Calculate vertical drop, grade, slope distance, or point-to-point angle from run, rise, angle, or two coordinates in m, cm, ft, or in.
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:
drop = run × tan(angle)
Solve mode (any one of three unknowns):
rise = run × tan(angle) run = rise / tan(angle) angle = arctan(rise / run)
Two points mode:
angle = arctan((y2 − y1) / |x2 − x1|)
Variables:
- run – horizontal distance
- rise or drop – vertical change (positive = drop in the first mode)
- angle – slope angle in degrees, 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.
- Solve rise/run/angle needs exactly two of the three values. It fills in the missing one using the matching rearrangement above.
- Two points takes the difference between coordinates and applies arctan to the rise over the absolute run.
Reference Tables
Use the first table to convert between angle, grade, and rise-per-run. Use the second table to judge whether the result is gentle, moderate, or steep for common applications.
| 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 |
|---|---|
| Drain pipe (plumbing) | 1/4 in per ft (≈2.08%) |
| Patio or yard drainage | 1% to 2% |
| ADA wheelchair ramp (max) | 8.33% (1:12) |
| Residential driveway (max) | 15% |
| Highway grade (max) | 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 matches the standard 1/4 in per ft plumbing slope.
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 solve mode and two points mode, a negative angle means the second point sits lower along the run, or the rise input was entered as negative. In drop-from-angle mode, a negative angle returns a negative drop, which means the surface rises rather than falls.
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 each output is shown in the unit you selected for that field.
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.