MCPCalc

Drain Slope Calculator

Calculate drainage gradient, vertical fall, pipe flow velocity, and self-cleansing check for foul drainage, stormwater, and waste pipe systems.

Scratchpad (not saved)

m

e.g. enter 40 for a 1:40 gradient. Used when 'Specify by Ratio' is selected.

e.g. enter 2.5 for 2.5%. Used when 'Specify by Percentage' is selected.

m

Total vertical drop for the pipe run. Used when 'Specify by Fall' is selected.

What This Calculator Does

The drain slope calculator converts between vertical fall, gradient ratio (1:n), and percentage slope for any pipe run length. It also calculates flow velocity using Manning's equation and checks whether the pipe meets the self-cleansing velocity threshold of 0.75 m/s — the minimum required by BS EN 752, AS/NZS 3500, and the IPC.

It combines Pipe Diameter, Pipe Run Length, Specify Gradient By, Ratio n (1:n) to estimate Vertical Fall, Gradient — Ratio, Gradient — Percentage.

Formula & Method

Gradient expressed as ratio 1 ⁣: ⁣n1\!:\!n where n=L/hn = L / h, percentage slope S=h/L×100S = h / L \times 100, degrees θ=arctan⁡(h/L)\theta = \arctan(h/L). Manning's flow velocity: v=1nM⋅Rh2/3⋅S1/2v = \frac{1}{n_M} \cdot R_h^{2/3} \cdot S^{1/2} where nMn_M is Manning's roughness coefficient and Rh=d/4R_h = d/4 for a full-bore circular pipe. Full-bore flow capacity Q=v⋅AQ = v \cdot A. Half-bore capacity uses Qhalf=0.5⋅QfullQ_{half} = 0.5 \cdot Q_{full}.

Notation used in the formulas: RR = Vertical Fall; x1x_{1} = Pipe Diameter; x2x_{2} = Pipe Run Length; x3x_{3} = Specify Gradient By; x4x_{4} = Ratio n (1:n); x5x_{5} = Slope (\%); x6x_{6} = Vertical Fall.

Method summary: inputs are normalized to consistent units, core equations are evaluated, then secondary values are derived and rounded for display.

Use this calculator for quick scenario analysis. Start with baseline values, change one driver at a time, and compare how sensitive the results are to each input shown above.

Worked Examples

100 mm PVC drain, 6 m run at 1:40 gradient

Pipe: 100 mm diameter, run L = 6 m, gradient 1:40 (slope S = 0.025). Vertical fall h = L × S = 6 × 0.025 = 0.15 m = 150 mm. Manning n = 0.009 (PVC), hydraulic radius Rh = 0.1/4 = 0.025 m. Full-bore velocity v = (1/0.009) × 0.025^(2/3) × 0.025^(1/2) = 111.1 × 0.0855 × 0.158 = 1.50 m/s. ✓ Exceeds 0.75 m/s self-cleansing threshold.

150 mm PVC drain — minimum gradient check

150 mm PVC, run = 12 m, gradient 1:60 (S = 0.01667, fall = 0.2 m). Rh = 0.15/4 = 0.0375 m. v = (1/0.009) × 0.0375^(2/3) × √0.01667 = 111.1 × 0.1125 × 0.129 = 1.62 m/s. Full-bore Q = v × π(0.075)² = 1.62 × 0.01767 = 0.0286 m³/s = 28.6 L/s.

Recommended Minimum Gradients by Code

Pipe diameterMin. gradient (ratio)Min. slope (%)Standard
100 mm / 4"1:402.5%UK Part H / AS/NZS 3500 / IPC
150 mm / 6"1:601.67%UK Part H / AS/NZS 3500
225 mm / 9"1:901.11%UK Part H
300 mm / 12"1:1500.67%UK Part H

Inputs Used

  • Pipe Diameter: Used directly in the calculation.
  • Pipe Run Length: Used directly in the calculation.
  • Specify Gradient By: Used directly in the calculation.
  • Ratio n (1:n): e.g. enter 40 for a 1:40 gradient. Used when 'Specify by Ratio' is selected.
  • Slope (%): e.g. enter 2.5 for 2.5%. Used when 'Specify by Percentage' is selected.
  • Vertical Fall: Total vertical drop for the pipe run. Used when 'Specify by Fall' is selected.
  • Pipe Material: Used directly in the calculation.

See Also

Related Calculators

Drain Slope Calculator — Gradient, Fall & Self-Cleansing Velocity | MCPCalc