What is the Pythagorean theorem?

The Pythagorean theorem states that in a right triangle the square of the hypotenuse (the side opposite the right angle) equals the sum of the squares of the two legs: a² + b² = c². It only holds for right triangles.

Which side is the hypotenuse?

The hypotenuse is the longest side of a right triangle and always sits opposite the 90° angle. The other two sides — the legs — meet at the right angle. In our calculator, c is the hypotenuse and must be larger than either leg.

How is this different from the Triangle calculator?

The Triangle calculator is a general SSS solver — it needs all three sides and returns area, perimeter, and all three angles for any triangle. This Pythagoras calculator is specialised: it assumes a right triangle, takes any two sides, and fills in the third.

Not directly here — this calculator focuses on the side. For angles in a right triangle use trigonometry (e.g. tan A = opposite / adjacent), or feed all three sides into the Triangle calculator.

GEOGeometry

Pythagorean Theorem Calculator

Fill in any two sides of a right triangle and we'll compute the third using the Pythagorean theorem (a² + b² = c²). Solves for either leg or the hypotenuse, with area thrown in.

Side a (leg)(optional)

Side b (leg)(optional)

Side c (hypotenuse)(optional)

Unit

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Enter values above to see results

How It Works

Formula

c = \sqrt{a^2 + b^2}

a = \sqrt{c^2 - b^2}

b = \sqrt{c^2 - a^2}

\text{Area} = \tfrac{1}{2} \cdot a \cdot b

Where

$a$: Leg a (one of the two perpendicular sides)
$b$: Leg b (the other perpendicular side)
$c$: Hypotenuse (longest side, opposite the right angle)
$\text{Area}$: Triangle area (½ × leg × leg)

Enter any two of three sides — leave the third blank. The calculator detects which is missing and applies a²+b²=c² in the appropriate form. Area (½×leg×leg) comes free.

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