Math
ATAN function: convert percent grade and rise-over-run slope into degrees
Turn road grade percentages (10%, 100%, -8%) or rise/run ratios into slope angles using DEGREES(ATAN(grade)).
Why 100% grade is 45 degrees—not 90 degrees
Civil engineering, drainage pipes, and road signs express slope as grade = vertical_rise / horizontal_run: a 10% grade rises 10 meters per 100 meters of horizontal run (ratio 0.10), and a 100% grade rises 1 meter per 1 meter of run (ratio 1.0).
Because rise / run equals tan(theta), ATAN(grade) returns the exact angle in radians in (-pi/2, +pi/2), and DEGREES(ATAN(grade)) converts it to degrees: 100% grade = 45°, and 10% grade = 5.7106°.
| Slope Grade (A) | ATAN(A) Radians | DEGREES(ATAN(A)) |
|---|---|---|
| 0 (flat) | 0 | 0° |
| 0.10 (10% uphill) | 0.099669 | 5.7106° |
| 1.00 (100% slope) | 0.785398 | 45° |
| -0.08 (-8% downhill) | -0.079830 | -4.5739° |
Convert decimal grade to degrees
Unlike ASIN and ACOS, ATAN accepts any finite real number—from gentle 0.01 drainage slopes up to steep cliff ratios like 10 (84.2894°)—without ever going out of domain.
=ROUND(DEGREES(ATAN(A2)), 4)When horizontal run can be zero, prefer ATAN2
If you calculate rise / run directly inside ATAN(rise / run) and horizontal run is 0 (a vertical 90° wall), the division raises #DIV/0! before ATAN runs. Use ATAN2(run, rise) whenever horizontal run can be zero.
=B2 / C2Try the example
Use the original values or change them to test your understanding.