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Pythagorean Theorem Calculator

Find any side of a right triangle, with the working shown.

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The working

The triangle

PartValue

Common Pythagorean triples

abc
345
51213
81517
72425
202129
94041

Hypotenuse (c)

—

Angles and measures

Angle A—
Angle B—
Area—
Perimeter—

—

Whether these sides form a Pythagorean triple

The theorem holds only for right triangles: a² + b² = c², with c the side opposite the right angle. For any other triangle you need the law of cosines, c² = a² + b² − 2ab·cos(C), which reduces to this when C is 90 degrees.

Quick Tool Overview

The Pythagorean Theorem Calculator finds the missing side of a right triangle from the other two, showing the squaring and square root step by step, and calculating the angles, area, perimeter and altitude alongside.

What it does
Finds any missing side of a right triangle
You give it
Two of the three side lengths
You get back
The third side, both angles, area and perimeter
Best for
Geometry homework, construction and diagonal measurements
Calculators Free, unlimited use No sign-up Runs in your browser

About the Pythagorean Theorem Calculator

Find the missing side of a right triangle from the other two, whether that is the hypotenuse or one of the legs. The substitution is shown step by step, and the angles, area, perimeter and altitude are calculated alongside it.

The theorem states that the square on the hypotenuse equals the sum of the squares on the other two sides, and it holds only for right triangles — a point the calculator enforces by checking whether the sides you enter could form one at all. Whole-number solutions such as 3-4-5 and 5-12-13 are called Pythagorean triples, and the tool flags them when your triangle happens to be one, since they are the cases worth recognising on sight.

Key features of the Pythagorean Theorem Calculator

Solves for any side

The hypotenuse or either leg, with the rearranged formula shown for each case.

Step-by-step working

Squaring, adding or subtracting, then the square root — the steps a marker wants to see.

Impossible triangles caught

If the hypotenuse is not the longest side, the tool says the triangle cannot exist rather than returning NaN.

Pythagorean triples flagged

Whole-number solutions like 3-4-5 and 5-12-13 are identified, since they are worth recognising on sight.

Angles and area included

Both acute angles, area, perimeter and the altitude to the hypotenuse.

How to use the Pythagorean Theorem Calculator

  1. 1

    Choose what to find

    The hypotenuse, or one of the two shorter sides.

  2. 2

    Enter the known sides

    The two lengths you already have, in any consistent unit.

  3. 3

    Read the answer

    The missing side, with the squaring and square root shown step by step.

  4. 4

    Use the extras

    Both acute angles, area, perimeter and the altitude to the hypotenuse.

Frequently asked questions

In a right triangle, a² + b² = c², where c is the hypotenuse — the side opposite the right angle — and a and b are the two shorter sides.

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