Everyday Tools

Pythagorean Theorem Calculator

Solve for the missing side of a right triangle using the Pythagorean theorem.

Updated April 13, 2026
Free online tool
Planning and research use

Why this page exists

Right-triangle math gets easier when the missing side is solved automatically instead of being rearranged by hand every time. This calculator helps visitors solve for a missing leg or the hypotenuse using the Pythagorean theorem.

Interactive tool

Run the estimate

Enter your numbers and read the result first, then use the sections below to understand what affects the outcome.

Calculator

Pythagorean theorem calculator

Solve for a missing side of a right triangle using the Pythagorean theorem.

Result

15.0000

Estimated missing side of a right triangle using the Pythagorean theorem and the values entered.

Calculated Hypotenuse c15.0000

Values useda = 9.00, b = 12.00

Triangle summarya = 9.00, b = 12.00, c = 15.0000

Formula usedc = sqrt(a^2 + b^2)

9.00^2 plus 12.00^2 gives a hypotenuse of about 15.0000.
The calculator assumes a right triangle, where the hypotenuse is the longest side.
Use the result for quick geometry, layout, and measurement checks where one side of a right triangle needs to be solved cleanly.

This is a standard right-triangle calculator. The leg and hypotenuse values entered must describe a possible right triangle for the missing-side result to be meaningful.

Planning note

Last updated April 13, 2026. Use this tool to compare scenarios and plan ahead, then confirm important details with the lender, employer, insurer, contractor, or other qualified provider involved in the final decision.

How it works

What the calculator is doing

Choose which side you want to solve for.

Enter the known sides of the right triangle.

The calculator applies the matching Pythagorean theorem formula and checks for impossible input cases when a leg is missing.

Understanding your result

This is a standard right-triangle calculator. It works only when the triangle can exist as a right triangle, which means the hypotenuse must be longer than either leg.

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Examples

Ways people use this tool

Example scenarios help turn a quick estimate into a more useful comparison or planning step.

Solve for a missing hypotenuse

Enter the two legs to estimate the longest side of a right triangle quickly.

Back out a missing leg

When you know the hypotenuse and one leg, the calculator can solve for the other leg and flag impossible values cleanly.

Use it with coordinate tools

The theorem often fits naturally beside distance-formula, slope, and midpoint checks.

FAQ

Common questions

When does the Pythagorean theorem apply?

It applies to right triangles, where the square of the hypotenuse equals the sum of the squares of the two legs.

Why can some leg calculations be impossible?

If the hypotenuse is not longer than the known leg, the inputs do not describe a real right triangle, so the missing side cannot be solved as a real number.

Which side is the hypotenuse?

The hypotenuse is the longest side of a right triangle and sits opposite the right angle.

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Keep comparing

Use these related tools to compare nearby scenarios, check a second estimate, or keep narrowing down the right decision.

Everyday ToolsUpdated April 12, 2026