Right Triangle Calculator

Find the hypotenuse, area and perimeter of a right triangle.

How it is calculated

You enter the two legs, a and b, the sides that meet at the 90-degree corner. The tool computes the hypotenuse c = √(a² + b²), the area A = a × b ÷ 2 and the perimeter P = a + b + c. Each result is rounded to two decimals. Both legs must be greater than zero. Use any length unit, as long as both legs share it; lengths come out in that unit and the area in its square. The calculator cannot start from the hypotenuse and one leg, so if you know c, you must work out the missing leg yourself first (b = √(c² − a²)). Angles are not shown.

Worked example

The legs are 6 and 9. Hypotenuse: 6² + 9² = 36 + 81 = 117, and the square root of 117 is about 10.8167, shown as 10.82. Area: 6 × 9 ÷ 2 = 27, shown as 27.00. Perimeter: 6 + 9 + 10.8167 = 25.8167, shown as 25.82. The perimeter uses the unrounded hypotenuse.

Try this example →

Common mistakes

  • Entering the hypotenuse as one of the legs. The longest side must not be typed in; it is calculated, and putting it in a or b gives a larger triangle than the one you have.
  • Using a side that does not meet the right angle. Both inputs must be the two sides forming the 90-degree corner.
  • Mixing units between the two legs, for example feet and inches, which makes the hypotenuse meaningless.
  • Expecting an answer when the right angle is not exactly 90 degrees. For any other angle use a law-of-cosines tool instead.
  • Reading the area as being in the same unit as the legs. If legs are in meters, the area is in square meters.

About this calculator

This calculator finds the hypotenuse (via the Pythagorean theorem, a² + b² = c²), area (half the product of the two legs, since they meet at a right angle) and perimeter of a right triangle from the lengths of its two legs. A right triangle is any triangle with one 90-degree angle, and the two shorter sides that form that angle are all that's needed to determine everything else about it.

It's used in construction and carpentry to check that a corner is truly square (using the classic 3-4-5 right triangle relationship) and to calculate the length of a diagonal brace, rafter or staircase stringer, and in surveying and navigation to find a direct distance between two points when only the horizontal and vertical distances are known. Students use it constantly as the entry point into trigonometry.

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