Pythagorean Theorem Calculator

Use our free Pythagorean theorem calculator to find the missing side of a right triangle. Simply enter the values of two sides, and our calculator will instantly compute the third side using the Pythagorean theorem.

How to Use the Pythagorean Theorem Calculator

1. Enter the values for any two sides of the right triangle (a, b, or c)
2. The calculator will automatically compute the missing side
3. The interactive visualization will update to show the right triangle with the given dimensions

The Pythagorean Theorem Formula

The Pythagorean theorem states that in a right triangle, the square of the length of the hypotenuse (c) equals the sum of the squares of the lengths of the other two sides (a and b):

a² + b² = c²

Where:

• a and b are the lengths of the two legs (the sides that form the right angle)
• c is the length of the hypotenuse (the side opposite to the right angle)

From this formula, we can derive:

• If we know a and b: c = √(a² + b²)
• If we know a and c: b = √(c² - a²)
• If we know b and c: a = √(c² - b²)

Applications of the Pythagorean Theorem

The Pythagorean theorem is one of the most useful principles in mathematics and has numerous applications:

• Construction: Ensuring corners are square and structures are properly aligned
• Navigation: Calculating distances and plotting courses
• Physics: Analyzing vectors and forces
• Computer Graphics: Determining distances between points in 2D and 3D space
• Surveying: Measuring distances and areas accurately

The interactive visualization helps you understand the relationship between the sides of a right triangle and how the Pythagorean theorem works.