Pythagorean Theorem Calculator – Find the Hypotenuse
Find the missing side of a right triangle with a² + b² = c².
About the Pythagorean Theorem Calculator
What is the Pythagorean Theorem Calculator?
A Pythagorean theorem calculator finds the missing side of a right triangle using a² + b² = c².
Why use this calculator?
From ladder heights to screen diagonals, right-triangle distances are everywhere. The theorem turns any right triangle into a simple equation.
How to use it
- Choose whether to find the hypotenuse or a missing leg.
- Enter the two known sides.
- Read the missing side with the identity check.
Formula
c = √(a² + b²) or a = √(c² − b²).
Only valid for right triangles — the 90°-angle relationship.
Frequently Asked Questions
Does it work for non-right triangles?
No — the relationship only holds at exactly 90°. Other triangles need the law of cosines.
What is a Pythagorean triple?
Three integers like 3-4-5 or 5-12-13 that satisfy the theorem exactly.
What order of operations does this use?
It follows standard PEMDAS/BODMAS rules: parentheses, exponents, multiplication and division, then addition and subtraction.
How precise are the answers?
The calculator uses double-precision floating-point math (about 15 significant digits) and rounds the display. For exact symbolic results use dedicated algebra software.
Can I enter negative numbers or decimals?
Yes. Negative values, decimals and very large or small numbers are all supported unless a field says otherwise.
What does it mean if I get an error?
Errors usually mean an invalid input, such as division by zero or a negative value where only positives make sense. Check your entries and try again.
Which units should I use?
Use one consistent unit for every input. The result will be in that unit (or its square or cube for area and volume).
How is area different from perimeter?
Perimeter is the distance around a shape; area is the space it covers. Perimeter is measured in units, area in square units.
Does the orientation of the shape matter?
No. Area, perimeter and volume depend only on the dimensions, not on how the shape is rotated or positioned.
Is this calculator free to use?
Yes. Every calculator on this site is completely free, with no hidden fees, no subscriptions and no limits on how many times you can use it.