Right Triangle Solver
Enter any two values, two sides or one side and one acute angle, to solve a right triangle for its sides, area, perimeter, angles, height, and inradius and circumradius.
Input
Pick a pair of inputs and enter the values to solve the right triangle for all remaining sides, area, and angles.
Two known values
Length in any unit
Length in any unit
Result
Area
6
Leg a
3
Leg b
4
Hypotenuse c
5
Perimeter
12
Angle A
36.869898 deg
Angle B
53.130102 deg
Height to hypotenuse
2.4
Inradius
1
Circumradius
2.5
Lengths use the same unit as the input, area uses that unit squared, and angles are shown in degrees.
How it works
- Let a and b be the legs around the right angle and c the hypotenuse, then a squared plus b squared equals c squared (the Pythagorean theorem) gives the remaining side.
- Area equals a times b divided by 2, and the perimeter is a plus b plus c.
- Acute angle A, opposite side a and adjacent to side b, comes from tan A equals a divided by b, and the other acute angle B equals 90 degrees minus A.
- Height to the hypotenuse is h equals a times b divided by c, the inradius is r equals (a plus b minus c) divided by 2, and the circumradius is R equals c divided by 2.
- When solving from a side and an angle, the angle must be greater than 0 and less than 90 degrees. When solving from a leg and the hypotenuse, the hypotenuse must be longer than the leg.
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Right Triangle Solver