Hypotenuse Calculator
Enter the two legs of a right triangle and get the hypotenuse instantly from c = √(a² + b²) — or switch modes to find a missing leg when you already know the hypotenuse.
Example: with What do you know? Both legs (a and b) · Leg a 3 · Leg b (both-legs mode) 4 · Hypotenuse c (hypotenuse mode) 5 → Missing side: c = 5.00.
Computed by the calculator below using its default values. Change any input to see your own numbers.
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Check it outHow to find the hypotenuse of a right triangle
The hypotenuse is the longest side of a right triangle — the one opposite the 90° angle. The hypotenuse formula is the Pythagorean theorem solved for c: c = √(a² + b²). Square each leg, add the squares, and take the square root. With legs of 3 and 4: 9 + 16 = 25, and √25 = 5. It works in any unit, as long as both legs use the same one.
To find a missing leg instead, rearrange the same equation: b = √(c² − a²). Knowing a hypotenuse of 13 and a leg of 5 gives √(169 − 25) = √144 = 12. The calculator also reports the two acute angles from α = arcsin(a ÷ c), so one pair of sides unlocks the whole triangle. Remember the theorem only holds for right triangles — for anything else you need the law of cosines.
How it’s calculated
Both-legs mode uses the Pythagorean theorem: c = √(a² + b²). Hypotenuse mode rearranges it to b = √(c² − a²), which is only defined when c is longer than the known leg. Angles come from α = arcsin(a ÷ c) and β = 90° − α, reported in degrees. Results are rounded to two decimals and are unit-agnostic.
Results update as you type and are estimates, not professional advice — verify important decisions with a qualified professional.
Common mistakes
- Adding the legs and taking the root of the sum — square each leg first: √(3² + 4²) = 5, not √(3 + 4).
- Applying the formula to a triangle without a 90° angle — the Pythagorean theorem only works for right triangles.
- In hypotenuse mode, entering a leg longer than the hypotenuse — c is always the longest side, so c² − a² must stay positive.
Frequently asked questions
How do you find the hypotenuse of a right triangle?
Square both legs, add the squares, then take the square root: c = √(a² + b²). For legs 3 and 4, that is √(9 + 16) = √25 = 5.
What is the hypotenuse formula?
c = √(a² + b²), the Pythagorean theorem solved for the hypotenuse. It applies only when the triangle has a 90° angle.
How do I find a leg if I already know the hypotenuse?
Rearrange to b = √(c² − a²). With a hypotenuse of 13 and a leg of 5: √(169 − 25) = 12.
Which side of a triangle is the hypotenuse?
The side opposite the right angle. It is always the longest of the three sides, and only right triangles have one.
Does the calculator work in feet, meters, or inches?
Yes. The math is unit-agnostic — enter both sides in the same unit and the answer comes back in that unit.