Pythagorean theorem calculator
Find a missing side of a right triangle from the other two. Students, builders and DIYers use it to check that corners are square and to work out diagonal lengths.
- Runs in your browser
- Free, no account needed
- Copy or download the result
Result
Example
Leg a: 3 Leg b: 4 Hypotenuse c:
Hypotenuse c: 5 c = √(a² + b²) = √(3² + 4²) Leg a: 3 Leg b: 4 Hypotenuse c: 5 Area: 6 Perimeter: 12 Angle A (across from a): 36.86989765° Angle B (across from b): 53.13010235°
How to use the pythagorean theorem calculator
- Fill in two of Leg a, Leg b and Hypotenuse c, and leave the unknown side blank.
- Press Run to find the missing side.
- Read the area, perimeter and angles under the result.
- Press Copy result or Download to keep the answer.
How it works
The theorem says a² + b² = c², where c is the hypotenuse across from the right angle. So c = √(a² + b²) and a leg = √(c² - other leg²).
Exactly two sides must be filled in, and each must be greater than zero. The hypotenuse must be longer than the leg you give.
When the inputs are whole numbers, a missing side that is not whole is also shown as a simplified radical, such as √2.
Area is a x b / 2, and the two acute angles come from the arctangent. Lengths are rounded to 12 significant digits.
Everything runs in your browser. Your input is not uploaded or stored.
Questions and answers
What is the Pythagorean theorem?
In a right triangle, the square of the hypotenuse equals the sum of the squares of the two legs: a² + b² = c².
How do I find a leg if I know the hypotenuse?
Subtract the square of the known leg from the square of the hypotenuse and take the square root. With c = 13 and a = 5, b = √(169 - 25) = 12.
What is a 3-4-5 triangle?
It is a right triangle with whole number sides 3, 4 and 5. Builders use it to check that a corner is exactly 90 degrees.