Calculator/Math Calculators/ Right Triangle Calculator

What is a Right Triangle?

A right triangle is a triangle with one 90-degree angle. The two sides forming the right angle are called legs, and the longest side opposite the right angle is called the hypotenuse.

Core Theory

Pythagorean Theorem

In a right triangle, the square of the hypotenuse equals the sum of squares of the other two sides.

a² + b² = c²
Trigonometry

Functions that describe the relationship between angles and sides in a right triangle.

sin A = a / c
cos A = b / c
tan A = a / b

Calculate the sides, angles, area, and perimeter of right triangles.

Right Triangle Calculator


How to Use

Enter 2 side lengths or 1 side and 1 angle to calculate the rest. Angle C is always 90° (right angle).

Example Values

Right Triangle Details

Pythagorean Theorem

The most important formula for right triangles. The square of the hypotenuse equals the sum of squares of the other two sides.

a² + b² = c²

  • c² = a² + b²
  • Using this formula, you can calculate any side if you know the other two.

Area Calculation

The area of a right triangle is half the product of the base and height.

Area = (a × b) / 2

Special Right Triangles

Commonly used right triangles with special ratios.

  • 3:4:5 triangle - The most basic Pythagorean triple
  • 30°-60°-90° triangle - Side ratio 1:√3:2
  • 45°-45°-90° triangle - Side ratio 1:1:√2

Frequently Asked Questions

Where is the Pythagorean theorem used?

Used in architecture, surveying, navigation, physics and many other fields to calculate distances and heights.

What are trigonometric ratios?

Trigonometric ratios (sin, cos, tan) are functions that describe the relationship between angles and side lengths in right triangles.

What is the sum of interior angles in a right triangle?

The sum of interior angles in any triangle is 180°. Since one angle is 90° in a right triangle, the other two angles sum to 90°.