CalcLibrary

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.

Examples

Two legs of 3 and 4 give a hypotenuse of 5.

Missing side
5 m
Solving for
c (hypotenuse)
Area
6 m²

Both legs are filled, so we solved for the hypotenuse c.

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Examples

How It Works

Formula

c=a2+b2c = \sqrt{a^2 + b^2}

a=c2−b2a = \sqrt{c^2 - b^2}

b=c2−a2b = \sqrt{c^2 - a^2}

Area=12⋅a⋅b\text{Area} = \tfrac{1}{2} \cdot a \cdot b

Variables

aa

Leg a (one of the two perpendicular sides)

bb

Leg b (the other perpendicular side)

cc

Hypotenuse (longest side, opposite the right angle)

Area\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.

Frequently Asked Questions

01What 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.
02Which 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.
03How 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.
04Can I find an angle?
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.
05Does this only work for right triangles?
Yes. The Pythagorean theorem applies only when one angle is exactly 90 degrees. For any other triangle, you need a different method such as the law of cosines or the law of sines.

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