Pythagorean Theorem Calculator

Calculate the hypotenuse or sides of a right triangle using the Pythagorean theorem: a² + b² = c²

Find Hypotenuse (c)

Find Side A

Find Side B

Pythagorean Theorem Formulas

Basic Formula

a² + b² = c²

The sum of squares of the two legs equals the square of the hypotenuse

Find Hypotenuse

c = √(a² + b²)

Example: a = 3, b = 4, c = √(9 + 16) = 5

Find Side

a = √(c² - b²)

Example: c = 5, b = 4, a = √(25 - 16) = 3

How to Use This Calculator

1

Choose What to Find

Select the tab for what you want to calculate: hypotenuse (c), side A, or side B.

2

Enter Known Values

Input the two known measurements. The calculator needs two values to find the third.

3

Calculate

Click Calculate to get the result with a step-by-step explanation of the calculation.

Example Calculations

Classic 3-4-5 Triangle

A right triangle has sides of 3 and 4 units. Find the hypotenuse.

Solution: c = √(3² + 4²) = √(9 + 16) = √25 = 5 units

Ladder Problem

A 13-foot ladder leans against a wall, reaching 12 feet high. How far is the base from the wall?

Solution: a = √(13² - 12²) = √(169 - 144) = √25 = 5 feet

Where the Pythagorean Theorem Is Used

Construction & Carpentry

Ensure walls are perpendicular, check if corners are square, and calculate diagonal measurements for framing and building projects.

Architecture & Design

Calculate roof slopes, staircase dimensions, and structural supports. Essential for creating accurate blueprints and plans.

Navigation & Surveying

Determine distances between points, calculate shortest paths, and measure land plots accurately in surveying work.

Education & Math

Fundamental concept in geometry, trigonometry, and physics. Used extensively in school mathematics and standardized tests.

Computer Graphics & Gaming

Calculate distances between objects, collision detection, and movement in 2D and 3D game development and graphics programming.

Engineering

Design mechanical systems, calculate forces and tensions, and solve structural problems in civil and mechanical engineering.

Frequently Asked Questions

What is the Pythagorean theorem?

The Pythagorean theorem states that in a right triangle, the square of the hypotenuse (longest side) equals the sum of squares of the other two sides: a² + b² = c².

What is the hypotenuse?

The hypotenuse is the longest side of a right triangle, opposite the right angle. It's always longer than either of the other two sides (called legs).

Does the Pythagorean theorem work for all triangles?

No, the Pythagorean theorem only works for right triangles (triangles with a 90-degree angle). For other triangles, use different formulas like the law of cosines.