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Pythagorean Theorem Calculator

Enter two sides of a right triangle to find the third, with the working shown, plus the triangle's area, perimeter and angles.

What do you want to find?

Hypotenuse

5

A whole number, so this is a Pythagorean triple

Sides a, b, c
3, 4, 5
Area
6
Perimeter
12
Angle opposite a
36.8699°
Angle opposite b
53.1301°
Right angle
90°

Step-by-step solution

Worked out with your numbers. Change any value above and the steps update.

  1. 1

    Pythagorean theorem

    a² + b² = c²

  2. 2

    Square the two legs and add them

    3² + 4² = 9 + 16 = 25

  3. 3

    Take the square root to find c

    c = √25 = 5

How it works

  • In a right triangle, a² + b² = c², where c is the hypotenuse (the longest side, opposite the right angle).
  • To find the hypotenuse: c = √(a² + b²). To find a leg: b = √(c² − a²).
  • With whole-number sides, the answer is also given in simplest radical form, such as 5√2.
  • The angles come from trigonometry: the angle opposite a is sin⁻¹(a ÷ c).

Frequently asked questions

What is a Pythagorean triple?

Three whole numbers that fit a² + b² = c², such as 3, 4, 5 or 5, 12, 13. The calculator tells you when your answer is a whole number.

Does it work for triangles without a right angle?

No. The theorem only holds for right triangles. For other triangles, use the law of cosines.

Results are estimates for general information and are not financial, medical or professional advice.