Geometry Tool

Pythagorean Calculator

Solve for magnitude of sides in a right triangle.

Σ The Formula

a² + b² = c² (for right triangles)

Real World Examples

Classic 3-4-5
a=3, b=4 → c=5
Find Leg
a=?, b=12, c=13 → a=5
Construction
Wall height=8ft, ladder=10ft → base distance=6ft
Screen Diagonal
Width=16in, Height=9in → Diagonal=18.4in

# About This Calculator

The Pythagorean Theorem is one of the oldest and most famous mathematical relationships, dating back over 2,500 years to ancient Greece (though Babylonians knew it earlier). It states that in any right triangle, the square of the hypotenuse equals the sum of squares of the other two sides: a² + b² = c².

This fundamental relationship has countless practical applications: construction workers use it to ensure corners are perfectly square (3-4-5 triangle method), architects calculate roof slopes and staircase dimensions, surveyors measure distances, and engineers design everything from bridges to smartphones.

The theorem only works for right triangles (one 90° angle). The hypotenuse (c) is always the longest side, opposite the right angle. The other two sides (a and b) are called legs. If you know any two sides, you can always calculate the third using this relationship.

This calculator handles all three scenarios: finding the hypotenuse when you know both legs, or finding either leg when you know the hypotenuse and the other leg. It provides step-by-step solutions showing the calculation process, making it perfect for homework, construction projects, or any situation requiring precise right-triangle measurements.

How To Use

  1. Enter any two side lengths.
  2. Leave the unknown side blank.
  3. Click Calculate.

Frequently Asked Questions

What is the hypotenuse?+

The hypotenuse is the longest side of a right triangle, always opposite the 90° angle. It's labeled 'c' in the formula a² + b² = c². The other two sides (a and b) are called legs and form the right angle.

Does this work for all triangles?+

No! The Pythagorean Theorem ONLY works for right triangles (triangles with one 90° angle). For other triangles, you need different formulas like the Law of Cosines or Law of Sines.

What are Pythagorean triples?+

These are sets of three whole numbers that satisfy a² + b² = c², like 3-4-5, 5-12-13, 8-15-17, and 7-24-25. They're useful in construction because they're easy to measure and guarantee a perfect right angle.

How do I use this in real life?+

Common uses: checking if corners are square in construction (3-4-5 method), calculating TV screen diagonals, finding ladder placement distances, measuring roof slopes, determining diagonal distances across rectangular spaces, and countless carpentry/DIY projects.

Can I find angles with this theorem?+

Not directly. The Pythagorean Theorem only finds side lengths. To find angles, you'd use trigonometry (sin, cos, tan) after finding the sides. However, knowing all three sides lets you calculate angles using inverse trig functions.

Is Pythagorean Calculator free to use?+

Yes, Pythagorean Calculator on Matheric is completely free to use. We believe in accessible education and utility for everyone.

About

The Pythagorean Theorem is one of the oldest and most famous mathematical relationships, dating back over 2,500 years to ancient Greece (though Babylonians knew it earlier). It states that in any right triangle, the square of the hypotenuse equals the sum of squares of the other two sides: a² + b² = c².

This fundamental relationship has countless practical applications: construction workers use it to ensure corners are perfectly square (3-4-5 triangle method), architects calculate roof slopes and staircase dimensions, surveyors measure distances, and engineers design everything from bridges to smartphones.

The theorem only works for right triangles (one 90° angle). The hypotenuse (c) is always the longest side, opposite the right angle. The other two sides (a and b) are called legs. If you know any two sides, you can always calculate the third using this relationship.

This calculator handles all three scenarios: finding the hypotenuse when you know both legs, or finding either leg when you know the hypotenuse and the other leg. It provides step-by-step solutions showing the calculation process, making it perfect for homework, construction projects, or any situation requiring precise right-triangle measurements.

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