Right Triangle Calculator

Which pairs of known values does it accept?

Five combinations: both legs, leg a with the hypotenuse, leg b with the hypotenuse, angle A with leg a, and angle B with leg b. Hypotenuse plus an angle is not offered; use a = c·sin A and b = c·cos A by hand. If you know a leg and the angle adjacent to it, subtract that angle from 90° to get the opposite angle and use the matching angle mode.

Which side is a and which angle is A?

Angle A sits opposite leg a, angle B sits opposite leg b, and the right angle C sits opposite the hypotenuse c. So in the 3-4-5 triangle, A is the angle across from the side of length 3. It comes out as 36.869898°, and B is 53.130102°.

Why do I get "Leg must be less than hypotenuse"?

In a right triangle the hypotenuse is strictly the longest side. If the leg you entered is equal to or longer than the hypotenuse, no triangle exists, so the calculator stops. Entering 8 and 8 in the leg and hypotenuse modes triggers this message. Zero and negative lengths are rejected too.

What are the valid angle values?

Greater than 0° and less than 90°, entered in degrees, not radians. The other acute angle is 90° minus the one you give. An entry of 90 or more returns the error "Angle must be between 0° and 90°". An entry of 45 produces a triangle with equal legs.

Are the results rounded?

Sides, area and perimeter are shown with up to six decimals and trailing zeros removed, so 17.320508 appears for 10√3. Angles use the same rule with a degree sign. Round further for practical use: six decimals of a measurement is more precision than any tape measure provides.

What units do area and perimeter use?

The unit you used for the sides, with the area in square units. The form never asks for a unit, so enter every length in the same one. A 3-by-4 triangle has an area of 6 and a perimeter of 12 regardless of whether those are centimetres or feet.

Does the calculator solve non-right triangles?

No. It assumes one angle is exactly 90°. For triangles without a right angle, use the Law of Cosines or the Law of Sines.

Can I use it to check a 3-4-5 style square corner?

Yes. Enter two legs and compare the computed hypotenuse with what you measured. A 3 and 4 give exactly 5, and 5 and 12 pair with 13 in the leg-hypotenuse mode (5 and 13 return a b of 12). If the diagonal you measure is longer or shorter, the corner is not 90°.