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: August 2019

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.

We have also added a free, downloadable spreadsheet to make calculations offline nice and easy!

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

Need Assistance Setting Pipe Position and Heights On Site?

THS Concepts provides Setting Out Engineers to help building contractors precisley positon pipes, piles, kerb lines, drainage runs and more.

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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

How to Calculate a Gradient Slope %

So how do you calculate a gradient slope %? 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 rise length by the ruj length, in a calculator this would be 12 ÷ 60 . This would equal a gradient slope of 0.2 which is 20% (multiply by 100 if you need to).

Example Calculations

Run length = 25 metres
Rise Length = 0.8 metres

Gradient = 0.8/ 25
Gradient %= 0.032

Gradient % = 0.032 x 100
Gradient % =3.2

Run length = 3200 mm
Rise Length = 750 mm

Gradient = 750/ 3200
Gradient %= 0.234

Gradient % = 0.032 x 100
Gradient % =23.438

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.

Free Download – Gradient Calculator Spreadsheet

  • Calculate gradient number
  • Calculate gradient ratio
  • Calculate gradient slope %
gradient calculator excel spreadsheet

Need Assistance Setting Pipe Position and Heights On Site?

THS Concepts provides Setting Out Engineers to help building contractors precisley positon pipes, piles, kerb lines, drainage runs and more.

Find Out More

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 |October 12th, 2018|Useful Guides|2 Comments

2 Comments

  1. Sanam September 13, 2019 at 7:59 pm - Reply

    Gradient can also be expressed in a 3rd way: percentage.
    For example, a 1:40 gradient (i.e., 1 unit rise over 40 unit run) is equal to fraction number 1/40 = 0.025 which in turn is the same as 2.5%.
    Percentage expression for gradient/slope is quite commonly used in civil engineering.

    • Francesca Burke September 20, 2019 at 7:59 am - Reply

      Hi Sanam,
      That’s a good point, thank you! We hope you enjoyed our post. :)

      THS Concepts

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