How To Calculate A Gradient For Drainage, Ramps, Slopes Etc

We Show You How To Calculate Slopes & Gradients By Hand and Using Our Calculator

Article By: Tom Ayre
Last Update: October 2018

Calculating a gradient slope is an important element of building and civil design. Gradients are crucial to a number of elements of construction. Typical situations to get your gradients correct are:

  • Pipe drainage fall rates – without a correct gradient the water in the pipe may not flow.
  • Access ramps – standards are very strict on things like disability ramps.
  • Stairs – like access ramps, stairs are a very important element to get right in terms of gradient/slope design.

In this blog article I will be showing you how to calculate the gradient by hand which will be useful for sites where you don’t have a calculator. We also have a calculator for each section making the process even easier.

Lets get started!

A Brief Introduction To Gradients

A gradient is a complicated word for quite a simple concept. The gradient refers to the change rate of a slope. Take for instance a gradient of slope that is 1 in 40 (1:40).

A 1:40 slope means that for every 40 metres along the ground, the slope height increases by 1 metre. A 1:0.5 slope means that for every 1 metre along the ground, the slope height increases by 0.5 metres.

A gradient can be expressed in 2 ways, a number or a ratio.

For instance a 1:40 gradient number is shown as 0.025 (example shown in calculation section).

The same number can be converted into a ratio

For instance, a ratio is shown as “1:40”

The following sketch should help.

gradient of a slope

How To Calculate A Gradient Number

So how do you calculate a gradient? This is very simple.  This is very simple. Just make sure you keep your run/rise units the same (meters, centimetres, miles, km etc)

Step 1: Work out the run length. This is the horizontal distance along the ground. Example number 60 metres.

Step 2: Work out the rise length. This is the vertical length going up. Example number 12 metres.

Step 3: Divide the rise length by the run length, in a calculator this would be 12 ÷ 60 . This would equal a gradient of 0.2.

Example Calculation

Run length = 25 metres
Rise Length = 0.8 metres
Gradient = 0.8 / 25
Gradient = 0.032

Run Length = 500 mm
Rise Length = 1200 mm
Gradient = 1200 / 500
Gradient = 2.4

How To Calculate A Gradient Ratio

So how do you calculate a gradient? This is very simple. Just make sure you keep your run / rise units the same (meters, centimeters, miles, km etc)

Step 1: Work out the run length. This is the horizontal distance along the ground. Example number 60 metres.

Step 2: Work out the rise length. This is the vertical length going up. Example number 12 metres.

Step 3: Divide the run length by the rise length, in a calculator this would be 60 ÷ 12 . This would equal a gradient of 5, this would then be shown as a ratio so = 1:5

Example Calculations

Run length = 25 metres
Rise Length = 0.8 metres
Gradient = 25/ 0.8
Gradient = 1:31.25

Run Length = 500 mm
Rise Length = 1200 mm
Gradient = 500/ 1200
Gradient = 1:0.4166

Outline British Standard Drainage Guidance

Rainwater Drains

  • Rainwater drains at 75 & 100 mm should be laid at ratios of 1:100 or less.
  • Rainwater drains at 150 mm should be laid at ratios of 1:150 or less.
  • Rainwater drains at 225 mm should be laid at ratios of 1:225 or less.

Waste Water Pipes (Self Cleaning)

  • Flows Less Than 1 litre per second (pipes not exceeding DN100) – should be laid at ratios of 1:40 or less.
  • Flows More Than 1 litre per second (pipes not exceeding DN100) – should be laid at ratios of 1:80 or less with at least 1 toilet connected to it.
  • DN150 pipe – should be laid at ratios of 1:150 or less with at least 5 toilets connected to it.

Hopefully this explains what a gradient is and how it is calculated. If you have any questions or queries I can help with then please let me know in the comments section. Happy to assist!

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By |2018-10-12T14:43:53+00:00October 12th, 2018|Useful Guides|0 Comments

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