Right Triangle Calculator - Sides and Angles
Solve a right triangle from two known values and find every side, acute angle, area, and perimeter.
Right triangle side and angle calculator
Enter two known values, including at least one side. Leave the unknown fields blank.
About the right triangle calculator
A right triangle contains one angle of exactly 90 degrees. The side opposite that angle is the hypotenuse, conventionally called c, while the perpendicular legs are called a and b. This calculator reconstructs the entire triangle from any sufficient pair of measurements: two legs, one leg and the hypotenuse, or one leg and an acute angle. Once the three sides are known, it also reports the area and perimeter.
When both legs are supplied, the calculator applies the Pythagorean theorem: c squared equals a squared plus b squared. When a leg and the hypotenuse are supplied, the same identity is rearranged to isolate the missing leg. These formulas only describe a valid triangle when every length is positive and the hypotenuse is longer than either leg. The calculator checks those requirements rather than displaying a misleading result.
A side paired with angle A is solved with elementary trigonometry. In this naming convention, side a lies opposite angle A and side b lies adjacent to it. Therefore sine A equals a divided by c, cosine A equals b divided by c, and tangent A equals a divided by b. The other acute angle is complementary, so B equals 90 degrees minus A. These SOHCAHTOA relationships are useful in surveying, construction, navigation, physics, and classroom geometry.
Area follows directly from the perpendicular legs: multiply a by b and divide by two. Perimeter is the sum a plus b plus c. The calculator keeps full floating-point precision during each operation and rounds only the displayed values, reducing accumulated rounding error. If your measurements have limited precision, interpret the answer with an appropriate number of significant figures rather than treating every displayed decimal as measured certainty.
You can use the solver to check homework, size a diagonal brace, estimate the length of a ramp, calculate a roof rafter, or recover inaccessible distances from an angle measurement. Be consistent with units: if the entered sides are centimeters, all returned lengths are centimeters, area is square centimeters, and angles remain degrees. For physical projects, allow for tolerances and verify important dimensions with suitable instruments.
Right triangle examples
| Known values | Calculated values | Method |
|---|---|---|
| a = 3, b = 4 | c = 5, area = 6 | The classic 3-4-5 triangle uses the Pythagorean theorem. |
| a = 5, c = 13 | b = 12, area = 30 | Rearrange the Pythagorean theorem to find the missing leg. |
| a = 10, A = 30° | b = 17.3205, c = 20 | Use tangent and sine to recover the adjacent leg and hypotenuse. |
How to solve a right triangle
- Identify the known measurements and match each side or angle to the diagram convention.
- Enter two known values, making sure at least one entry is a side length.
- Leave every unknown field blank so the calculator can determine what must be solved.
- Select Calculate triangle and review the sides, angles, area, and perimeter.
Right triangle calculator FAQ
What information is needed to solve a right triangle?
You need two independent values and at least one must be a side length. Two angles alone determine only the shape, not the scale of the triangle.
Which side is the hypotenuse?
The hypotenuse is opposite the 90-degree angle and is always the longest side. This calculator labels it c.
Can I enter an angle greater than 90 degrees?
No, the entered angle A must be acute, meaning greater than zero and less than 90 degrees. The right angle is already fixed at 90 degrees.
What units does the calculator use?
It works with any consistent length unit. Results use that same unit, while area uses its squared form.
Why might my measured triangle differ slightly?
Real measurements include rounding and instrument error. Use consistent precision and allow practical tolerances for construction or surveying work.