Hydraulic Gradient Calculator

Compute the hydraulic gradient S = hf / L and derived pressure quantities. Solve for S, head loss, or pipe length.

Pipe Networks · Gradient

Scenario Presets

Inputs

Solve for:

Head loss hf (m)

Pipe length L (m)

Fluid density ρ (kg/m³)

Theory

Definition

S = hf / L [m/m — dimensionless]

S% = S × 100 [%]

ΔP/L = ρ g S [Pa/m]

Rearrangements

hf = S × L (head loss from gradient and length)

L = hf / S (length from head loss and gradient)

Gradient Classification

Class	S (m/m)	S (%)	Typical use
Flat	< 0.001	< 0.1	Long transmission mains, flat terrain
Mild	0.001–0.005	0.1–0.5	Standard gravity water distribution
Moderate	0.005–0.01	0.5–1	Efficient gravity sewers, hilly terrain
Steep	0.01–0.05	1–5	Mountain supply, high-head segments
Very steep	> 0.05	> 5	Pressure breaks / energy dissipators needed

The hydraulic gradient S is the slope of the hydraulic grade line (HGL). For uniform pipe flow it equals the friction slope Sf = hf/L. In pressurised pipes S drives the flow; in open channels S must exceed the minimum self-cleansing gradient to prevent sediment deposition.