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Right Triangle Calculator

Enter two sides, or one side and an acute angle, to get the other sides, both angles, the area and the perimeter. Legs 3 and 4 give a hypotenuse of 5. How it works

Use the Right Triangle Calculator

Area
Enter two sides, or one side and one angle
Perimeter —

abcAB90°

a² + b² = c²

About the Right Triangle Calculator

A right triangle with legs 3 and 4 has a hypotenuse of 5, angles of 36.8699° and 53.1301°, an area of 6 and a perimeter of 12. Give the right triangle calculator two sides, or one side and one acute angle, and it fills in the rest with the Pythagorean theorem and sin, cos and tan, to four decimals.

How to use this tool

  1. Type two sides, or one side and one of the two acute angles in degrees. Side c is the hypotenuse, angle A is opposite side a and angle B is opposite side b.
  2. Leave the other boxes empty. The missing sides, both angles, the area and the perimeter appear as you type.
  3. Pick cm, m, in or ft to label the answer. The menu does not convert between units.

Frequently asked questions

How do you find a side of a right triangle from an angle?
Use sin and cos with the hypotenuse and tan with a leg. With c = 10 and angle A = 30°, side a = 10 × sin 30° = 5.0000 and side b = 10 × cos 30° = 8.6603. With side a = 5 and angle A = 40°, side b = 5 ÷ tan 40° = 5.9588 and c = 5 ÷ sin 40° = 7.7786.
How do you find the angles from two sides?
With both legs, A = atan(a ÷ b): a ramp that rises 1 over a run of 12 climbs at 4.7636°. With a leg and the hypotenuse, A = asin(a ÷ c). The other angle is 90° minus the first, because the two acute angles of a right triangle add up to 90°.
What happens when I enter all three sides?
The page checks that a² + b² = c². If the sides fit, it shows both angles, the area and the perimeter (sides 3, 4 and 5 give 36.8699° and 53.1301°). Three sides that do not fit the rule get a message under side c.
Can I solve a right triangle from two angles?
No. Two angles fix the shape but not the size, so at least one side is needed. If you enter both angles and a side, the angles have to add up to 90°, or a message appears under angle B.
Does the unit menu convert feet to meters?
No. It only labels the answer, so legs of 3 and 4 give 5.0000 cm or 5.0000 ft depending on the menu. Enter every side in the same unit; the area is in that unit squared.

Ladders, ramps and roof pitches

Legs of 3 and 4 give a hypotenuse of 5.0000, angles of 36.8699° and 53.1301°, an area of 6.0000 and a perimeter of 12.0000. A 13 ft ladder with its foot 4 ft from the wall reaches 12.3693 ft up the wall and meets the ground at 72.0798°. A ramp that rises 1 unit over a 12 unit run is 12.0416 long and climbs at 4.7636°. A 6/12 roof (6 in of rise per 12 in of run) is pitched at 26.5651°, with 13.4164 in of rafter for every 12 in of run.

Enter two values that fix the triangle, either two sides or one side and one acute angle, and the results update as you type. With all three sides filled in, the page checks that they fit a² + b² = c² and, if they do, shows both angles, the area and the perimeter.

Which formula each pair of inputs uses

a and b are the legs and c the hypotenuse; angle A is opposite a and angle B opposite b, so A + B = 90°.

  • Two sides: c = √(a² + b²) or a = √(c² − b²), then A = atan(a ÷ b) or asin(a ÷ c)

  • One side and an angle: a = c × sin A, b = c × cos A, b = a ÷ tan A, c = a ÷ sin A

Everything is shown to four decimals, with the area a × b ÷ 2 and the perimeter. Sides must be above 0 and at most 1 billion. Angles are in degrees, above 0 and below 90. A leg as long as the hypotenuse, two angles that do not add up to 90°, or three sides that fail a² + b² = c² are rejected with a message. Two angles alone give no answer, since they fix the shape but not the size. If two sides and an angle are entered, the angle is recomputed from the sides. The unit menu (cm, m, in, ft) labels the answer and does not convert.

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