Math

Pythagorean Theorem Solver with Steps

Free Step-by-Step Pythagorean Theorem Solver

Unlike competitors that paywall their step-by-step solutions, this solver shows all work for free. See each step from formula statement through substitution, squaring, arithmetic, and final answer.

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 Pythagorean Theorem Solver with Steps.

Read the complete guide

The Five Steps

Every Pythagorean theorem solution follows the same five steps:

Write the formula
Substitute your values
Square each side
Add or subtract
Take the square root

Examples

Step-by-Step: (5, 12, ?)

Find the hypotenuse of a right triangle with legs 5 and 12.

c = √(5² + 12²) = √(25 + 144) = √169 = 13

Key takeaway: Each step builds on the previous one, making the solution traceable and verifiable.

Getting the Most from Step-by-Step Solutions

Use step-by-step solutions effectively:

Try solving the problem yourself first, then check each step
Identify which step you struggled with to target your learning
Practice with different triples to build fluency

Frequently Asked Questions about Pythagorean Theorem Solver with Steps

Why are step-by-step solutions important?

Seeing each step helps build procedural fluency. Students need to understand the squaring, addition/subtraction, and square-root operations as separate steps rather than memorizing the final formula.

What steps does the solver show?

The solver shows: (1) the formula, (2) substitution of your values, (3) squaring each side, (4) the arithmetic operation, and (5) the final square root to get the answer.

Does the solver simplify square roots?

Yes. When the result is irrational, the solver displays both the exact radical form (e.g., 2√13) and the decimal approximation, so you can use whichever form your homework requires.