Right Triangle Calculator
Enter any two known values (sides, angles, area, or perimeter) to calculate all missing sides, interior angles, area, perimeter, and circumradius with step-by-step solutions.
Right Triangle Solver
Provide any 2 values below to compute the rest of the triangle parameters:
Right Triangle Formulas & Definitions
A right triangle (or right-angled triangle) is a triangle in which one angle is a right angle ($90^\circ$). The side opposite to the right angle is called the hypotenuse ($c$). The other two sides are called legs ($a$ and $b$).
- Pythagorean Theorem: $c = \sqrt{a^2 + b^2}$
- Trigonometric Ratios: $\sin(\alpha) = \frac{a}{c}, \quad \cos(\alpha) = \frac{b}{c}, \quad \tan(\alpha) = \frac{a}{b}$
- Area (A): $\text{Area} = \frac{1}{2} \times a \times b$
- Perimeter (P): $P = a + b + c$
- Inradius (r): $r = \frac{a + b - c}{2}$
- Circumradius (R): $R = \frac{c}{2}$
Frequently Asked Questions (FAQs)
A right triangle is a three-sided polygon where one of the interior angles equals $90$ degrees. The non-right angles are acute angles whose sum is always $90^\circ$.
You need at least 2 independent values (such as two sides, or one side and one acute angle, or one side and the area) because the right angle ($90^\circ$) is already known.
The Inradius ($r$) is the radius of the circle inscribed inside the right triangle, while the Circumradius ($R$) is the radius of the circle passing through all three vertices, equal to half the hypotenuse length ($c / 2$).
The area is calculated by multiplying the lengths of the two perpendicular legs ($a$ and $b$) and dividing by 2 ($\text{Area} = \frac{1}{2} \cdot a \cdot b$).
These are special right triangles with known side ratios. A 45-45-90 triangle is isosceles with side ratio $1 : 1 : \sqrt{2}$, while a 30-60-90 triangle has side ratio $1 : \sqrt{3} : 2$.