Right Triangle Calculator

What is the Right Triangle Calculator?

The right triangle calculator solves for any missing side or angle when you know at least two measurements. It uses the Pythagorean theorem for sides and trigonometric ratios for angles. This is the calculator for geometry homework, construction layouts, navigation, and any situation where you need to know the third side of a right triangle. CalciHub's version returns all sides, all angles, the perimeter, and the area in one calculation.

How Does It Work?

In a right triangle, one angle is always 90 degrees. The two shorter sides are called legs (a and b). The longest side — always opposite the right angle — is the hypotenuse (c). The Pythagorean theorem connects all three. For angles, sine, cosine, and tangent relate each angle to the ratio of two sides.

Pythagorean theorem: a² + b² = c² sin(A) = a/c, cos(A) = b/c, tan(A) = a/b Angle sum: A + B = 90°

• a, b = legs of the right triangle

• c = hypotenuse (longest side)

• A = angle opposite leg a

• B = angle opposite leg b

• sin, cos, tan = trigonometric ratios

How to Use CalciHub's Right Triangle Calculator

1. Enter any two known values — these can be two sides, or one side and one angle.

2. Leave the fields for unknown values blank.

3. Click Calculate — the tool fills in all remaining sides and angles.

4. Perimeter and area appear at the bottom of the results.

Tip: You can't enter two angles and no sides — angles alone don't define the size of the triangle, only its shape.

A Quick Example

You know leg a = 9 and hypotenuse c = 15. The calculator finds leg b using a² + b² = c²: 81 + b² = 225, so b² = 144, b = 12. Angle A = arcsin(9/15) = arcsin(0.6) ≈ 36.87°. Angle B = 90 − 36.87 = 53.13°. Perimeter = 9 + 12 + 15 = 36. Area = (1/2) × 9 × 12 = 54 square units. This is the 3-4-5 triangle scaled by 3.

Recognising that 9-12-15 is a 3-4-5 triple saves time in exams — Pythagorean triples always give exact whole-number answers.

Frequently Asked Questions