Angle from Two Sides
Rise divided by run is the tangent; the inverse tangent gives the angle. A 3:4 slope is 36.87°.
Your numbers
Angle (°)
36.87°
Radians
0.6435rad
Hypotenuse
5cm
Formula
Angle (°) = atan(Rise ÷ Run) × 180 ÷ π
Use it for ramps, stairs and roof pitches. To express the same slope as a percentage, use the grade calculator.
What to enter
| Input | Default | Accepted range |
|---|---|---|
| Rise (cm)How far it climbs, straight up. | 3 | 0 and up |
| Run (cm)How far it travels horizontally. | 4 | 0 and up |
Step by step
Quick reference table
Results when only Rise (cm) changes and everything else stays put.
| Rise (cm) | Angle (°) (°) | Radians (rad) | Hypotenuse (cm) |
|---|---|---|---|
| 1.5 | 20.556 | 0.3588 | 4.272 |
| 2.25 | 29.358 | 0.5124 | 4.589 |
| 3 | 36.87 | 0.6435 | 5 |
| 4.5 | 48.366 | 0.8442 | 6.021 |
| 6 | 56.31 | 0.9828 | 7.211 |
What each result means
| Result | At default values |
|---|---|
| Angle (°) (°)An angle in degrees; a full turn is 360°. | 36.87 |
| Radians (rad)An angle in radians; a full turn is 2π. | 0.6435 |
| Hypotenuse (cm)The longest side of a right triangle, facing the right angle. | 5 |
Common mistakes
Use it for ramps, stairs and roof pitches. To express the same slope as a percentage, use the grade calculator.
Glossary
- Rise
- How far it climbs, straight up.
- Run
- How far it travels horizontally.
- Angle (°)
- An angle in degrees; a full turn is 360°.
- Radians
- An angle in radians; a full turn is 2π.
- Hypotenuse
- The longest side of a right triangle, facing the right angle.
Frequently asked questions
Q. How is Angle from Two Sides calculated?
Angle (°) = atan(Rise ÷ Run) × 180 ÷ π — Rise divided by run is the tangent; the inverse tangent gives the angle. A 3:4 slope is 36.87°.
Q. Can you walk through an example?
With Rise 3cm, Run 4cm, the answer is Angle (°) 36.87°.
Q. What do I need to enter?
Enter Rise, Run. The result recalculates as you type, and an empty box counts as zero.
Q. How much does the answer move if I change a number?
Changing only Rise (cm) moves the answer to Rise (cm) 1.5 → Angle (°) (°) 20.556 and Rise (cm) 6 → Angle (°) (°) 56.31. The table below lays out five steps.
Q. How 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.
Q. Anything to watch out for?
Use it for ramps, stairs and roof pitches. To express the same slope as a percentage, use the grade calculator.
Related calculators
Keep your length units consistent across inputs — mixing centimetres and metres throws results far off.