Pythagorean Theorem
Square both legs, add them, take the square root. Enter 3 and 4 and you get exactly 5.
Your numbers
Hypotenuse
5cm
Area
6cm²
Angle (°)
36.87°
Formula
Hypotenuse = √(Side a² + Side b²)
The angle shown is the one opposite side a. Only the two legs adjoining the right angle belong in the inputs.
What to enter
| Input | Default | Accepted range |
|---|---|---|
| Side a (cm)The length of the first side. | 3 | 0 and up |
| Side b (cm)The length of the second side. | 4 | 0 and up |
Step by step
Quick reference table
Results when only Side a (cm) changes and everything else stays put.
| Side a (cm) | Hypotenuse (cm) | Area (cm²) | Angle (°) (°) |
|---|---|---|---|
| 1.5 | 4.272 | 3 | 20.56 |
| 2.25 | 4.5894 | 4.5 | 29.36 |
| 3 | 5 | 6 | 36.87 |
| 4.5 | 6.0208 | 9 | 48.37 |
| 6 | 7.2111 | 12 | 56.31 |
What each result means
| Result | At default values |
|---|---|
| Hypotenuse (cm)The longest side of a right triangle, facing the right angle. | 5 |
| Area (cm²)The space a shape covers — length squared. | 6 |
| Angle (°) (°)An angle in degrees; a full turn is 360°. | 36.87 |
Common mistakes
The angle shown is the one opposite side a. Only the two legs adjoining the right angle belong in the inputs.
Glossary
- Side a
- The length of the first side.
- Side b
- The length of the second side.
- Hypotenuse
- The longest side of a right triangle, facing the right angle.
- Area
- The space a shape covers — length squared.
- Angle (°)
- An angle in degrees; a full turn is 360°.
Frequently asked questions
QHow is Pythagorean Theorem calculated?
Hypotenuse = √(Side a² + Side b²) — Square both legs, add them, take the square root. Enter 3 and 4 and you get exactly 5.
QCan you walk through an example?
With Side a 3cm, Side b 4cm, the answer is Hypotenuse 5cm.
QWhat do I need to enter?
Enter Side a, Side b. The result recalculates as you type, and an empty box counts as zero.
QHow much does the answer move if I change a number?
Changing only Side a (cm) moves the answer to Side a (cm) 1.5 → Hypotenuse (cm) 4.272 and Side a (cm) 6 → Hypotenuse (cm) 7.2111. The table below lays out five steps.
QHow are the numbers rounded?
Money is shown to the nearest whole unit, percentages to one decimal place and everything else to two. What you see is rounded; the calculation itself carries the unrounded value forward.
QAnything to watch out for?
The angle shown is the one opposite side a. Only the two legs adjoining the right angle belong in the inputs.
Related calculators
Keep your length units consistent across inputs — mixing centimetres and metres throws results far off.