Right Triangle Calculator
Give any two of the legs, hypotenuse and acute angles of a right triangle and get the rest: sides, angles, area, perimeter, altitude, inradius and circumradius.
Every side and angle of the triangle, its area and perimeter, and the altitude and circle radii — with the identity used (Pythagoras or the ratio) stated.
Example: Legs 3 and 4 give a hypotenuse of 5, angles 36.87° and 53.13°, area 6, perimeter 12, an altitude of 2.4 to the hypotenuse, inradius 1 and circumradius 2.5.
Two facts
fix the triangle.
Which two inputs are enough, how each case is solved, and what the extra figures mean.
Solving
A right triangle has one 90° angle, so its two acute angles add to 90° and any two of the five remaining quantities — legs a and b, hypotenuse c, angles A (opposite a) and B (opposite b) — determine it, except two angles alone, which fix the shape but not the size. Two sides are solved with Pythagoras, c² = a² + b², and A = atan(a/b). A side and an angle use the definitions of sine, cosine and tangent: a = c·sin A, b = c·cos A, a = b·tan A. Angles are in degrees.
The other figures
Area is ab/2. The altitude from the right angle to the hypotenuse is h = ab/c and it splits the hypotenuse into p = a²/c and q = b²/c (Euclid VI.8: each leg is the geometric mean of the hypotenuse and its adjacent segment). The inscribed circle has radius r = (a + b − c)/2 and the circumscribed circle, whose centre is the midpoint of the hypotenuse, has R = c/2.
Limits
Lengths are unit-free; results are in whatever unit you typed. A leg equal to or longer than the hypotenuse is refused. For triangles without a right angle use the Triangle Solver. Nothing leaves the browser; the same four anonymous usage counts as the rest of the site apply.
SOURCES
- Euclid, Elements, Book I, Proposition 47 (Pythagoras) and Book VI, Proposition 8 (altitude to the hypotenuse)
Last reviewed 19 September 2026. How results are checked: How we verify.