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Right Triangle Calculator

Solve right triangles by entering any two known values (sides or angles). Calculate all missing sides, angles, area, and perimeter with detailed step-by-step explanations and visual diagrams.

Right Triangle Calculator
Quick Examples
3-4-5 Classic
5-12-13 Pythagorean
45-45-90 Isosceles
30-60-90 Special
Live Preview
? ? ? A B C ? ? 90°
Enter Known Values
Vertical leg
Horizontal leg
Longest side
0° < A < 90°
0° < B < 90°
Enter exactly 2 known values. The calculator will solve for all remaining measurements using the Pythagorean theorem and trigonometric ratios.

Embed Right Triangle Calculator Widget

About Right Triangle Calculator

Welcome to our Right Triangle Calculator, a professional-grade tool for solving right triangles with precision and clarity. Enter any two known values—whether sides or angles—and instantly compute all missing measurements including sides, angles, area, perimeter, and more with detailed step-by-step solutions and interactive diagrams.

What is a Right Triangle?

A right triangle (or right-angled triangle) is a triangle containing one angle of exactly 90 degrees. This special property makes right triangles fundamental to trigonometry, geometry, and countless real-world applications.

The key components of a right triangle:

Essential Formulas

Pythagorean Theorem

Pythagorean Theorem
$$a^2 + b^2 = c^2$$

This fundamental relationship states that the square of the hypotenuse equals the sum of the squares of the two legs.

Trigonometric Ratios

Basic Trig Ratios (SOH-CAH-TOA)
$$\sin(A) = \frac{a}{c} \quad \cos(A) = \frac{b}{c} \quad \tan(A) = \frac{a}{b}$$

Area and Perimeter

Area & Perimeter
$$\text{Area} = \frac{1}{2} \times a \times b \qquad \text{Perimeter} = a + b + c$$

Special Right Triangles

Certain right triangles have special angle relationships with exact trigonometric values:

45-45-90 Triangle
Side ratio: 1 : 1 : √2

An isosceles right triangle where both legs are equal and the hypotenuse is √2 times either leg.

30-60-90 Triangle
Side ratio: 1 : √3 : 2

The shortest side is opposite the 30° angle, the medium side (×√3) is opposite 60°, and the longest side (×2) is the hypotenuse.

How to Use This Calculator

  1. Identify your known values: Determine which two measurements you have (any combination of sides a, b, c or angles A, B).
  2. Enter the values: Input your known values in the corresponding fields. Leave all other fields empty.
  3. Click Calculate: The calculator will determine all missing values using the Pythagorean theorem and trigonometric ratios.
  4. Review results: Examine the complete solution including all measurements, step-by-step calculations, and the interactive triangle diagram.
  5. Verify accuracy: Check the verification section confirming that results satisfy both the Pythagorean theorem and angle sum property.

Solving Methods

When Two Sides Are Known

When One Side and One Angle Are Known

Applications of Right Triangles

Right triangles are essential in numerous fields:

Important Notes

Frequently Asked Questions

What is a right triangle?

A right triangle (or right-angled triangle) is a triangle with one angle exactly equal to 90 degrees. The side opposite the right angle is called the hypotenuse and is always the longest side. The other two sides are called legs or catheti.

What is the Pythagorean theorem?

The Pythagorean theorem states that in a right triangle, the square of the hypotenuse (c) equals the sum of the squares of the other two sides (a and b): a² + b² = c². This fundamental relationship allows you to calculate any side if you know the other two.

How do I solve a right triangle with two sides known?

When you know two sides of a right triangle: 1) Use the Pythagorean theorem to find the third side. 2) Use inverse trigonometric functions (arcsin, arccos, arctan) to find the angles. For example, if you know sides a and b, then c = √(a² + b²) and angle A = arctan(a/b).

What are the special right triangles?

The two most common special right triangles are: 1) The 45-45-90 triangle (isosceles right triangle) with sides in ratio 1:1:√2, and 2) The 30-60-90 triangle with sides in ratio 1:√3:2. These triangles have exact trigonometric values and appear frequently in mathematics and engineering.

How do I calculate the area of a right triangle?

The area of a right triangle is calculated using the formula: Area = ½ × base × height. Since the two legs of a right triangle are perpendicular, you simply multiply them together and divide by 2: Area = ½ × a × b, where a and b are the two legs.

Additional Resources

Reference this content, page, or tool as:

"Right Triangle Calculator" at https://MiniWebtool.com/right-triangle-calculator/ from MiniWebtool, https://MiniWebtool.com/

by miniwebtool team. Updated: Jan 13, 2026

You can also try our AI Math Solver GPT to solve your math problems through natural language question and answer.

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