Calculator
Example data table
| Method | Inputs | Angle (°) | Angle (rad) | Grade (%) |
|---|---|---|---|---|
| Rise & Run | Rise=3, Run=12 | 14.036 | 0.244 | 25.000 |
| Height & Length | Height=2, Length=5 | 23.578 | 0.412 | 43.589 |
| Two Points | (0,0) → (10,4) | 21.801 | 0.381 | 40.000 |
| Percent Grade | Grade=8% | 4.573 | 0.080 | 8.000 |
| Vector Components | Vx=15, Vy=−3 | 11.310 | 0.197 | −20.000 |
Formula used
- Rise & Run: slope = rise/run, angle = atan(rise/run). For signed angles use atan2(rise, run).
- Two Points: Δx = x2−x1, Δy = y2−y1, slope = Δy/Δx, angle = atan2(Δy, Δx).
- Percent Grade: slope = grade/100, angle = atan(grade/100), grade = 100×slope.
- Height & Length: run = √(length²−height²), angle = asin(height/length) = atan(height/run).
- Pitch (x:12): pitch = slope×12 (rise per 12 units of run).
How to use this calculator
- Select the method that matches your known measurements.
- Enter values in consistent units (the label is for display).
- Enable normalization for a standard 0–90° inclination.
- Press Calculate to see degrees, radians, slope, grade, and pitch.
- Use the CSV/PDF buttons to export the current result or history.
FAQs
1) What is an inclination angle in engineering?
It is the angle between a line or surface and the horizontal reference plane. It is commonly used for ramps, conveyors, roofs, pipelines, road grades, and drainage fall calculations.
2) Why does normalization matter?
Normalization reports a practical inclination between 0° and 90°. Without it, quadrant-aware calculations can exceed 90° when the horizontal direction is negative, which is correct mathematically but often not desired for slope reporting.
3) How do I convert grade (%) to degrees?
Use angle = atan(grade/100). For example, an 8% grade gives atan(0.08) ≈ 4.57°. This calculator performs the conversion automatically and also returns radians and pitch.
4) Which method should I choose?
Use Rise & Run when you know vertical and horizontal change. Use Height & Length for hypotenuse measurements. Use Two Points for survey coordinates. Use Percent Grade for road or ramp specifications. Use Vector Components for directional data.
5) Do units affect the result?
Angles depend on ratios, so consistent units cancel out. Just ensure rise and run use the same unit system. The units label is included in the display and exported reports for clarity.
6) What is roof pitch (x:12)?
Pitch is the rise per 12 units of run, common in roofing. It is computed as pitch = slope×12. For example, slope 0.5 corresponds to a 6:12 pitch.
7) Can I export multiple calculations?
Yes. Each calculation is saved to a session history (up to 10 entries). You can export the current result or the full history as CSV or PDF, then clear history when needed.
8) How accurate are the results?
Accuracy depends on your inputs. The math uses standard trigonometric relationships and quadrant-aware atan2 where appropriate. For field work, measure rise/run carefully and keep units consistent to avoid scaling mistakes.