EngineerHub.org2% slope over 12 m
Required fall = 12 × 0.02 = 0.24 m.
2% = 1.15° = 1:50
Choose how you know the slope
Use rise and run for engineering layout, two points for coordinate geometry, or convert directly between percent grade, degrees and 1:n gradient.
Example: 1 m rise over 10 m run = 10% = 5.71° = 1:10 = 10.05 m slope length.
Rise & Run
Example: 12 m at 2% requires 0.24 m of rise or fall.
Useful for finding the horizontal distance needed to stay below a target grade.
Point 1
Point 2
Coordinates may use any consistent length unit. The slope itself is dimensionless.
10% means 10 units of rise for 100 units of horizontal run.
Results
Slope visual
The triangle updates from the active calculation so rise, horizontal run, angle and true sloping length remain easy to compare.
Line equation—
Percent slope10.00% means rise divided by horizontal run, multiplied by 100.
Gradient ratio1 : 10.00 means 1 unit vertical for the stated horizontal proportion.
Angle5.71° is measured from horizontal, not vertical.
Tip: 100% slope is 45°, not 90°. A vertical surface would have zero horizontal run, so the slope ratio becomes undefined.
How to read slope
Engineering, construction and mathematics often express the same slope differently. This calculator keeps the formats together.
- Percent grade is common for roads, ramps and drainage.
- Degrees are common for geometry and some roof or earthwork work.
- Gradient ratio is often used for ramps, embankments and drawings.
- Sloping length is the real surface distance along the incline.
| Example | Grade | Equivalent |
|---|---|---|
| Very light drainage | 1% | 0.57° · 1:100 |
| General drainage / paving | 2% | 1.15° · 1:50 |
| 1:12 gradient reference | 8.33% | 4.76° · 1:12 |
| Road / ground reference | 10% | 5.71° · 1:10 |
| Equal rise and run | 100% | 45° · 1:1 |
Exact requirements depend on the project, code, and local standard. Use this table as a general reminder, not as a design rule.
Worked slope examples
Three common calculations showing how percent grade, angle and gradient ratio relate.
1:12 gradient
One unit of rise for 12 units of horizontal run gives 8.33%.
1:12 = 8.33% = 4.76°
10% grade
A 10% grade rises 1 unit for every 10 units of horizontal run.
10% = 5.71° = 1:10
Background
Engineering basis, equations, assumptions, interpretation and practical limitations for this calculator.
Slope % = (rise ÷ run) × 100
Angle = arctan(rise ÷ run)
Gradient 1:n → n = run ÷ |rise|
Two-point slope m = (y₂ − y₁) ÷ (x₂ − x₁)
Line equation: y = mx + b, where b = y₁ − mx₁
Drainage, ramps, roads and roofs may have minimum or maximum slopes set by design standards and local requirements.
Frequently Asked Questions
Practical questions about assumptions, inputs, interpretation and limitations.
A 10% slope means the vertical rise or fall is 10 units for every 100 units of horizontal run. It is equivalent to a rise/run ratio of 0.10.
No. A 100% slope means rise equals horizontal run, which corresponds to 45°. A vertical slope approaches an infinite percentage.
A 1:12 slope means one unit of vertical rise for every twelve units of horizontal run. That is approximately 8.33% or 4.76°.
Slope percent is 100 × rise/run. The angle is arctan(rise/run). They describe the same geometry but use different scales.
No. If rise and run are converted consistently, the dimensionless rise/run ratio, slope percentage and angle remain unchanged. Only the displayed lengths change.