In any right triangle, the square on the hypotenuse equals the sum of the squares on the other two sides. The rule underpins distance calculations, construction layout and navigation.
How to use it
Enter both legs to get the hypotenuse. To find a missing leg, type the known hypotenuse into the result box and side a is solved.
Practical use: squaring a corner
Builders use the 3-4-5 rule: mark 3 units along one wall and 4 along the other; if the diagonal is exactly 5, the corner is square.
Inputs explained
| Field | What to enter |
|---|---|
| Side a | Units: m, cm, mm, km, in, ft … |
| Side b | Units: m, cm, mm, km, in, ft … |
What each result means
- Hypotenuse c = sqrt([Side a]^2 + [Side b]^2)
- Triangle area = [Side a]×[Side b]÷2
- Angle opposite a = deg(atan2([Side a], [Side b]))
Example values
How the main result changes when Side a changes and everything else stays at the example values above:
| Side a (m) | Hypotenuse c (m) |
|---|---|
| 1.5 | 4.27 |
| 2.25 | 4.59 |
| 3 | 5 |
| 3.75 | 5.48 |
| 4.5 | 6.02 |
| 6 | 7.21 |
Formula
c = √(a² + b²)a = √(c² − b²)Worked example
Legs a = 3 m and b = 4 m.
c = √(3² + 4²) = √25 = 5 m. Area = 3 × 4 ÷ 2 = 6 m². Angle opposite a ≈ 36.87°.
Key terms
- Hypotenuse
- The longest side of a right triangle, opposite the right angle.
- Leg
- Either of the two sides that form the right angle.
- Pythagorean triple
- Whole numbers that satisfy a² + b² = c², such as 3, 4, 5.
Frequently asked questions
Does it work for any triangle?
Only right triangles. Use the law of cosines for others.
Can I mix units?
Yes, each side has its own unit menu and is converted automatically.
How do I find distance between two points?
Treat the x and y differences as the legs.
What formula does the Pythagorean Theorem Calculator use?
c = √(a² + b²).
Can I work backwards from the result?
Yes. Type the result you want into Hypotenuse c and the calculator finds the matching side a.