What is the Pythagorean theorem?

For a right triangle, the square of the hypotenuse equals the sum of the squares of the two legs: a² + b² = c². The hypotenuse c is the longest side, opposite the right angle.

Which side is the hypotenuse?

The hypotenuse is the side opposite the 90° angle — always the longest of the three. The other two sides (the legs) form the right angle.

How are the angles found?

From the sides: angle A (opposite leg a) is arctan(a / b), and the two acute angles always add up to 90°, so B = 90° − A.

Why do I get an error with the hypotenuse?

The hypotenuse must be longer than either leg. If you enter a hypotenuse that is shorter than or equal to the leg, no valid triangle exists.

Right Triangle Calculator

Enter any two sides of a right triangle and this calculator finds the rest: the missing side via the Pythagorean theorem (a² + b² = c²), both acute angles via inverse tangent, plus the area and perimeter. Choose whether you know the two legs, or one leg and the hypotenuse. The diagram labels the legs a and b (meeting at the 90° corner) and the hypotenuse c opposite it. Handy for geometry homework, construction and carpentry (rise/run, rafter and brace lengths), screen and TV diagonals, and any layout where you need a square corner. Everything is computed locally in your browser.

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Known sides

Leg aLeg b

Leg a

Leg b

Hypotenuse c

Area

Angle A (opposite a)

36.87°

Angle B (opposite b)

53.13°

Perimeter

Angles are in degrees. Legs a and b meet at the 90° corner; c is the hypotenuse opposite it.

How to use

Pick what you know: the two legs, or one leg and the hypotenuse.
Type the two values into the fields.
Read the remaining side, both acute angles (A opposite a, B opposite b), the area and the perimeter.

Frequently asked questions

What is the Pythagorean theorem?: For a right triangle, the square of the hypotenuse equals the sum of the squares of the two legs: a² + b² = c². The hypotenuse c is the longest side, opposite the right angle.
Which side is the hypotenuse?: The hypotenuse is the side opposite the 90° angle — always the longest of the three. The other two sides (the legs) form the right angle.
How are the angles found?: From the sides: angle A (opposite leg a) is arctan(a / b), and the two acute angles always add up to 90°, so B = 90° − A.
Why do I get an error with the hypotenuse?: The hypotenuse must be longer than either leg. If you enter a hypotenuse that is shorter than or equal to the leg, no valid triangle exists.

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