Pythagorean Theorem Calculator
Enter any two sides of a right triangle to find the third, along with the area and perimeter.
Reviewed by the OmniCalc teamMethod verified 2026-07-01
a² + b² = c² — leave one field blank
5
Hypotenuse c is 5- Leg a
- 3
- Leg b
- 4
- Hypotenuse c
- 5
- Area
- 6
- Perimeter
- 12
- Hypotenuse c
- 5
Show steps
- The hypotenuse is unknown, so c = √(a² + b²).
- c = √(3² + 4²) = √(9 + 16) = √25 = 5.
- Area = ½·a·b = ½·3·4 = 6; perimeter = a + b + c = 12.
How to use the Pythagorean theorem calculator
- 1Enter the two legs (a and b) to find the hypotenuse, or a leg and the hypotenuse to find the other leg.
- 2Leave exactly one field blank — that is the side the calculator solves for.
- 3Read the missing side, plus the triangle’s area and perimeter.
Worked example
With legs a = 3 and b = 4, the hypotenuse is c = √(3² + 4²) = √25 = 5 — the classic 3-4-5 right triangle.
Frequently asked questions
What is the Pythagorean theorem?
In a right triangle, the square of the hypotenuse (the side opposite the right angle) equals the sum of the squares of the other two sides: a² + b² = c².
Can I find a leg, not just the hypotenuse?
Yes. Leave any one of the three fields blank. To find a leg, rearrange to a = √(c² − b²); the hypotenuse must be the longest side, so c has to be larger than the known leg.
What are common Pythagorean triples?
Whole-number right triangles like 3-4-5, 5-12-13 and 8-15-17. Any multiple of a triple (such as 6-8-10) is also a right triangle.