CalcCommonsHow 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.
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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