Gradient and Fall Reference Tables
SiteCalculators · sitecalculators.net · values rounded as labelled
Use this sheet for an independent gradient or drainage-fall check. A ratio written as 1:40 or 1 in 40 means one unit of vertical change for every 40 units of horizontal run. The ratio has no measurement unit, so the same slope can be expressed in metric or US customary units.
Gradient definitions and exact formulas
Let n be the denominator in a falling gradient of 1:n. Use horizontal plan distance for the run unless the project explicitly requires another convention. Vertical fall and horizontal run must use the same unit before a ratio is calculated.
vertical fall = horizontal run ÷ n
percentage = (vertical fall ÷ horizontal run) × 100 = 100 ÷ n
mm per metre = 1,000 ÷ n
degrees = atan(1 ÷ n) × 180 ÷ π
To convert an angle measured from horizontal back to gradient, use:
percentage = tan(degrees × π ÷ 180) × 100
inches per horizontal foot = 12 ÷ n
The equations describe gradient magnitude. On a drawing or site record, identify the direction separately with levels, an arrow or clear upstream/downstream labels. A positive number alone does not prove which way the line falls.
What is a 1 in 40 fall per metre?
A 1 in 40 fall equals exactly 25 mm per horizontal metre because 1,000 ÷ 40 = 25. It is also exactly 2.5%, approximately 1.432°, and 0.3 inches per horizontal foot. Over 12 m, the vertical fall is 12 ÷ 40 = 0.3 m, or 300 mm.
“Per metre” is useful shorthand, but the original 1:40 ratio does not mean the run must be one metre long. Multiply 25 mm/m by any horizontal length in metres to obtain fall in millimetres.
Metric gradient and fall table
Metric fall values below use horizontal distance. Percentage, degrees and millimetres per metre are rounded to no more than three decimal places where necessary; calculate from the formulas when more precision is justified.
| Gradient | Percent (%) | Degrees (°) | Fall (mm/m) | Fall over 10 m (mm) |
|---|---|---|---|---|
| 1:20 | 5 | 2.862 | 50 | 500 |
| 1:25 | 4 | 2.291 | 40 | 400 |
| 1:30 | 3.333 | 1.909 | 33.333 | 333.333 |
| 1:40 | 2.5 | 1.432 | 25 | 250 |
| 1:50 | 2 | 1.146 | 20 | 200 |
| 1:60 | 1.667 | 0.955 | 16.667 | 166.667 |
| 1:80 | 1.25 | 0.716 | 12.5 | 125 |
| 1:100 | 1 | 0.573 | 10 | 100 |
| 1:150 | 0.667 | 0.382 | 6.667 | 66.667 |
| 1:200 | 0.5 | 0.286 | 5 | 50 |
US customary gradient and fall table
The same dimensionless ratios can be expressed as inches of vertical fall per horizontal foot. Values are rounded to no more than three decimal places where necessary. One foot contains exactly 12 inches.
| Gradient | Percent (%) | Degrees (°) | Fall (in/ft) | Fall over 10 ft (in) | Fall over 100 ft (in) |
|---|---|---|---|---|---|
| 1:20 | 5 | 2.862 | 0.6 | 6 | 60 |
| 1:25 | 4 | 2.291 | 0.48 | 4.8 | 48 |
| 1:30 | 3.333 | 1.909 | 0.4 | 4 | 40 |
| 1:40 | 2.5 | 1.432 | 0.3 | 3 | 30 |
| 1:50 | 2 | 1.146 | 0.24 | 2.4 | 24 |
| 1:60 | 1.667 | 0.955 | 0.2 | 2 | 20 |
| 1:80 | 1.25 | 0.716 | 0.15 | 1.5 | 15 |
| 1:100 | 1 | 0.573 | 0.12 | 1.2 | 12 |
| 1:150 | 0.667 | 0.382 | 0.08 | 0.8 | 8 |
| 1:200 | 0.5 | 0.286 | 0.06 | 0.6 | 6 |
Worked gradient and drainage checks
Calculate drainage fall and downstream invert
A drainage run has an upstream invert of 145.750 m, a horizontal plan length of 18 m and a specified falling gradient of 1:80. The fall is 18 ÷ 80 = 0.225 m = 225 mm. The downstream invert is 145.750 − 0.225 = 145.525 m. This geometric check does not assess pipe capacity, minimum self-cleansing velocity, cover, bedding or specification compliance.
Find gradient from two known levels
An upstream invert of 75.340 m and downstream invert of 75.190 m give a fall of 0.150 m. Over a 12 m horizontal run, the slope is 0.150 ÷ 12 = 0.0125. The ratio denominator is 12 ÷ 0.150 = 80, so the run is 1:80, 1.25% or 12.5 mm/m.
Convert degrees to gradient
For an angle of 1° measured from horizontal, tan(1°) is approximately 0.017455. The equivalent gradient is approximately 1:57.290, 1.746%, 17.455 mm/m or 0.209 inches per horizontal foot. Do not treat 1° as 1%; one percent is approximately 0.573°.
Practical use and assumptions
- Use horizontal run: the standard formulas use plan distance, not measured distance along the slope. Confirm the convention shown on the design.
- Keep one datum: levels used in one calculation must refer to the same vertical datum and unit.
- State direction: a ratio normally gives magnitude. Label upstream/downstream, start/end or rise/fall so the intended direction is unambiguous.
- Distinguish invert and cover: a ground-to-invert depth is not cover to the pipe crown. Diameter and wall thickness affect actual cover.
- Use design tolerances: the mathematical conversion does not set an acceptable construction or survey tolerance.
- Retain working precision: calculate with unrounded levels and distances, then round the reported answer only to a precision supported by the inputs.
- Check governing requirements: minimum and maximum gradients depend on the asset, material, hydraulic design, accessibility, authority and project specification.
Engineering-adjacent reference: These conversions support checking and communication. They do not certify drainage design, hydraulic performance, road geometry, accessibility, finished levels or construction compliance. Work from current approved information and obtain competent review where required.