Pythagorean theorem calculator

Pick the side you need, enter the other two and get the answer instantly. The calculator uses a² + b² = c² and also reports the area, the perimeter and the two acute angles of the right triangle.

Find
Missing side5
Area
6
Perimeter
12
Angle A (opposite a)
36.8699 °
Angle B (opposite b)
53.1301 °

Runs in your browser: nothing you enter is sent anywhere.

How to use it

  1. Choose which side to find: the hypotenuse c or one of the legs.
  2. Enter the two sides you know. The missing side appears immediately.
  3. Read the area, perimeter and the two acute angles below it.

Formulas

Find Formula
Hypotenuse c = √(a² + b²)
Leg a = √(c² − b²) or b = √(c² − a²)
Area a × b ÷ 2
Angle A arctan(a ÷ b), angle B = 90° − A

Worked examples

  • Legs 3 and 4. c = √(9 + 16) = √25 = 5. The area is 6, the perimeter 12, and angle A is 36.87°.
  • Hypotenuse 17, leg 8. The other leg is √(289 − 64) = √225 = 15.
  • Legs 1 and 1. The hypotenuse is √2, about 1.4142, and both angles are 45°.

Common mistakes

  • Using the theorem on any triangle. It holds only when one angle is exactly 90°.
  • Treating a leg as the hypotenuse. When finding a leg, c must be the longest side; otherwise the square root of a negative number appears and the calculator reports an error.
  • Forgetting to take the root. a² + b² gives c², not c.

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. The hypotenuse c is the side opposite the right angle and is always the longest.

How do I find a missing leg?

Subtract the squares and take the root, a = √(c² − b²). For a hypotenuse of 13 and a leg of 12 the other leg is √(169 − 144) = √25 = 5.

What are Pythagorean triples?

They are whole-number sets that satisfy the theorem, such as 3-4-5, 5-12-13, 8-15-17 and 7-24-25. Any multiple of a triple works too, for example 6-8-10.

Does it work for triangles without a right angle?

No, the theorem needs a 90° angle. For other triangles use the triangle calculator, which applies the laws of sines and cosines.

More in Math

All tools in this category: Math ·Updated November 3, 2026

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