Hypotenuse Calculator

The formula

The hypotenuse is the side opposite the right angle, always the longest side of a right triangle. The Pythagorean theorem relates it to the two legs:

c = sqrt(a^2 + b^2)

where a and b are the legs (the two sides that form the 90° angle) and c is the hypotenuse. The same two legs also give you the rest of the triangle:

• Area = (a × b) / 2
• Perimeter = a + b + c
• Angle A = atan2(a, b) in degrees (the angle opposite leg a)
• Angle B = 90° − Angle A

A worked example

Take legs of a = 6 and b = 8.

c = sqrt(6^2 + 8^2) = sqrt(36 + 64) = sqrt(100) = 10

The hypotenuse is exactly 10, this is the 3-4-5 triple scaled by 2. The area is (6 × 8) / 2 = 24, the perimeter is 6 + 8 + 10 = 24, and the acute angles are roughly 36.87° and 53.13°.

Common right triangles

Pitfalls to avoid

• Mixed units. Both legs must use the same unit. Mixing inches and centimetres gives a meaningless answer.
• Using it on a non-right triangle. The formula assumes a 90° angle between the legs. For any other triangle, use the law of cosines instead.
• Confusing a leg with the hypotenuse. If you already know the hypotenuse and one leg, you are solving for a leg: a = sqrt(c^2 − b^2), not this calculator’s direction.
• Zero or negative inputs. A side length must be positive. The calculator rejects zero and negative values so you can correct the measurement rather than silently changing it.