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Hypotenuse Calculator

The hypotenuse is the longest side of a right triangle, opposite the right angle. Find it from both legs, from one leg and an angle, or from one leg and the triangle’s area.

Quick examples
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Hypotenuse10 ft
Other leg
8 ft
Angle opposite leg a
36.87 °
Angle opposite the other leg
53.13 °
Area
24 ft²
Perimeter
24 ft

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      Formula

      From both legs: c = √(a² + b²)
      From a leg and the angle opposite it: c = a ÷ sin(angle)
      From a leg and the angle next to it: c = a ÷ cos(angle)
      From a leg and the area: b = 2 × area ÷ a, then c = √(a² + b²)

      How to use it

      1. Choose what you know about the triangle.
      2. Enter leg a and the second value.
      3. Read the hypotenuse, along with the other leg, both acute angles, the area and the perimeter.

      Worked examples

      Legs of 6 ft and 8 ft: hypotenuse 10 ft, which is 3.048 m

      Hypotenuse
      10 ft
      Area
      24 ft²
      Perimeter
      24 ft

      A 5 m leg opposite a 30° angle

      Hypotenuse
      10 m
      Other leg
      8.66 m
      Angle opposite the other leg
      60 °

      A 5 m leg next to a 60° angle

      Hypotenuse
      10 m
      Other leg
      8.66 m
      Angle opposite leg a
      30 °

      A 6 m leg and an area of 24 m²

      Hypotenuse
      10 m
      Other leg
      8 m

      Everyday hypotenuses

      Screen sizes are a hypotenuse: a TV panel 48 inches wide and 27 inches tall is sold as a 55-inch screen. So are ladder lengths, stair stringers, roof rafters and the diagonal brace on a gate.

      Questions people ask

      What is the hypotenuse of a triangle with legs 6 and 8?

      10, because 6² + 8² = 100.

      How do I find the hypotenuse with one side and an angle?

      Divide the side by the sine of the angle opposite it, or by the cosine of the angle next to it. A 5 m leg opposite a 30° angle gives 5 ÷ 0.5 = 10 m.

      Is the hypotenuse always the longest side?

      Yes. It sits opposite the 90° angle, the largest angle in a right triangle, so it is always longer than either leg.

      Related calculators

      Pythagorean Theorem CalculatorFind the missing side of a right triangle with a² + b² = c².Right Triangle CalculatorSolve a right triangle from two sides, or one side and an angle.Triangle CalculatorSolve any triangle: missing sides, angles, area and perimeter.Screen Size CalculatorWidth, height and area of a screen from its diagonal.Distance Formula CalculatorDistance between two points in 2D or 3D, exact and decimal.