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.

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Put these formulas into practice with our instant, step-by-step Right Triangle Calculator.

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Use our free **right triangle calculator** to **solve sides, angles, and area** of any right-angled triangle instantly. This **right triangle calculator** uses the **Pythagorean theorem** and **trigonometric ratios** (sin, cos, tan) to find all unknown dimensions with step-by-step results. Whether you need to **find the hypotenuse**, **calculate angles**, or **compute area and perimeter**, this tool provides accurate results. 100% free — no signup required!

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. Click Calculate to solve the right triangle using the Pythagorean theorem and trigonometry.
  3. Check the computed missing side lengths and angles (in degrees and radians).
  4. Examine the area, perimeter, and altitude of the right triangle.
  5. Review the step-by-step trigonometric ratio calculations (SOH CAH TOA).
  6. Verify your results by checking that a² + b² = c² and A + B = 90°.
  7. Copy or save your right triangle solution for reference or further calculations.

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 a right triangle calculator?

A right triangle calculator solves for all unknown sides, angles, area, and perimeter of a right-angled triangle. It uses the Pythagorean theorem and trigonometric ratios (sin, cos, tan) to compute results given any two known dimensions.

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.

Is this right triangle calculator free to use?

Yes, this right triangle calculator is 100% free with no signup required. Use it unlimited times for geometry, trigonometry, and construction problems.

How do I find the hypotenuse of a right triangle?

Use the Pythagorean theorem: c = √(a² + b²), where a and b are the two legs. Enter any two known sides into the calculator to find the third.

What are common mistakes when solving right triangles?

Common mistakes include confusing the hypotenuse with a leg, using the wrong trig function (sin vs. cos), and forgetting that acute angles must sum to 90°.

Who should use this right triangle calculator?

This calculator is ideal for geometry and trigonometry students, architects, construction workers, surveyors, engineers, and anyone who needs to solve right triangle problems.

Can this calculator find the area of a right triangle?

Yes. The area is calculated as (base × height) / 2, where the two legs serve as the base and height. The calculator computes this automatically.

What is a Pythagorean triple?

A Pythagorean triple is a set of three positive integers (a, b, c) that satisfy a² + b² = c². Common examples include (3, 4, 5), (5, 12, 13), and (8, 15, 17).

How do I verify my right triangle solution?

Check two conditions: (1) a² + b² should equal c² (Pythagorean theorem), and (2) angles A + B should equal 90°. The calculator helps verify these automatically.