Right Triangle Calculator

A right triangle is a geometric figure with one right angle (90°). The remaining two angles are acute and sum to 90°.

Main Elements of a Right Triangle

• Hypotenuse (c) — the longest side, opposite the right angle. Calculated by the Pythagorean theorem: $$c=\sqrt{a^2+b^2}$$
• Legs (a, b) — the two sides that form the right angle.
• Acute angles (α, β) — always sum to 90°. Found through trigonometric functions: $$\alpha =\arctan \left(\frac{a}{b}\right)$$
• Area (S) — half the product of the legs: $$S=\frac{a\cdot b}{2}$$
• Perimeter (P) — the sum of all three sides: $$P=a+b+c$$
• Height to the hypotenuse (h) — a perpendicular from the right angle vertex to the hypotenuse: $$h=\frac{a\cdot b}{c}$$

Supported Calculation Cases

• By two legs (a, b) — full calculation of all parameters.
• By hypotenuse and leg (c, a) — finds the second leg and angles.
• By hypotenuse and acute angle (c, α) — finds both legs.
• By leg and adjacent angle (a, β) — finds the remaining sides.
• By leg and opposite angle (a, α) — alternative calculation.
• By area and leg (S, a) — finds the second leg and remaining parameters.
• By height to the hypotenuse and leg (h, a) — full calculation.