Math

a² + b² = c² Calculator

Solving the Pythagorean Formula

The equation a² + b² = c² relates the three sides of every right triangle, where a and b are the legs and c is the hypotenuse. Enter any two values to solve for the third.

Pythagorean Theorem Tips

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Try an Example

Pick a scenario to see how the calculator works, then adjust the values

Ladder Against Wall

A 10-foot ladder leans against a wall with the base 6 feet away. How high does it reach?

Key values: Leg a = 6 ft · Hypotenuse c = 10 ft · Solve for leg b

TV Screen Diagonal

Find the diagonal of a TV with a 16:9 aspect ratio (width 40", height 22.5").

Key values: Width = 40 in · Height = 22.5 in · Find diagonal

Classic 3-4-5 Triangle

Verify that sides 3, 4, and 5 form a right triangle (the most famous Pythagorean triple).

Key values: Sides: 3, 4, 5 · Right triangle · Primitive triple

Documentation

This calculator is also known as a² + b² = c² Calculator.

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Understanding the Formula

The equation a² + b² = c² states that the sum of the squares of the two shorter sides (legs) equals the square of the longest side (hypotenuse). The formula can be rearranged to solve for any side.

Examples

Classic 3-4-5 Triangle

Given legs a = 3 and b = 4, find c.

c = √(3² + 4²) = √(9 + 16) = √25 = 5

Key takeaway: (3, 4, 5) is the most famous Pythagorean triple.

Working with the Formula

Key steps for using a² + b² = c²:

Identify which side is the hypotenuse (always opposite the right angle)
Square each known side before adding or subtracting
Remember to take the square root at the final step

Frequently Asked Questions about a² + b² = c² Calculator

What does a² + b² = c² mean?

It means the sum of the squares of the two shorter sides (legs) of a right triangle equals the square of the longest side (hypotenuse). For example, 3² + 4² = 9 + 16 = 25 = 5².

How do I solve for c?

Take the square root of both sides: c = √(a² + b²). Enter both leg values and the calculator computes it automatically.

How do I solve for a missing leg?

Rearrange the formula: a = √(c² - b²). Subtract the square of the known leg from the square of the hypotenuse, then take the square root.

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Choose from 5 specialized versions of this calculator, each optimized for specific use cases and calculation methods.

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