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Hypotenuse Calculator

Solve the hypotenuse of a right triangle instantly.

How it is calculated

The two legs are the sides that meet at the right angle. The hypotenuse is the side opposite that angle and is found with the Pythagorean theorem: c = √(a² + b²), where a and b are the leg lengths. The area is a × b ÷ 2, because the right triangle is half of the rectangle the two legs would make.

The tool has no unit setting. Enter both legs in the same unit (cm, inches, metres, anything) and the hypotenuse comes out in that unit, with the area in the square of it. Both legs must be greater than zero, otherwise there is no result. Results are rounded to two decimals. The tool starts from two legs only: to find a missing leg when you know the hypotenuse, you need √(c² − a²), which is not what this calculator does.

Worked example

Suppose a stair has a rise of 7 and a run of 11, both in inches, and you want the length of the sloped edge. The legs are a = 7 and b = 11. Squares: 7² = 49 and 11² = 121, sum 170. The hypotenuse is √170 = 13.04 inches. The area of the triangle is 7 × 11 ÷ 2 = 38.50 square inches. Because the sloped side is always longer than either leg, 13.04 is greater than 11, which is a quick sense check.

Try this example →

Common mistakes

  • Entering the hypotenuse as one of the legs. If you already know the longest side, the answer here will be too large, since it is treated as a leg.
  • Mixing units, for example one leg in feet and the other in inches. Convert both to the same unit first.
  • Adding the legs instead of using squares: 7 + 11 = 18 is not the diagonal. The diagonal is shorter than the sum of the legs.
  • Using the tool for a triangle with no right angle. The formula only holds when the two legs meet at 90°.
  • Reading the area as a length. It is in square units of whatever unit you used.

About this calculator

The Pythagorean theorem states that in a right triangle, the square of the hypotenuse (the side opposite the right angle) equals the sum of the squares of the other two legs: c = √(a² + b²). This is one of the oldest and most widely proven results in mathematics, with independent proofs going back to ancient Babylonian, Chinese and Greek mathematics, and it holds true for every right triangle regardless of its specific proportions.

Beyond geometry class, the hypotenuse formula is a daily working tool in carpentry and construction — framers use it to cut roof rafters and stair stringers to the correct diagonal length, and the "3-4-5 rule" (a triangle with legs 3 and 4 always has a hypotenuse of 5) is a standard trick builders use to square up corners without any angle-measuring tool. It's equally essential in navigation and surveying for calculating direct-line distances from two perpendicular measurements, and in physics for resolving vector components back into a resultant magnitude.

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