What this calculator does
A right triangle has one 90° angle. The calculator uses the Pythagorean theorem for sides and trigonometric ratios for the acute angles.
Right triangle formulas used by this calculator
| Goal | Formula | When to use it |
|---|---|---|
| Find hypotenuse | c = √(a² + b²) | Both legs are known |
| Find missing leg a | a = √(c² − b²) | Hypotenuse and leg b are known |
| Find missing leg b | b = √(c² − a²) | Hypotenuse and leg a are known |
| Find acute angle | tan(A) = opposite / adjacent | Two side lengths are known |
| Find area | A = a × b ÷ 2 | The two legs are perpendicular |
Right triangle examples
3-4-5 triangle
If the legs are 3 and 4, the hypotenuse is 5. This is the most common Pythagorean triple and a useful check for the calculator.
5-12-13 triangle
If the legs are 5 and 12, the hypotenuse is 13. This is another common whole-number right triangle.
45-45-90 triangle
In a 45-45-90 right triangle, the two legs are equal and the hypotenuse is leg × √2.
30-60-90 triangle
In a 30-60-90 right triangle, the side ratio is 1 : √3 : 2. This is useful when the angles are known but one side is missing.
When a right triangle calculator is not enough
This page assumes one angle is exactly 90°. If your triangle is not right-angled, use the general triangle solver, the law of cosines page, or the law of sines page. Non-right triangles usually require at least three pieces of information, including at least one side.
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