Pythagorean Theorem Calculator
A 2,500-Year-Old Formula That Still Gets Used Daily
Attributed to the Greek mathematician Pythagoras but known even earlier to Babylonian and Egyptian surveyors, the relationship between the three sides of a right triangle is one of the few pieces of school geometry that carpenters, engineers, and programmers all reach for regularly. Give this calculator any two known values — two legs, or a leg and the hypotenuse — and it solves for the missing side.
The Formula
Find a leg: b = √(c² − a²)
Both directions use the same underlying relationship — the sum of the squares of the two legs (a and b) always equals the square of the hypotenuse (c), the side opposite the right angle.
Common Applications
- Construction squaring — the classic 3-4-5 rule confirms a corner is exactly 90° without a protractor.
- Ladder and safety calculations — finding how far a ladder's base should sit from a wall for a given height and length.
- Screen and display sizing — diagonal screen measurements are the hypotenuse of the width and height.
- Navigation and surveying — converting east-west and north-south offsets into a direct-line distance.
| Leg A | Leg B | Hypotenuse C |
|---|---|---|
| 3 | 4 | 5 |
| 5 | 12 | 13 |
| 6 | 8 | 10 |
| 13 | known leg 5 | 12 (solved for leg) |
The 3-4-5 and 5-12-13 combinations are "Pythagorean triples" — whole-number solutions that satisfy the formula exactly, which is why builders favor them for quick on-site checks.
How to Use This Calculator
- Choose a mode: Find Hypotenuse or Find a Leg.
- For Find Hypotenuse, enter Side A and Side B.
- For Find a Leg, enter the Hypotenuse (c) and the Known Leg.
- Select Calculate to see the missing side and the worked-out formula.
Related Calculations
Need the hypotenuse specifically, without the leg-solving option? The Hypotenuse Calculator is a dedicated single-purpose version. For area, perimeter, and other triangle measurements, see the Geometry Calculator.