Pythagorean Theorem Calculator · Practical guide
How to Find the Hypotenuse of a Right Triangle
Square each leg, add the squares, and take the square root: c = √(a² + b²). The calculator above does it in one step.
At a glance
Quick answer
The hypotenuse of a right triangle is c = √(a² + b²): square the two legs, add them, and take the square root. With legs of 6 and 8, that is √(36 + 64) = √100 = 10. Enter the two legs above and the calculator returns the hypotenuse to four decimal places, plus the triangle's area and perimeter.
Interactive tool
Pythagorean Theorem Calculator
Enter your own values, then compare the result with the examples below.
Results
Formula: a² + b² = c²
Worked Example Step by Step
For legs a = 6 and b = 8: 6² = 36 and 8² = 64, so a² + b² = 100, and c = √100 = 10. The same triangle has an area of (6 × 8) ÷ 2 = 24 and a perimeter of 6 + 8 + 10 = 24 — both shown alongside the answer.
Common Leg Pairs and Their Hypotenuses
| Leg a | Leg b | Hypotenuse c |
|---|---|---|
| 3 | 4 | 5 |
| 6 | 8 | 10 |
| 5 | 12 | 13 |
| 9 | 12 | 15 |
| 8 | 15 | 17 |
| 7 | 24 | 25 |
When the Answer Is Not a Whole Number
Most real measurements do not form perfect triples. Legs of 7 and 9 give c = √(49 + 81) = √130 ≈ 11.4018, and legs of 10 and 10 (a 45-45-90 triangle) give c = √200 ≈ 14.1421. The calculator rounds to four decimal places, which is plenty for homework, layouts, and cuts.
Finding a Leg Instead
If you already know the hypotenuse and one leg, flip the formula: a = √(c² − b²). A hypotenuse of 13 with one leg of 5 gives √(169 − 25) = √144 = 12. Leave the unknown side blank above and the calculator detects which value to solve for.
Frequently Asked Questions
Which side is the hypotenuse?
The hypotenuse is the longest side of a right triangle, always opposite the 90-degree angle. It is the side c in a² + b² = c².
Does the formula work if I only know one side?
No — you need two sides (or one side plus an angle, which requires trigonometry). With a single side, infinitely many right triangles are possible.
Can the hypotenuse ever be shorter than a leg?
Never. Because c² = a² + b², the hypotenuse is always strictly longer than either leg. The calculator warns you if your inputs would violate this.
What units does the answer use?
Whatever units you entered. Legs in inches give a hypotenuse in inches; legs in meters give meters. Just keep both legs in the same unit.