Convert between run, gradient and fall, work a 1:40 drain example step by step, and see why a fall can be too shallow or too steep.
Core idea
A gradient written 1:N means one unit of vertical fall for every N units of horizontal run. Use the same units before calculating. Fall equals horizontal run divided by N. Gradient denominator equals run divided by fall. State the direction: the pipe falls towards the downstream point.
What to recognise
- Convert metres to millimetres before dividing when the answer is needed in millimetres.
- Use horizontal run rather than sloping pipe length for the basic gradient calculation.
- For 1:40 over 6 m, calculate 6000 ÷ 40 = 150 mm fall.
- Check the result against the available levels and required cover.
- A steeper numerical fall has a smaller 1:N denominator, so 1:40 is steeper than 1:80.
Worked example: a branch waste at 1:40
A branch waste pipe runs 6 metres and is to be laid at a gradient of 1 in 40, written 1:40: for every 40 units measured along the pipe horizontally, it drops 1 unit vertically. The figures are chosen for the example.
- Divide the run by the ratio number: 6 m ÷ 40 = 0.15 m.
- Convert to millimetres: 0.15 m × 1000 = 150 mm of fall over the 6 metre run.
Converting first gives the same answer: 6000 mm ÷ 40 = 150 mm. On site, the end farthest from the stack is set 150 mm higher than the end at the stack, so water runs towards the stack.
Apply it
Start with a labelled sketch showing upstream level, downstream level and horizontal run. Calculate the required fall, subtract it in the direction of flow, then compare with measured invert levels. Recheck units before setting out clips or excavation depths.
Limits
The sum does not tell you whether a gradient, diameter or layout complies. Use the drainage design guidance for capacity, self-cleansing, branch layout, ventilation, access and bedding, and keep track of which kind of pipe you are dealing with. An unventilated appliance branch has set combinations of bore, length and fall that protect its trap from self-siphonage. The below-ground drain table gives minimum gradients linked to flow and the appliances connected. Steep underground runs need suitable channels and chambers where the fast flow arrives, so debris does not settle there. There is no single slope above which water always leaves solids behind.
Falls that are too shallow, and checking the whole run
Too little fall for the bore and the flow can leave solids behind to build up. Check the specified gradient and the expected flow together: the slope alone does not tell you the fault.
Checking the fall only at the two ends is not enough either. A support clip fixed slightly high or low can leave a sag or a local hump partway along an otherwise correctly calculated run, and that dip holds water and debris exactly like a badly graded pipe would. Check the level along the whole installed run, before it is concealed, not just the calculated start and finish.