Right Triangle Calculator
Solve Every Side, Angle, Area & Perimeter
Enter any two of the four values below — leg a, leg b, hypotenuse c, or angle A — and leave the other two blank to solve the entire right triangle.
Understanding the Right Triangle Calculator
A right triangle is fully determined by any two of its four core measurements — two sides, or a side and an angle. This calculator solves the whole triangle from whichever two you know.
Unlike a calculator that only accepts sides, this tool solves from any pair of the four values — leg a, leg b, hypotenuse c, or angle A — giving you six different valid starting combinations.
Every calculation returns both legs, the hypotenuse, both acute angles, the area, and the perimeter — the complete geometry of the triangle in a single result.
The Formulas
Given angle A and any one side, the other two sides follow directly from these trig ratios; given any two sides, the Pythagorean theorem finds the third and inverse trig functions find angle A.
The Full Solver, Not the Narrow One
If you only need to find one missing side from two known sides, the leaner Pythagorean Theorem Calculator does exactly that and nothing more. This Right Triangle Calculator goes further: it accepts an angle as one of your two known values, and always returns the entire triangle — every side, both acute angles, the area, and the perimeter — not just the one value you were missing. And if your triangle doesn't have a right angle at all, neither tool applies; use the Triangle Calculator instead, which solves general (oblique) triangles with the Law of Cosines and Law of Sines.
Legs a and b meet at the 90° angle; the hypotenuse c is always opposite it.
Any two of the four values — two sides, or a side and angle A — are enough to solve the rest.
Both legs, the hypotenuse, both acute angles, the area, and the perimeter.
Key Takeaways
- Any two of four values are enough — two sides, or a side plus angle A — to solve the whole right triangle.
- The hypotenuse is always the longest side and must be strictly longer than either leg.
- The two acute angles always sum to 90°, since the right angle already accounts for the other 90°.
- Only need one missing side? The Pythagorean Theorem Calculator is the leaner tool for that.
Frequently Asked Questions
- Enter any two of the four values — leg
a, legb, hypotenusec, or angleA(in degrees). - Leave the other two fields blank.
- Click "Calculate" to solve every remaining side, both acute angles, the area, and the perimeter.
The Pythagorean Theorem Calculator is intentionally narrow — it only solves a missing side from the other two sides using a² + b² = c². This Right Triangle Calculator is the fuller solver: it accepts any two of four values (either side, including an angle), and returns both legs, the hypotenuse, both acute angles, the area, and the perimeter in one pass.
Yes. In addition to any two of the three sides, you can enter angle A (the angle opposite side a, in degrees) together with one known side — leg a, leg b, or hypotenuse c — and the calculator will solve the rest using standard right-triangle trigonometry.
That combination is mathematically impossible — the hypotenuse is always the longest side of a right triangle, so it must be strictly longer than either leg. If you see this error, double-check which value belongs in the hypotenuse (c) field.
Angle A is one of the two acute angles in a right triangle, so it must be strictly greater than 0° and strictly less than 90°. A value of 0° or 90° would collapse the triangle into a flat line rather than a real shape, since the third angle is already fixed at 90° and the two acute angles must add up to exactly 90°.
No — this calculator specifically assumes one angle is exactly 90°. If your triangle is oblique (no right angle), use the Triangle Calculator instead, which solves any general triangle from side-side-side, side-angle-side, or angle-side-angle inputs using the Law of Cosines and Law of Sines.