Pythagorean Theorem Calculator
Choose whether you want the hypotenuse or a missing leg, enter the two sides you know and get the third side with the area and perimeter.
Updated
Report a problem
Formula
- Hypotenuse:
c = √(a² + b²) - Missing leg:
b = √(c² − a²) - Area:
a × b ÷ 2 - Perimeter:
a + b + c
Worked example
Legs 3 and 4: c = √(3² + 4²) = √25 = 5. The area is 3 × 4 ÷ 2 = 6 and the perimeter is 3 + 4 + 5 = 12.
Leg 5 and hypotenuse 13: b = √(13² − 5²) = √144 = 12, giving an area of 30 and a perimeter of 30.
Frequently asked questions
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. With legs 3 and 4, c² = 9 + 16 = 25, so c = 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. With leg 5 and hypotenuse 13: 169 − 25 = 144, and the square root is 12.
Why must the hypotenuse be longer than the other side?
The hypotenuse is the longest side of a right triangle. If the hypotenuse you enter is not longer than the leg, the subtraction would give zero or a negative number, so no triangle exists.
Does the theorem work in any unit?
Yes, as long as all sides use the same unit. Sides of 3 m and 4 m give a hypotenuse of 5 m, and sides of 3 ft and 4 ft give 5 ft. The area is then in square units.