Pythagorean Theorem Calculator

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

Fill in exactly two sides. Leave the one you want to find empty.
Missing side
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    Angle A–
    Angle B–
    Area–
    Perimeter–
    a b c

    The Pythagorean theorem

    The theorem describes how the three sides of a right triangle relate to each other. If the two shorter sides, called legs, are a and b, and the longest side, the hypotenuse, is c, then:

    a² + b² = c²

    Rearranging the formula lets you find any side from the other two:

    • Hypotenuse: c = √(a² + b²)
    • Leg: a = √(c² − b²) or b = √(c² − a²)

    How to use the calculator

    1. Enter the two sides you know. Use the same unit for both.
    2. Leave the side you want to find empty.
    3. Read the missing side, the steps, and the triangle's angles, area and perimeter.

    Real-life examples

    How high will a ladder reach?

    A 13-foot ladder stands with its base 5 feet from the wall. The ladder is the hypotenuse, so the height it reaches is √(13² − 5²) = √(169 − 25) = √144 = 12 feet.

    How wide is a 55-inch TV?

    TV sizes are measured diagonally. A 16:9 screen has sides in the ratio 16 to 9, and √(16² + 9²) ≈ 18.36. So a 55-inch TV is about 55 × 16 ÷ 18.36 ≈ 47.9 inches wide and 55 × 9 ÷ 18.36 ≈ 27.0 inches tall.

    Is the corner square?

    Builders mark 3 feet along one wall and 4 feet along the other. If the diagonal between the marks measures 5 feet, the corner is exactly 90°. This is the 3-4-5 rule, a Pythagorean triple in action.

    Common Pythagorean triples

    These whole-number sets fit the formula exactly and show up often in homework and construction: 3-4-5, 5-12-13, 8-15-17, 7-24-25 and 20-21-29. Multiplying a triple by any number, such as 6-8-10 or 9-12-15, gives another triple.

    Last reviewed October 2026.

    Frequently asked questions

    What is the Pythagorean theorem?

    In any right triangle, the square of the longest side (the hypotenuse) equals the sum of the squares of the other two sides: a² + b² = c². It only works for triangles with a 90° angle.

    Which side is the hypotenuse?

    The hypotenuse is the side opposite the right angle. It is always the longest side of a right triangle. In the formula it is called c.

    Can I find a leg if I know the hypotenuse?

    Yes. Rearrange the formula to a = √(c² − b²). Enter the hypotenuse and one leg, leave the other leg empty, and the calculator solves for it.

    What is a Pythagorean triple?

    A set of three whole numbers that fit a² + b² = c², such as 3-4-5, 5-12-13, 8-15-17 and 7-24-25. Any multiple of a triple, like 6-8-10, is also a triple.

    Does the theorem work for triangles that are not right triangles?

    No. For other triangles you need the law of cosines, c² = a² + b² − 2ab × cos(C), which reduces to the Pythagorean theorem when angle C is 90°.

    How do builders use the 3-4-5 rule?

    To check a corner is square, measure 3 units along one side and 4 units along the other. If the distance between the two marks is exactly 5 units, the corner is a true 90° angle. Larger multiples like 6-8-10 feet give more accuracy.