Calculate the vertical drop from a horizontal run and an angle or grade, or find the drop angle from rise and run, in metres, feet or inches.
Angle Drop Formula
The calculator uses standard right-triangle trigonometry. Each mode rearranges the same relationship between rise, run, and angle.
Drop from angle mode:
Choose the value to solve:
Two points mode:
Variables:
- run – horizontal distance
- rise or drop – vertical change (positive = drop in the first mode)
- angle – downward slope angle in drop/run modes; upward angle in two-point mode, strictly between -90° and 90°
- grade – rise/run expressed as a percent
- slope distance – straight-line length along the slope, equal to √(run² + rise²)
Assumptions: the surface is treated as a straight line between the two points. Angles are measured from horizontal, not from vertical. The calculator converts every input to meters internally, then converts the result back to your chosen unit, so you can mix unit selections per field in solve mode.
How each mode applies the formula:
- Drop from angle multiplies your run by the tangent of the angle to return the vertical drop, plus grade, ratio, and slope distance.
- Angle or horizontal run uses the two values shown for the selected solve target; the other field is hidden.
- Two points takes the difference between coordinates and applies arctan to the rise over the absolute run.
Reference Tables
Use the first table to compare angle, grade, and rise-per-run. The second table illustrates geometries; it does not establish a universal design limit or code compliance.
| Angle | Grade (%) | Rise : Run | Drop per 100 ft |
|---|---|---|---|
| 1° | 1.75% | 1 in 57 | 1.75 ft |
| 2° | 3.49% | 1 in 28.6 | 3.49 ft |
| 5° | 8.75% | 1 in 11.4 | 8.75 ft |
| 10° | 17.6% | 1 in 5.67 | 17.6 ft |
| 15° | 26.8% | 1 in 3.73 | 26.8 ft |
| 20° | 36.4% | 1 in 2.75 | 36.4 ft |
| 30° | 57.7% | 1 in 1.73 | 57.7 ft |
| 45° | 100% | 1 in 1 | 100 ft |
| Application | Typical drop |
|---|---|
| Small horizontal drainage pipe (check adopted code and pipe size) | 1/4 in per ft (≈2.08%) |
| Patio or yard drainage | 1% to 2% |
| ADA ramp running slope (general maximum; exceptions and other criteria apply) | 8.33% (1:12) |
| Driveway example, not a universal maximum | 15% |
| Road grade example, not a universal maximum | 6% to 7% |
| Stairs (rise/run) | ≈30° to 35° |
Worked Examples
Example 1: Drop over a known run. A 25 m driveway slopes down at 4°. Drop = 25 × tan(4°) = 25 × 0.0699 = 1.75 m. Grade is 6.99%. Slope distance is 25.06 m.
Example 2: Solve for angle. A pipe drops 0.5 in over a 24 in run. Angle = arctan(0.5 / 24) = 1.19°. Grade is 2.08%, which equals 1/4 in per ft; required drainage slope depends on pipe size and the locally adopted code.
Example 3: Two points. Point 1 is (0, 12) and point 2 is (40, 9), measured in feet. Run = 40 ft, rise = -3 ft. Angle = arctan(-3 / 40) = -4.29°. The negative sign means point 2 is lower than point 1.
FAQ
Is grade the same as angle? No. Grade is the rise divided by run as a percent. Angle is the inverse tangent of that ratio. They only match in trend, not in value. A 100% grade equals a 45° angle, not a 100° angle.
What does a negative angle mean? In the two-point mode, a negative angle means point 2 is lower. In the drop and run modes, a positive angle means downward and a negative angle means upward; a negative drop therefore represents a rise.
Why does the calculator block 90°? At 90° the run is zero, so tangent is undefined and the formulas fail. Use values strictly between -90° and 90°.
Can I mix units? Yes. In solve mode you can enter rise in inches and run in feet. The math is done in meters internally and length outputs use your input length unit unless you choose a different result length unit (or the run unit when solving angle).
What is slope distance used for? Slope distance is the actual length you would measure along the surface, useful for ordering pipe, ramp material, or cable that follows the slope rather than the horizontal projection.
