Workshop
Slope calculator
In short
A slope is worked out from the tilt angle θ: p = 100 × tan θ in %, q = 1000 × tan θ in mm per metre, N = 1 / tan θ for a 1:N slope. The rise is Δ = L × sin θ for a length measured along the part, Δ = L × tan θ for a horizontal length.
Calculation
Example calculated with the tool’s default values.
Inputs
- I enter
- An angle (°)
- Tilt angle
- 1°
- The length is measured
- Along the part
Results
- Slope
- 1.75%
- Angle
- 1.00°
Worked example
Every value in this section belongs to the example, calculated with the tool’s default values.
Other results of the example
- Slope in mm per metre
- 17.5mm/m
- Slope as 1 in N
- 1:57.31 mm of rise for N mm
- A phone sensor is not a site spirit level: measure twice, turning the phone end for end, and keep the average. Lay the phone flat against the part, on a clean support.
Step-by-step calculation
Slope in %
p = 100 × tan θ
100 × tan 1.000° = 1.75 %
Slope in mm/m
q = 1000 × tan θ
1000 × tan 1.000° = 17.5 mm/m
Slope as 1:N
N = 1 / tan θ
1 / 0.01746 = 57.3
Usual drain slopes (DTU 60.11, France: 1 to 3 cm/m)
| cm/m | Slope (%) | mm/m | Angle (°) | 1:N |
|---|---|---|---|---|
| 1 | 1.0 | 10 | 0.573 | 1:100 |
| 2 | 2.0 | 20 | 1.146 | 1:50.0 |
| 3 | 3.0 | 30 | 1.718 | 1:33.3 |
How to use it
- Choose what you enter: an angle in degrees, a slope in % or a slope in mm/m.
- Enter the tilt angle (from −89.9° to 89.9°; positive when the part rises to the right) or the wanted slope.
- Enter the part length if needed, and say whether it is measured along the part or horizontally.
- Read the slope in %.
Frequently asked questions
How does a slope calculator work out a percentage?
The slope in % is the rise in cm per horizontal metre: p = 100 × tan θ, with θ the tilt angle. Example: 100 × tan 1.000° = 1.75 %. The other way round, the angle of a slope is atan(p / 100). A 1 % slope means 1 cm of rise per metre.
How do I express a slope as rise over run?
In mm per metre: q = 1000 × tan θ, so 1000 × tan 1.000° = 17.5 mm/m for 1°. As 1:N: N = 1 / tan θ, so 1 / 0.01746 = 57.3, that is 1 mm of rise for 57.3 mm. 10 mm/m equals 1 %.
What slope for construction drain pipes?
For waste-water drains, the French DTU 60.11 recommends 1 cm/m and its diameter tables apply to slopes of 1 to 3 cm/m; NF DTU 60.11 P2 sets a 1 % minimum for branch pipes and collectors. 1 cm/m = 1 % = 10 mm/m, that is 1:100; 2 cm/m = 20 mm/m; 3 cm/m = 30 mm/m, that is 1:33.3.
How do I work out the rise of a sloped pipe?
With the part length L: Δ = L × sin θ if L is measured along the part, Δ = L × tan θ if it is measured horizontally. The calculation also gives the other length, horizontal or along the part.
Limits
Indicative results. An angle read from a phone sensor is not a site spirit level: measure twice, turning the device end for end, and keep the average. The calculation flags a slope below the 1 % minimum or above 3 cm/m for a waste-water drain (French DTU 60.11 rules).
Sources
- Pente et angle d’inclinaison : Géométrie : p = tan θ (trigonométrie du triangle rectangle)
- Évacuation d’appareils : pente recommandée 1 cm/m ; diamètres des tableaux valables pour des pentes de 1 à 3 cm/m : DTU 60.11 (P 40-202), octobre 1988, § 3.2.1 et 3.2.2 (link)
- Pente minimale 1 % des conduites de raccordement et des collecteurs EU/EV : NF DTU 60.11 P2, § 6.1 et 6.3 (synthèse Progineer, consultée le 08/11/2026) (link)