Find the hypotenuse of a right triangle from two legs, or find a missing leg from the hypotenuse and one leg.
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How to use
Enter the lengths of both legs of a right triangle. The calculator finds the hypotenuse using c = √(a² + b²), plus area, perimeter, and both acute angles.
Also in Triangles
Geometry
The hypotenuse calculator finds the longest side of a right triangle from the two legs using the Pythagorean theorem. It also solves for a missing leg when the hypotenuse and one leg are known.
In a right triangle, the square of the hypotenuse equals the sum of the squares of the two legs: c = sqrt(a^2 + b^2). To find a missing leg instead, rearrange: a = sqrt(c^2 - b^2).
The theorem only applies to triangles with a 90-degree angle. The hypotenuse is always the side opposite the right angle and is always the longest side.
c = sqrt(a^2 + b^2)
Hypotenuse from two legs.
a = sqrt(c^2 - b^2)
Missing leg from hypotenuse and one leg.
Pythagorean triples are integer side lengths that satisfy the theorem exactly. The most common are 3-4-5, 5-12-13, 8-15-17, and 7-24-25. Any multiple of a triple is also a triple (e.g. 6-8-10).
Recognising triples speeds up mental calculations in construction, carpentry, and standardised tests where right-angle verification is needed.
Frequently asked questions
5. sqrt(9 + 16) = sqrt(25) = 5. This is the classic 3-4-5 Pythagorean triple.
No. The hypotenuse is always the longest side of a right triangle because it is opposite the largest angle (90 degrees).
Square all three sides. If the largest squared value equals the sum of the other two squared values, it is a right triangle.
Related
These related calculators come from the same leaf category, nearby sibling categories, or the same top-level topic.
Solve a triangle using the law of cosines — find a missing side from two sides and the included angle, or find an angle from three sides.
Solve a triangle using the law of sines — find missing sides or angles from a known side-angle pair and one additional measurement.
Calculate the area, perimeter, height, base angles, and leg length of an isosceles triangle from any two known measurements.
Solve for the missing side of a right triangle using the Pythagorean theorem, with perimeter and area included.
