Education & Math

Right Triangle Calculator

Solve a right triangle from two sides or one side and an acute angle.

01 · Set it up

Your inputs

Choose a quick value or enter your own. Example inputs are filled in to get you started.

02 · A little clarityEXAMPLE RESULT

Enter your measurements and calculate.

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How to use

Select the pair of known measurements. Enter the first side as X and the second side or angle A as Y. Side c is the hypotenuse; A is opposite side a. Use degrees for angles and the same length unit for every side.

For related tasks, try the Area Calculator.

Formula & how it works

a² + b² = c². sin A = a/c; cos A = b/c; tan A = a/b. Area = ab/2; perimeter = a + b + c.

a3b4c5A36.8699 °B53.1301 °Area6 units²
Example inputs · Right triangle. Schematic, not to scale.
Right triangle with legs a and b, hypotenuse c, and angle A opposite a.

Worked example

Example 1

Legs 3 and 4 give hypotenuse 5, area 6, perimeter 12, angle A ≈ 36.8699°, and angle B ≈ 53.1301°.

Assumptions & practical notes

The triangle must contain a right angle. Side c is always the hypotenuse, and angle A is opposite side a.

Use one consistent length unit; area will be in its square units. Acute angles must be strictly between 0° and 90°.

See our calculation methodology for unit definitions and testing practices.

Frequently asked questions

Why must c be longer than a leg?

The hypotenuse is opposite the right angle and is the longest side.

Can I solve from one side alone?

No. Another independent side or acute angle is needed.

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