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Pythagorean Theorem Calculator

Enter any two sides of a right triangle and leave the third empty. The calculator finds the missing side, then shows the area, the perimeter and the two acute angles.

Your numbers

Result

How we calculate it

In a right triangle, the square of the hypotenuse c equals the sum of the squares of the two legs: a² + b² = c². To find c, take the square root of a² + b². To find a leg, take the square root of (c − the other leg) × (c + the other leg).

The area is a × b ÷ 2 and the perimeter is a + b + c. Angle A, opposite side a, is the arctangent of a ÷ b, and angle B is 90° minus angle A. For legs of 3 and 4 the hypotenuse is 5, the area is 6, angle A is 36.87° and angle B is 53.13°.

Assumptions and limits

  • This works for right triangles only. Use the triangle calculator when there is no right angle.
  • Leave exactly one side empty, and use the same unit for every side.
  • The hypotenuse is always the longest side, so it must be longer than either leg.

Frequently asked questions

What is the Pythagorean theorem?

It says that in a right triangle the square on the longest side (the hypotenuse) equals the sum of the squares on the other two sides. It is written a² + b² = c².

How do I find a leg when I know the hypotenuse?

Subtract the square of the known leg from the square of the hypotenuse, then take the square root. With c = 13 and a = 5, b is the square root of 169 − 25, which is 12.

What is a Pythagorean triple?

A set of three whole numbers that fit the theorem exactly, such as 3, 4, 5 and 5, 12, 13 and 8, 15, 17. Builders use the 3, 4, 5 triangle to check that a corner is square.

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Worked example (a fixed example using the starting numbers, it does not change as you type)

Inputs: Side a (a leg) = 3; Side b (the other leg) = 4.

  • Missing side 5
  • Side a 3
  • Side b 4
  • Hypotenuse c 5
  • Area 6
  • Perimeter 12
  • Angle A 36.87 degrees
  • Angle B 53.13 degrees

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Last reviewed: . Formulas and assumptions are described on our methodology page. For information only; not professional advice.