Math July 13, 2026 · 8 Min Read

Right Triangle Calculator – Guide & Formulas

Solve all unknown sides, angles, area, and perimeter of a right triangle given any two inputs. Uses Pythagorean theorem and trigonometry laws.

Completely solve any right-angled triangle. Provide any two known dimensions (such as one side and one angle, or two sides) to calculate the remaining sides, angles, area, and perimeter.

Key Takeaway

Use the free Right Triangle Calculator to solve all unknown sides, angles, area, and perimeter of a right triangle given any two inputs. uses pythagorean theorem and trigonometry laws. Get instant results with step-by-step explanations.

How to Use the Right Triangle Calculator

  1. Input any two values: side a, side b, hypotenuse c, or acute angles A and B.
  2. Check the computed missing side lengths and angles (in degrees and radians).
  3. Examine the area, perimeter, and altitude of the right triangle.

The Formula

a^2 + b^2 = c^2 | sin(A) = a/c | cos(A) = b/c

Variable Definitions

  • a, b: The perpendicular legs of the triangle
  • c: The hypotenuse opposite the 90-degree angle
  • A, B: The acute angles opposite sides a and b respectively

Solving a Right Triangle with Leg 3 and Hypotenuse 5

Find side b and the acute angles for a right triangle with side a = 3 and hypotenuse c = 5.

  1. Step 1: Set side a = 3 and hypotenuse c = 5.
  2. Step 2: Solve side b using b = √(c² - a²) = √(25 - 9) = 4.
  3. Step 3: Solve angle A = arcsin(3/5) ≈ 36.87°.
  4. Step 4: Solve angle B = 90° - 36.87° ≈ 53.13°.

Frequently Asked Questions

What is the SOH CAH TOA rule?

It is a mnemonic to remember basic trig ratios: Sine = Opposite / Hypotenuse (SOH), Cosine = Adjacent / Hypotenuse (CAH), and Tangent = Opposite / Adjacent (TOA).

Why do the acute angles always add up to 90 degrees?

The sum of all angles in a triangle is 180 degrees. Since a right triangle has a fixed 90-degree angle, the remaining two angles must sum to 180 - 90 = 90 degrees.

Can I enter three sides in this calculator?

If you enter two sides, the third side is automatically determined by the Pythagorean theorem.