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Math

Hypotenuse Calculator

Find the hypotenuse — or any missing side — of a right triangle instantly.

What do you want to find?

Enter Both Legs

c = √(a² + b²)

Result

Hypotenuse (c)5√(3² + 4²)
a = 3b = 4c = 5
Leg a3
Leg b4
Hypotenuse c5
Perimeter (a+b+c)12
Area (½·a·b)6
Angle α (opposite a)36.8699°
Angle β (opposite b)53.1301°
Right angle90°

About the Pythagorean Theorem

Pythagorean Theorem
In any right triangle, a² + b² = c², where c is the hypotenuse (the side opposite the 90° angle).
Hypotenuse
The longest side of a right triangle. Always opposite the right angle.
Legs (a and b)
The two shorter sides that form the right angle. Their squares sum to the square of the hypotenuse.
Pythagorean Triples
Integer solutions such as (3, 4, 5), (5, 12, 13), (8, 15, 17), and (7, 24, 25).
Area
For a right triangle, area = ½ × leg a × leg b.
Angles
The two non-right angles always add up to 90°. Use tan⁻¹(opposite/adjacent) to find each.
About

Use this hypotenuse calculator to instantly apply the Pythagorean theorem (a² + b² = c²) to any right triangle. Enter both legs to find the hypotenuse, or provide the hypotenuse and one leg to solve for the missing side. Each calculation also returns the triangle's area, perimeter, and the two non-right angles — no manual arithmetic needed.

FAQ
What is the hypotenuse of a right triangle?+

The hypotenuse is the longest side of a right triangle — the side directly opposite the 90° angle. Its length equals the square root of the sum of the squares of the other two sides: c = √(a² + b²).

How do I find a missing leg if I know the hypotenuse?+

Rearrange the Pythagorean theorem: a = √(c² − b²). Enter the hypotenuse and the known leg into the 'Find Missing Leg' mode and the calculator solves it instantly.

What are Pythagorean triples?+

Pythagorean triples are sets of three positive integers that satisfy a² + b² = c² exactly. Common examples include (3, 4, 5), (5, 12, 13), (8, 15, 17), and (7, 24, 25). They appear frequently in geometry and construction.

Can this calculator handle non-integer values?+

Yes. You can enter any positive decimal number for the legs or hypotenuse. The result is computed with full floating-point precision and displayed to six significant figures.

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