How to use the Pythagorean Theorem Calculator

Quick start

1. Choose whether to find the hypotenuse, leg a, or leg b.
2. Enter the two side lengths you already know.
3. Add a unit label such as cm, ft, or in if it helps your notes.
4. Press Calculate side to solve the missing side.
5. Read the result card and formula steps before copying the answer.
6. Fix the inputs if the calculator says the hypotenuse is not the longest side.

Best uses

The Pythagorean Theorem Calculator is most useful when one side of a right triangle is missing and you already know the other two sides.

• Find the hypotenuse when both legs are known.
• Find a missing leg when one leg and the hypotenuse are known.
• Check classic triples such as 3-4-5, 5-12-13, and 8-15-17.
• Work with decimal side lengths and optional unit labels.

Quick answer

If you know both legs, choose the hypotenuse mode. For a = 3 and b = 4, the calculator uses c = sqrt(3^2 + 4^2), so c = 5.

If you know the hypotenuse and one leg, choose the missing-leg mode. For b = 12 and c = 13, it uses a = sqrt(13^2 - 12^2), so a = 5.

What each side means

Leg a and leg b are the two shorter sides that meet at the 90-degree angle. The hypotenuse, usually called c, is the side across from the right angle.

The hypotenuse must be the longest side. If c is shorter than a known leg, the calculator rejects the input because that set of sides cannot describe a right triangle.

• Use a and b for the two sides that form the square corner.
• Use c for the side across from the square corner.
• Keep every side in the same unit before entering the numbers.

Finding the hypotenuse

Use this mode when both legs are known and the diagonal side is missing. The calculator squares each leg, adds the squares, and takes the square root.

For a 6 ft by 8 ft rectangle corner, the diagonal is c = sqrt(6^2 + 8^2), which is 10 ft. This is the same 3-4-5 pattern scaled up by 2.

• a = 5.5 and b = 7.2 gives c about 9.06.
• a = 8 and b = 15 gives c = 17.
• a = 9 and b = 12 gives c = 15.

Finding a missing leg

Use a missing-leg mode when you know the hypotenuse and one leg. The calculator subtracts the known leg squared from the hypotenuse squared, then takes the square root.

For a = 8 and c = 17, the missing leg is b = sqrt(17^2 - 8^2), which is 15. The subtraction step is why the hypotenuse must be known and must be longest.

• Find a when b and c are known.
• Find b when a and c are known.
• Do not use missing-leg mode if you only know the two legs.

Decimals, units, and rounding

Decimal side lengths work. The result may be a rounded decimal because many square roots do not land on a whole number.

The unit label is only a label. If you type ft, the result shows ft, but the calculator does not convert inches to feet or centimeters to meters for you.

• Enter 5.5 and 7.2 if both sides use the same unit.
• Convert mixed units before calculating.
• Use the formula steps when you need to show how the rounded answer was found.

Common mistakes and impossible inputs

The biggest mistake is mixing up the hypotenuse with a leg. The hypotenuse is not just the side you are solving for. It is specifically the side opposite the right angle.

Another mistake is using the theorem on a triangle that is not known to be a right triangle. If you only know three side lengths and need area, perimeter, or angle checks, use the Triangle Calculator or Right Triangle Calculator instead.

• Do not enter 0 or negative side lengths.
• Do not make c shorter than a or b.
• Do not use the formula for a triangle unless the 90-degree angle is part of the problem.

When not to rely on it alone

The calculator solves the numbers you enter. It does not prove that a real wall corner, deck frame, screen, ramp, or drawing is actually square.

For construction or layout work, measure carefully, keep units consistent, and use the result as a planning check. Local code, safety rules, material tolerances, and real-world measurement error still matter.

• Use the Triangle Calculator for any triangle from three sides.
• Use the Right Triangle Calculator when you also need area, perimeter, and angles.
• Use the Distance Calculator when the problem is about two coordinate points.

Worked examples for Pythagorean Theorem Calculator

FAQ in plain language

Sources

Use these if you want to compare the formula, inputs, or limits with a trusted outside explanation.

• OpenStax Prealgebra: Geometric formulas
• OpenStax Algebra and Trigonometry: Radicals and rational exponents

Related tools

• Right Triangle CalculatorSolve a right triangle from two sides, including the missing side, area, perimeter, and acute angles.
• Distance CalculatorStraight-line distance between two 2D points, plus distance squared, deltas, midpoint, and formula steps.
• Triangle CalculatorCheck three triangle sides, find a possible third-side range, or calculate SSS area, perimeter, angles, and type.

Keep exploring

If the problem is close but not exactly one missing right-triangle side, these nearby tools can handle the next shape or coordinate step.

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• All calculator and utility guidesFind more plain-language examples, formulas, mistakes, and result explanations.
• Free calculator resourcesStart here when you are not sure which calculator page fits.

Privacy and copying results

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Use Copy answer when you want to save the inputs and result in notes, homework, a message, or a project list. Check the units, labels, and limits before copying.