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Hydraulic Gradient

i=ΔhLi = \frac{\Delta h}{L}
sig figs

Worked example: 1.2 m of head over 8 m → i = 0.15. Press Try an example to run it live, then adjust anything.

Enter your known values, leave one input blank, and solves for the missing one. Tap a variable’s symbol to see what it means, with a typical value. Change any unit and the answer follows.

Where Hydraulic Gradient fits

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Darcy's Law for Groundwater FlowHazen–Williams Velocity
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See also

Darcy's Law for Groundwater Flow: Both use hydraulic gradient.Hazen–Williams Velocity: Both use hydraulic gradient.Kirpich Time of Concentration: Both use flow path length.SCS Lag Time of Concentration: Both use flow path length.Travel Time of Flow Along a Segment (Length over Velocity): Both use flow path length.Darcy–Weisbach Head Loss: Both use head loss.
6 more relatedEnergy Balance Between Two Sections with Losses: Both use head loss.Energy Loss in a Hydraulic Jump: Both use head loss.Hazen–Williams Head Loss: Both use head loss.Minor Loss from K Factor: Both use head loss.Net Positive Suction Head Available (NPSHa): Both use head loss.Total Dynamic Head: Both use head loss.
Learning zone

Hydraulic Gradient explained

iΔhL

Water in soil moves because total head, elevation plus pressure head, is higher at one end of the path than the other, and the gradient is simply that loss spread over the distance travelled. A 1.2 m head difference across an 8 m long path gives i = 0.15, meaning fifteen centimetres of head are consumed by friction for every metre of travel. Both quantities are lengths, so i has no units at all and is the same number in metres or feet.

The trap is the flow path length, not the straight-line distance. Water going under a sheet pile wall travels down one side, around the toe and back up, and using the horizontal wall spacing instead of the true path length will overstate the gradient badly. The second trap is direction: upward seepage subtracts from effective stress, and when the upward gradient reaches the critical value ic=γ′/γw≈1.0i_c = \gamma'/\gamma_w \approx 1.0, the effective stress hits zero and the sand boils. That is quicksand, and it is why cofferdam design checks exit gradient long before it checks anything else.

Hydraulic Gradient formula

i=ΔhLi = \frac{\Delta h}{L}
Where
  • ii= Hydraulic gradient (m/m)
  • Δh\Delta h= Head loss (m)
  • LL= Flow path length (m)
In this toolkit

Darcy's law and seepage

4 formulasGroundwater through soil: hydraulic gradient, Darcy discharge, the faster real velocity in the pores, and layered permeability.

Revised 16 October 2026
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formula.expert. (2026, October 16). Hydraulic Gradient Formula & Calculator. https://formula.expert/solvers/hydraulic-gradient

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