Right Triangle Calculator

Calculate angles, sides, area, and perimeter of any right triangle

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Enter Known Values

Enter any two values to calculate the others

Side A (Adjacent)

Side B (Opposite)

Side C (Hypotenuse)

Angle α (degrees)

Angle β (degrees)

Area

Perimeter

Right Triangle Diagram

α + β = 90°

a² + b² = c²

Angle Distribution

Total: 180°

Angle α

Angle β

Right Angle (90°)

Calculation Results

Side A (Adjacent) –

Side B (Opposite) –

Side C (Hypotenuse) –

Angle α –

Angle β –

Area –

Perimeter –

Right Triangle Formulas

Understand the mathematical principles behind right triangle calculations

Pythagorean Theorem

The fundamental relationship between the sides of a right triangle:

a² + b² = c²

Where c is the hypotenuse, and a and b are the other two sides.

Area Calculation

The area of a right triangle is half the product of its two legs:

Area = (a × b) / 2

This works because a right triangle is exactly half of a rectangle.

Perimeter Calculation

The perimeter is the sum of all three sides:

P = a + b + c

Where a, b, and c are the three sides of the triangle.

Angle Calculations

Angles can be found using trigonometric functions:

sin(α) = opposite/hypotenuse

cos(α) = adjacent/hypotenuse

tan(α) = opposite/adjacent

Right Triangle Calculator: Complete Guide

What is a Right Triangle?

A right triangle is a geometric shape with three sides and three angles, where one angle measures exactly 90 degrees. This special angle, called the right angle, creates unique mathematical relationships between the sides and angles.

What is a Right Triangle Calculator?

A right triangle calculator is a specialized tool that computes unknown measurements of a right triangle when given limited information. Our calculator can determine missing sides, angles, area, and perimeter using mathematical formulas.

Where is Right Triangle Calculation Used?

Right triangle mathematics has extensive applications across various fields:

Construction and Architecture: Calculating roof pitches, stair angles, and structural supports
Surveying and Navigation: Determining distances and bearings between points
Physics and Engineering: Analyzing forces, vectors, and motion components
Computer Graphics: Calculating perspectives, rotations, and 3D transformations

Understanding Trigonometric Functions

Trigonometry forms the foundation of right triangle calculations. The three primary functions—sine, cosine, and tangent—relate angles to side ratios:

Sine (sin): Ratio of opposite side to hypotenuse
Cosine (cos): Ratio of adjacent side to hypotenuse
Tangent (tan): Ratio of opposite side to adjacent side

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Disclaimer

This calculator provides mathematical calculations for educational purposes. Always verify critical calculations through multiple methods.

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