Pythagorean Theorem Formula

a² + b² = c²

The Pythagorean theorem formula a² + b² = c² links the two legs of a right triangle to the hypotenuse.

Use a² + b² = c² whenever you have a right angle and want to solve the unknown side. This is the same relationship people describe as a squared plus b squared equals c squared.

Leg a

One right-side leg

a is a leg that meets the right angle.

Leg b

The other leg

b is the second leg forming the 90° angle.

Hypotenuse c

The longest side

c is opposite the right angle and is always the longest.

A Squared Plus B Squared Equals C Squared Calculator

These search phrases all point to the same right-triangle formula. Use the calculator when you know two sides and need the missing value for a, b, or c.

Exact phrase

A squared plus b squared equals c squared

Write the theorem in words when you want to remember what a² + b² = c² means.

a² + b² = c²

Short phrase

A squared plus b squared equals calculator

If the final side is unknown, enter the two known side lengths and let the calculator complete the equation.

c = √(a² + b²)

Compact notation

A2 B2 C2 triangle calculator

A2, B2, and C2 usually mean a², b², and c². The formula only applies when the triangle has a 90° angle.

a² + b² = c²

?Why this formula works

Right angle
The relationship only holds when one angle is exactly 90°.
Squares add up
The areas of the squares on the legs equal the area of the square on the hypotenuse.
Solve any side
Rearrange the formula to solve for a, b, or c.
Real-world use
Used in construction, design, and navigation for reliable distances.

Formula FAQ

Q1.Is the formula only for right triangles?

Yes. The formula is valid only when one angle is 90°.

Q2.Can I solve for a or b?

Absolutely. Rearrange to a = √(c² - b²) or b = √(c² - a²).

Q3.Is this the same as an a squared plus b squared equals c squared calculator?

Yes. That phrase describes the same formula, a² + b² = c². Enter two known side lengths in the calculator to find the missing side.

Related guides

Pythagorean theorem examples

Walk through classic substitutions, squaring, and square-root steps.

Word problems calculator

Turn ladders, diagonals, layouts, and distance stories into calculator inputs.

How to find the hypotenuse

Use c = √(a² + b²) when both legs are known.

Ready to calculate a missing side?

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