CalcaTools

Pythagorean Theorem Calculator

A Pythagorean Theorem Calculator is a free online tool that solves a squared plus b squared using a squared plus b squared, hypotenuse calculator, right triangle formula. Students, teachers, and engineers use it to check homework, prep for exams, and verify hand calculations.

Last updated: June 2026 · Free · No sign-up required

Results

Enter values above and click Calculate to see your result instantly.

Quick reference

Pythagorean tripleCheck
3, 4, 59 + 16 = 25
5, 12, 1325 + 144 = 169
8, 15, 1764 + 225 = 289
7, 24, 2549 + 576 = 625

functions Shows the working, not just the answer

For students and teachers, the final number is only half the value. Every math tool here exposes the formula it applied, the intermediate steps, and the rounding rule, so you can follow along, check your homework, or use the answer in a proof or report with confidence.

calculate Accurate to the spec

Calculations use 64-bit floating point with sensible rounding for the domain (currency to 2 decimals, percentages to 4 decimals, algebra to 6 significant figures). Where exact rational arithmetic matters — fractions, factorials, simplification — we use a dedicated BigNumber path so 1/3 + 1/6 returns ½, not 0.49999.

school Free for classroom use

Educators are welcome to link to any math calculator on CalcaTools from a class site, Google Classroom, or worksheet. The pages are mobile-friendly, free, ad-supported (so we can keep them free) and have no sign-up wall — students just click and use them in class or at home.

tips_and_updates Pair with the spoke articles

Below the calculator we link a small set of plain-English explainer pages — "What is a percentage?", "Why does PEMDAS matter?", and so on. They cover the underlying concept in 4–6 short paragraphs. Read those before the calculator if the topic is new, or after if you want the extra context.

Interpretation guide

Solving for…Rearranged formula
Hypotenuse cc = √(a² + b²)
Leg aa = √(c² - b²)
Leg bb = √(c² - a²)

Formula & methodology

Formula: a² + b² = c² (a and b are legs, c is the hypotenuse)

How the Pythagorean theorem works

In any right triangle, the square of the hypotenuse (the side opposite the right angle) equals the sum of the squares of the other two sides.

Example: legs 6 and 8

c = √(6² + 8²) = √(36 + 64) = √100 = 10.

Finding a leg

If c = 13 and one leg b = 5, then a = √(13² - 5²) = √(169 - 25) = √144 = 12 (the 5-12-13 triple).

The theorem only applies to right triangles. Whole-number side sets like 3-4-5 are called Pythagorean triples.

Frequently asked questions

What is the Pythagorean theorem?
In a right triangle, the square of the hypotenuse equals the sum of the squares of the other two sides: a² + b² = c², where c is the hypotenuse (the side opposite the 90-degree angle) and a and b are the legs. It lets you find any one side when the other two are known.
How do you find the hypotenuse?
Square both legs, add them, and take the square root: c = √(a² + b²). For legs of 6 and 8, c = √(36 + 64) = √100 = 10. The hypotenuse is always the longest side and lies opposite the right angle.
How do you find a missing leg?
Rearrange the formula to subtract instead of add: a = √(c² - b²). If the hypotenuse is 13 and one leg is 5, the other leg is √(169 - 25) = √144 = 12. Make sure you subtract the known leg's square from the hypotenuse's square, not the other way around.
What is a Pythagorean triple?
A Pythagorean triple is a set of three whole numbers that satisfy a² + b² = c², such as 3-4-5, 5-12-13, and 8-15-17. Any multiple of a triple is also a triple (6-8-10, for example). Recognizing them lets you solve right triangles instantly without a calculator.
Does the Pythagorean theorem work for all triangles?
No, only for right triangles — those with a 90-degree angle. For non-right triangles you need the law of cosines, c² = a² + b² - 2ab cos(C), which reduces to the Pythagorean theorem when angle C is 90 degrees (because cos 90 = 0).