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Right Triangle Calculator

A right triangle has one 90° corner, so two more facts are enough to solve it. Enter two sides, or one side and one of the acute angles, and get the remaining sides and angles, the area, the perimeter and the height to the hypotenuse.

Quick examples
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Hypotenuse c13 ft
Leg a
5 ft
Leg b
12 ft
Angle A (opposite a)
22.62 °
Angle B (opposite b)
67.38 °
Area
30 ft²
Perimeter
30 ft
Height to the hypotenuse
4.62 ft

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      Formula

      Pythagorean theorem: a² + b² = c²
      sin(A) = a ÷ c, cos(A) = b ÷ c, tan(A) = a ÷ b
      Angle B = 90° − angle A
      Area = ½ × a × b
      Height to the hypotenuse = a × b ÷ c

      How to use it

      1. Choose what you know.
      2. Enter the values. Legs a and b meet at the right angle; c is the hypotenuse; angle A is opposite leg a.
      3. Read the missing sides, both acute angles, the area and the perimeter.

      Worked examples

      Legs of 5 ft and 12 ft: hypotenuse 13 ft (3.9624 m), area 30 ft²

      Hypotenuse c
      13 ft
      Area
      30 ft²
      Perimeter
      30 ft
      Angle A (opposite a)
      22.62 °
      Angle B (opposite b)
      67.38 °

      A leg of 8 m and a hypotenuse of 17 m

      Leg b
      15 m
      Area
      60 m²
      Perimeter
      40 m

      A 4 m leg opposite a 35° angle

      Leg b
      5.71 m
      Hypotenuse c
      6.97 m
      Angle B (opposite b)
      55 °
      Area
      11.43 m²

      A 10 m hypotenuse with a 30° angle

      Leg a
      5 m
      Leg b
      8.66 m
      Area
      21.65 m²

      Two special right triangles

      A 45°-45°-90° triangle has equal legs and a hypotenuse of leg × √2 (about 1.414). A 30°-60°-90° triangle has sides in the ratio 1 : √3 : 2, so the hypotenuse is exactly twice the short leg.

      Practical uses

      Roof pitch, ramps, stairs, ladders and bracing are all right-triangle problems. The rise and run are the legs; the rafter, ramp surface or ladder is the hypotenuse; the slope angle is the angle opposite the rise.

      Questions people ask

      What is the hypotenuse of a right triangle with legs 5 and 12?

      13, because 5² + 12² = 169 and √169 = 13. Its angles are 22.62° and 67.38°.

      How do I find a leg from the hypotenuse and an angle?

      Multiply the hypotenuse by the sine of the angle opposite that leg. With a hypotenuse of 10 and a 30° angle, the opposite leg is 10 × 0.5 = 5.

      Can a right triangle have two equal sides?

      Yes — the two legs can be equal, which makes a 45°-45°-90° triangle. The hypotenuse is always the longest side.

      Related calculators

      Pythagorean Theorem CalculatorFind the missing side of a right triangle with a² + b² = c².Hypotenuse CalculatorLongest side of a right triangle from legs, an angle or the area.Triangle CalculatorSolve any triangle: missing sides, angles, area and perimeter.Triangle Area CalculatorArea from base and height, three sides, or two sides and an angle.Roof Pitch CalculatorPitch, angle, slope and rafter length from rise and run.Stair CalculatorRisers, riser height, total run and stringer length for stairs.