Pythagorean theorem calculator
Calculator
The calculator needs JavaScript. The tables below give the same numbers for common cases.
How it is worked out
- c² = a² + b² = 9 + 16 = 25.
- c = √25 = 5.
| Inputs | Answer |
|---|---|
| Find: Hypotenuse c (enter legs a and b); Leg a: 3; Leg b: 4; Hypotenuse c: 0 | In this right triangle, c = 5. |
| Find: Leg a (enter leg b and hypotenuse c); Leg a: 0; Leg b: 12; Hypotenuse c: 13 | In this right triangle, a = 5. |
| Find: Hypotenuse c (enter legs a and b); Leg a: 8; Leg b: 15; Hypotenuse c: 0 | In this right triangle, c = 17. |
How to use it
In a right triangle, the square of the hypotenuse c equals the sum of the squares of the legs: a² + b² = c². Given any two sides, the third follows: c = √(a² + b²), or a = √(c² − b²).
The calculator also gives the area, the perimeter and the two acute angles. The hypotenuse is always the longest side, opposite the right angle.
Frequently asked questions
How do I find the hypotenuse?
Square both legs, add them and take the square root. For legs 3 and 4: √(9 + 16) = 5.
How do I find a missing leg?
Subtract the square of the known leg from the square of the hypotenuse and take the square root.
What are Pythagorean triples?
Sets of whole numbers that satisfy the theorem, such as 3-4-5, 5-12-13 and 8-15-17.
Method: standard arithmetic shown step by step; no outside data is used. Checked 2026-11-12.
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