Pythagorean Theorem Calculator

Calculate the hypotenuse or missing leg of a right triangle using the Pythagorean theorem (a² + b² = c²).

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Side A (Leg)
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Side B (Leg)
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Side C (Hypotenuse)
a = 0
b = 0
c = 0

Pythagorean Theorem Calculator

Enter any two sides to calculate the third side of a right triangle.

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units
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Pythagorean Theorem Formula

a² + b² = c²
Where c is the hypotenuse, and a & b are the other two sides

Calculation Steps

1. Square both known sides
2. Add them together (for hypotenuse) or subtract (for leg)
3. Take the square root of the result

Pythagorean Theorem Guide

What is the Pythagorean Theorem?

The Pythagorean theorem states that in a right-angled triangle, the square of the hypotenuse (the side opposite the right angle) is equal to the sum of the squares of the other two sides.

• Applies only to right triangles
• One of the most famous mathematical theorems
• Named after Greek mathematician Pythagoras

When to Use It

  • • Finding the hypotenuse when you know both legs
  • • Finding a missing leg when you know the hypotenuse and other leg
  • • Checking if a triangle is right-angled
  • • Calculating distances in coordinate geometry

How to Calculate

To find hypotenuse (c): √(a² + b²)
To find a leg (a or b): √(c² - other leg²)

Real-world Applications

  • • Construction and architecture
  • • Navigation and GPS systems
  • • Computer graphics and game development
  • • Surveying and cartography
  • • Physics and engineering calculations

Historical Context

While named after Pythagoras, the theorem was known to the Babylonians and Egyptians over 1000 years earlier. Pythagoras may have been the first to prove it.

• Oldest known proof: Chinese text Zhoubi Suanjing (1046-256 BCE)
• Appears in Euclid's Elements (300 BCE)

Quick Tips

  • • The hypotenuse is always the longest side
  • • All sides must be positive numbers
  • • Works only for right triangles
  • • Remember to square and square root correctly
  • • Check your units (all sides should be same unit)

Pythagorean Theorem Calculator Answers

What does the Pythagorean theorem calculator do?

It calculates the length of a side in a right triangle using the Pythagorean theorem formula: a² + b² = c².

What is the Pythagorean theorem?

The Pythagorean theorem states that in a right-angled triangle, the square of the hypotenuse (longest side) equals the sum of the squares of the other two sides.

Which sides do I need to enter?

You need to enter the lengths of any two sides—either the two legs or one leg and the hypotenuse—to calculate the missing side.

Can this calculator be used for non-right triangles?

No, it only applies to right triangles. For other triangles, use the law of cosines or sines.

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