Logo
CalculatorsPlus
HomemathPythagorean Theorem

Pythagorean Theorem

Calculate the missing side of a right triangle using the Pythagorean theorem (a² + b² = c²).

Our free Pythagorean Theorem lets you calculate the missing side of a right triangle using the Pythagorean theorem (a² + b² = c²). It is built for students, teachers, engineers, and professionals who need fast, reliable math results who need fast, reliable results without installing software or creating an account.

Pythagorean Theorem runs entirely in your browser on CalculatorsPlus — enter your values, get instant results, and copy or share your output in one click. Your data never leaves your device; we do not store inputs on any server.

Use the pythagorean theorem to verify manual work, explore "what if" scenarios, and save time on repetitive calculations. For learning, try solving the problem by hand first, then check your answer here.

Results update in real time as you change inputs, so you can explore "what if" scenarios — adjust one variable at a time to see how it affects the outcome before committing to a purchase, plan, or decision.

This page includes step-by-step instructions, frequently asked questions, and practical tips below the calculator. Bookmark it for repeat use — many math tasks come up weekly during projects, studies, or financial planning.

Common Uses

  • Homework verification and exam preparation
  • Quick checks during work, shopping, or DIY projects
  • Teaching demonstrations and classroom examples
  • Engineering and spreadsheet formula validation

How to Use the Pythagorean Theorem

  1. 1

    Enter known sides

    Input the lengths of two sides of the right triangle.

  2. 2

    Select which side to find

    Indicate whether the unknown side is a leg or the hypotenuse.

  3. 3

    View the result

    See the missing side length and area of the triangle.

💡 Tips & Tricks

  • The hypotenuse is always the longest side and is opposite the right angle.
  • Use this for distance calculations — the distance formula is derived from the Pythagorean theorem.
  • Remember common triples (3-4-5, 5-12-13) for quick mental math.

Frequently Asked Questions

What is the Pythagorean theorem?
In a right triangle, the square of the hypotenuse (c) equals the sum of squares of the other two sides: a² + b² = c². It only applies to right triangles (one 90° angle).
How do I find the hypotenuse?
c = √(a² + b²). If the two legs are 3 and 4: c = √(9 + 16) = √25 = 5.
How do I find a missing leg?
If you know the hypotenuse c and one leg a: b = √(c² – a²). For c=13, a=5: b = √(169 – 25) = √144 = 12.
What are Pythagorean triples?
Pythagorean triples are sets of three integers that satisfy a² + b² = c². Common examples: (3,4,5), (5,12,13), (8,15,17), (7,24,25).