📐 Right Triangle Calculator

Q: How do you find the hypotenuse of a right triangle?

Square both legs, add them, and take the square root: c = (a + b ). For legs of 3 and 4, the hypotenuse is 5.

Q: How do you find the angles of a right triangle?

Use the inverse trig functions. Angle A = arctan(a b) when you know both legs, and angle B = 90° A.

Quick answer: To solve a right triangle, use the Pythagorean theorem — a² + b² = c² — for the sides, and inverse trig (arctan, arcsin) for the angles. Enter any two values below to solve the rest.

Enter any two values — the two legs, a leg and the hypotenuse, or a side and an angle — and this solver finds every other side and angle.

Published by Muhammad Ahmad · Formulas derived from published code tables and manufacturer specifications
See our methodology

Side a (leg)

Side b (leg)

Side c (hypotenuse)

Angle A (degrees, opposite a)

Fill in any two fields and clear the rest. Angle A is opposite side a; the right angle is C (90°).

Solved Triangle

SIDE a

SIDE b

HYPOTENUSE c

ANGLE A

36.87°

ANGLE B

53.13°

AREA

Perimeter and more appear once two values are entered.

How the Right Triangle Solver Works

A right triangle has one 90° angle (angle C). Once you know any two of its measurements — two sides, or one side and one non-right angle — every other value is fixed. This tool applies the Pythagorean theorem and basic trigonometry:

Two legs (a, b): hypotenuse c = √(a² + b²); angle A = arctan(a ÷ b).
Leg and hypotenuse: the other leg = √(c² − leg²); angle A = arcsin(a ÷ c).
Side and angle: the remaining sides come from sine, cosine, and tangent of the known angle.

Angles A and B always add to 90°, the area is ½ × a × b, and the perimeter is a + b + c.

The 3-4-5 ruleThe classic 3-4-5 right triangle (and its multiples like 6-8-10) is how carpenters check for square. Mark 3 feet along one edge and 4 feet along the other; if the diagonal is exactly 5 feet, the corner is a perfect 90°. Enter 3 and 4 above to see it.

Frequently Asked Questions

How do you find the hypotenuse of a right triangle?

Square both legs, add them, and take the square root: c = √(a² + b²). For legs of 3 and 4, the hypotenuse is 5.

How do you find the angles of a right triangle?

Use the inverse trig functions. Angle A = arctan(a ÷ b) when you know both legs, and angle B = 90° − A.

What are the sides of a right triangle called?

The two shorter sides are the legs (a and b); the longest side, opposite the right angle, is the hypotenuse (c).

Can I use this to check if a corner is square?

Yes. Enter your two edge measurements as the legs; if the real diagonal matches the calculated hypotenuse, the corner is square. This is the basis of the 3-4-5 method.

🔗 Related Tools You Might Need

Common right triangles at a glance

Side c is the hypotenuse. Angle A is opposite side a. Every row is the same Pythagorean calculation the tool runs.

Side a	Side b	Hypotenuse c	Angle A	Angle B	Area
3	4	5.00	36.9°	53.1°	6.0
5	12	13.00	22.6°	67.4°	30.0
6	8	10.00	36.9°	53.1°	24.0
7	24	25.00	16.3°	73.7°	84.0
8	15	17.00	28.1°	61.9°	60.0
9	12	15.00	36.9°	53.1°	54.0
12	16	20.00	36.9°	53.1°	96.0
20	21	29.00	43.6°	46.4°	210.0
10	10	14.14	45.0°	45.0°	50.0
12	12	16.97	45.0°	45.0°	72.0

The 3-4-5 triangle and its multiples (6-8-10, 9-12-15, 12-16-20) give exact whole-number hypotenuses, which is why builders use them to square a layout.