Slope Calculator
About Slope Calculation
The slope calculator converts between slope angle and height difference for inclined surfaces. It is used for roofs, gravity pipes and drainage, stairs, ramps, roads, and any place where slope must be set or checked in different units.
Reference points and recommendations
Geometric model
Calculation model is based on a right triangle. The horizontal projection is the run B (m, mm). The vertical height difference is the rise H (m, mm). Slope is defined by the ratio H/B and can be expressed in degrees, percent, per mille, or as a ratio 1:n.
H/B = tan(α)
Conversions between slope units
Degrees show the angle α between the slope line and the horizontal. Calculations use tangent and arctangent.
α = arctan(H/B)
Percent shows how many units of rise correspond to 100 units of run.
i% = (H/B) · 100
Per mille shows how many units of rise correspond to 1000 units of run.
i‰ = (H/B) · 1000
Ratio 1:n means that for every n units of run there is 1 unit of rise. This is the same slope written as a ratio.
H/B = 1/n
Quick reference helps you sanity-check input. For example, 1% = 10‰ = 1:100. Also, 2% = 20‰ = 1:50. For small angles, approximately 1° ≈ 1.75%, but the exact conversion is calculated using tan(α).
How the required values are calculated
If run B and slope are known, the rise H is calculated using the selected slope unit:
H = B · tan(α)
H = B · (i%/100)
H = B · (i‰/1000)
H = B / n
If run B and rise H are known, the ratio H/B is found first, then it is converted into the required output unit:
α = arctan(H/B)
i% = (H/B) · 100
i‰ = (H/B) · 1000
1:n, where n = B/H
If rise H and slope are known, the run B is calculated as the inverse conversion:
B = H / tan(α)
B = H · 100 / i%
B = H · 1000 / i‰
B = H · n
Length of the sloped segment can be calculated if needed using the Pythagorean theorem and may be used to check a drawing or set out on site.
L = √(B² + H²)
Rounding and output format
Rounding affects the displayed value but does not change the physical meaning. For degrees, percent, and per mille, 2 decimal places are usually sufficient. For the 1:n format, practitioners often use an integer n so the ratio is easy to set out and verify on site.
Related European standards and where slope matters in design
Roofs and snow actions depend on the roof angle. In Eurocode 1 (EN 1991-1-3), the roof angle is used when selecting snow load shape coefficients for different roof types. That means slope affects the final design load through normative coefficients.
Building drainage by gravity is designed with specified gradients for horizontal runs to ensure stable gravity flow. For these systems, EN 12056 (series on gravity drainage systems inside buildings) is used.
Drainage systems outside buildings and gravity sewers are also set with gradients to achieve the required flow regime. For systems outside buildings, EN 752 is used.
FAQs
What is the difference between degrees, percent, per mille, and 1:n?
They are different ways to describe the same slope via the ratio H/B. Percent and per mille directly scale that ratio, while 1:n is convenient for set-out because it tells you the horizontal distance per 1 unit of vertical rise.
Why can the same slope look “different” after conversion?
Conversion to degrees uses trigonometry through tan(α), while percent and per mille are linear scalings of H/B. For small angles the numbers are close, but exact equivalence is always defined by the formulas.
How can I tell whether the result is reasonable?
Use quick checks: 1% = 10‰ = 1:100, 2% = 20‰ = 1:50. If you entered B and H, the ratio H/B should match the computed slope after conversion to the chosen unit.
What matters more in practice: B and H or the angle in degrees?
For set-out on site, B, H, and either 1:n or percent are often more practical. For design checks against standards (for example snow actions on roofs), the angle in degrees is often required because tables and coefficients are defined as functions of α.
Why is 1:n sometimes better given as an integer?
The 1:n format is commonly used as a “site” ratio for set-out and verification. Rounding n to an integer keeps it practical, while higher precision can be kept by using percent or per mille when needed.