Right Triangle Calculator
Solve a right triangle from any two known values — two legs, a leg and hypotenuse, or a side and angle. Get all sides, angles, area and perimeter free.
About the Right Triangle Calculator
A right triangle is fully determined by any two of its measurements (besides the 90° angle). This free right triangle calculator lets you pick what you know — two legs, a leg and the hypotenuse, a leg and an acute angle, or the hypotenuse and an angle — and instantly solves the remaining sides, both acute angles, the area and the perimeter.
Under the hood it uses the Pythagorean theorem a² + b² = c² together with basic trigonometry: sin A = a/c, cos A = b/c and tan A = a/b. Students learning trigonometry, plus carpenters, surveyors and engineers checking squareness or slope, use these relationships daily — from a 3-4-5 wall check on a construction site in Lahore to a roof-pitch calculation anywhere in the world.
How to Use the Right Triangle Calculator
- 1Choose which pair of measurements you know from the dropdown.
- 2Enter the two values (angles in degrees, between 0° and 90°).
- 3Read all three sides, all angles, the area and perimeter instantly.
Frequently Asked Questions
How do I find the hypotenuse from two legs?
Use the Pythagorean theorem: c = √(a² + b²). With legs 3 and 4, c = √(9 + 16) = √25 = 5. The area is (3 × 4) ÷ 2 = 6 and the perimeter is 3 + 4 + 5 = 12. The acute angles come out as 36.87° and 53.13°.
How do I solve a right triangle from one side and one angle?
With leg a = 10 and angle A = 30° (the angle opposite a): hypotenuse c = a ÷ sin 30° = 10 ÷ 0.5 = 20, and leg b = a ÷ tan 30° = 10 ÷ 0.5774 ≈ 17.32. The other acute angle is 90° − 30° = 60°.
Why must a leg be shorter than the hypotenuse?
The hypotenuse is opposite the 90° angle, the largest angle, so it is always the longest side. If you enter a leg of 10 with a hypotenuse of 8, no real triangle exists — b² = c² − a² would be negative. The calculator rejects such inputs instead of showing an error value.
What are common right-triangle side ratios worth remembering?
The 3-4-5 triangle (and multiples like 6-8-10) is the classic integer example. A 45-45-90 triangle has sides in ratio 1 : 1 : √2, and a 30-60-90 triangle in ratio 1 : √3 : 2. Builders use 3-4-5 to check corners are square with just a tape measure.