Pythagorean Theorem Calculator
Enter any two sides of a right triangle to find the third, with a live SVG diagram and the formula worked out step by step.
Using the Pythagorean theorem (a² + b² = c²), enter the lengths of any two sides of a right triangle and get the third instantly — whether you're solving for the hypotenuse or a leg. An interactive triangle diagram redraws to match your dimensions, so you can see the shape you're actually working with.
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How to use
- Choose the side you want to solve for — the hypotenuse (c) or a leg (a or b) — from the dropdown.
- Enter the two known side lengths in the remaining fields.
- The missing length appears along with the full substitution worked out in math notation.
- The triangle diagram on the left redraws live with your dimensions so you can see the shape and proportions at a glance.
FAQ
- What should I watch out for when solving for a leg instead of the hypotenuse?
- By definition, the hypotenuse (c) is the longest side of a right triangle — it's always opposite the right angle. So when solving for a or b, the value you enter for c has to be a positive number larger than the other known side, or no valid triangle exists.
- Where does the Pythagorean theorem show up in real life?
- It's everywhere in construction and woodworking for squaring corners (the classic 3-4-5 rule), and it's how screen sizes are measured as a diagonal in inches. It's also the basis for calculating straight-line distance between two coordinates on a map.
- If the result doesn't come out to a clean whole number like the classic 3-4-5 triangle, how is it shown?
- Unless the sides happen to form one of the special integer ratios known as Pythagorean triples (like 3-4-5 or 5-12-13), the result is almost always an irrational number. In those cases, the calculator can't display the exact value, so it shows a decimal approximation rounded to a few places instead.