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How to find the hypotenuse

Q: Is the hypotenuse always the longest side?

Yes. In a right triangle the hypotenuse is opposite the right angle and is longer than either leg.

Square each leg, add those squares, and take the square root. Legs of 3 and 4 give a hypotenuse of 5, because 9 + 16 = 25 and the square root of 25 is 5.

When this works

The rule applies only to a right triangle, the kind with one 90° angle. The two sides that meet at that angle are the legs. The hypotenuse is the side opposite the right angle, and it is always the longest side.

In this calculator the right angle is C, the hypotenuse is side c, side a is opposite angle A, and side b is opposite angle B. You do not need to rearrange the formula if you keep that convention.

Steps

Confirm the triangle has a right angle. If it does not, this formula does not apply.
Measure or copy both legs. Call them a and b.
Square each leg: a² and b².
Add the squares.
Take the square root. That length is c, the hypotenuse.

c = √(a² + b²)

A numeric check

For 5 and 12, the squares are 25 and 144. Their sum is 169, and the square root is 13. So 5-12-13 is a right triangle with hypotenuse 13.

Tips

Keep the same unit on both legs. The hypotenuse comes out in that unit.
If the lengths are not perfect squares, leave the result as a rounded decimal only at the end. The app rounds for display and keeps the calculation itself unrounded until then.
A whole-number result such as 3-4-5 or 5-12-13 is a Pythagorean triple. See what that means.

Common mistakes

Adding the legs instead of adding their squares.
Forgetting the square root, which leaves you with c² rather than c.
Using the formula on a triangle that is not right. Check the three sides first if you are not sure.

How the app does it

In Basic mode, enter the two legs as a and b and leave c empty, then tap Calculate. The missing side is c, and the step-by-step solution shows the formula, the substitution, and the result. If you also want the acute angles, open the measurements after the solve. Angles are covered separately.

Get Pythagorean Theorem Calculator on Google Play

Related guides

Questions

What if I only know one leg?

The hypotenuse cannot be found from one leg alone. You need both legs, or one side together with one acute angle. That second case uses Advanced mode.

Is the hypotenuse always the longest side?

Yes. It is opposite the right angle, so it is longer than either leg. The calculator rejects a hypotenuse that is not strictly longer than both legs.