c to be longer than the other leg? Because a² = c² − b² would otherwise be negative, which has no real solution. The hypotenuse must be the longest side.
Can sides be zero or negative? No. Lengths must be positive numbers. The calculator validates input.
What about non-right triangles? The Pythagorean theorem only applies to right triangles. For other triangles, the Law of Cosines is needed.
Does the calculator support decimal inputs? Yes, any positive real number works, including decimals and fractions.