Calculator
Pick an input method, enter values, and calculate slope angle, grade, and ratio. Results appear above this form.
Example data table
Typical grading scenarios for ramps, drainage, and access roads.
| Scenario | Rise | Run | Grade (%) | Angle (°) | Ratio (1 : n) |
|---|---|---|---|---|---|
| Walkway ramp | 0.50 m | 10.00 m | 5.00 | 2.862 | 1 : 20.0 |
| Driveway | 1.20 m | 12.00 m | 10.00 | 5.711 | 1 : 10.0 |
| Drainage channel | 0.30 m | 30.00 m | 1.00 | 0.573 | 1 : 100.0 |
| Steep access road | 3.00 m | 15.00 m | 20.00 | 11.310 | 1 : 5.0 |
Formula used
m = rise / runθ = atan(m)θ° = θ × 180/πGrade% = m × 100L = √(rise² + run²)rise = y2 − y1 and run = x2 − x1, then apply the same equations.
How to use this calculator
- Select an input method: use Rise & Run for field measurements, or Two Points for survey coordinates.
- Enter values: keep units consistent. Negative rise indicates a downward slope.
- Choose precision: increase decimals for design checks, reduce for reporting.
- Press Calculate: results appear below the header, above the form.
- Download outputs: export CSV for spreadsheets; export PDF for quick sharing.
Engineering note: if run is near zero, small measurement error can cause large angle changes. Re-check the baseline distance and instrument alignment.
Practical notes
Design checks for ramps and roads
Use slope angle to validate accessibility ramps, driveways, and haul roads. A 5% grade equals 2.862°; a 10% grade equals 5.711°. For short ramps, small run errors change angle quickly: if rise is 0.50 m and run is measured as 9.8 m instead of 10.0 m, grade shifts from 5.00% to 5.10%.
Drainage and surface runoff planning
Surface drainage often targets 0.5%–2% grades to avoid ponding while limiting erosion. At 1% grade the angle is about 0.573°. With a 30 m run, a 1% fall is 0.30 m. Pair the calculator’s hypotenuse output with material takeoff: for rise 0.30 m and run 30 m, slope length is 30.001 m, essentially equal to run.
Survey coordinates and site layouts
When you input two points, the calculator uses Δy and Δx from coordinates. This helps verify as-built slopes from total-station data. Example: Point A (0, 102.000) and Point B (25, 102.750) gives rise 0.750 and run 25, so grade is 3.00% and angle is 1.718°. Negative rise indicates downhill toward the second point. If Δx is zero, the line is vertical and angle is undefined in this model.
Communicating slope as ratio and grade
Construction documents may specify slopes as ratios, such as 1:20, or as percent grade. The calculator reports 1:n using |run/rise|. For a 0.50 m rise over 10 m run, the ratio is 1:20. Ratios become undefined when rise is zero; in that case the surface is level and angle is 0°. For steep work, combine ratio with a maximum grade limit to reduce slip risk.
Quality control and tolerance awareness
Angle tolerances are easier to understand when converted to grade. A ±0.5° tolerance near 0° is roughly ±0.87% grade, but near 12° it becomes larger in percent terms. Always check the “run cannot be zero” rule; very small runs amplify noise. Re-measure baseline distance and use consistent units for repeatable QA results. Record the same precision setting across teams.
Reporting and exporting deliverables
Use CSV export for spreadsheet logs and batch checks. Use PDF export for field packs, design reviews, and approvals. Store rise, run, angle, and grade together with the method label. If you compare alternatives, keep run constant and vary rise to see angle trends; doubling rise doubles grade but the angle increase is nonlinear because atan() curves. This supports quick sensitivity checks during value engineering for preliminary cost estimates too.
FAQs
What inputs does the calculator accept?
It accepts rise and run measurements, or two coordinate points. Both methods compute the same slope, angle, grade, ratio, and hypotenuse values, so you can use field data or survey data interchangeably.
Why is run not allowed to be zero?
Run is the horizontal baseline used in rise/run. If it is zero, the slope becomes infinite and the angle cannot be computed with atan(rise/run). Use a different baseline or the points method with nonzero Δx.
Does a negative rise change the results?
Yes. A negative rise indicates a downward slope. The grade and angle become negative, while the ratio is reported using absolute values so it remains easy to read in construction-style notation.
What is the difference between grade and angle?
Grade is a percent ratio of rise to run. Angle is the geometric inclination in degrees or radians. They relate through θ = atan(grade/100), so the relationship is nonlinear at higher grades.
How accurate are the results?
The math is exact for the provided inputs. Practical accuracy depends on measurement quality, especially run length. Longer baselines reduce noise, and consistent units prevent scaling mistakes.
How do the downloads work?
CSV is generated on the server from the last calculated result. PDF is created in your browser from the on-page result table and chart, making it convenient for sharing without extra software.