Hydraulic Gradient Calculator
The hydraulic gradient describes how steeply the hydraulic head changes along a flow path. Enter the head loss and the distance between two piezometers (or pipe ends) to find i = Δh/L. Add a hydraulic conductivity and cross-sectional area to also compute the Darcy seepage velocity (v = Ki) and volumetric flow rate (Q = KiA).
m
m
m/s
m²
Head loss per unit length of flow path — dimensionless
- 1
Head loss
Δh = 5 m = 5 - 2
Flow path length
L = 100 m = 100 - 3
Hydraulic gradient
i = 5 ÷ 100 = 0.050000Head loss per unit length of flow path — dimensionless.
How does this calculator work?
The hydraulic gradient i = Δh/L measures head loss per unit length of flow path. Combined with Darcy's law (v = Ki), it estimates groundwater seepage velocity through a porous medium. Enter head loss and distance; optionally add hydraulic conductivity and area to compute v and Q = KiA.
Formula
How this is calculated
The hydraulic gradient i is defined as the head loss Δh divided by the length L of the flow path. It is dimensionless (metre per metre) and represents the slope of the hydraulic grade line (HGL). A gradient of 0.05 means 5 cm of head is lost for every metre of travel. The steeper the gradient, the faster the flow for a given medium.
When a hydraulic conductivity K is provided, the calculator applies Darcy's law (v = Ki) to estimate the apparent seepage velocity through the medium. Multiplying by the cross-sectional area A of the flow cross-section gives the volumetric flow rate Q. Darcy's law assumes laminar flow through a porous medium with a constant, isotropic conductivity — it does not apply to turbulent pipe flow or highly heterogeneous soils.
The head-profile plot shows how hydraulic head decreases linearly along the flow path, which is the classic Darcy assumption. For real soils with layered conductivities the profile would be piecewise linear, but the overall i = Δh/L remains a useful average.
Frequently asked questions
It is the ratio of head loss to flow-path length (i = Δh/L). A larger gradient drives faster flow in the same medium. It equals the slope of the piezometric surface, and is dimensionless — often quoted as m/m or ft/ft.
Darcy's law (v = Ki) links the seepage velocity v to the hydraulic gradient i and the hydraulic conductivity K of the porous medium. It is valid for laminar, steady flow through a saturated, homogeneous medium, typically when the Reynolds number is below about 10.
In natural aquifers gradients are often 0.001–0.01 (very mild). Filters in water treatment run at 0.1–0.5. Earthen dams are designed so the exit gradient stays well below the critical value (~1.0) to prevent piping failure.
Also known as
TG we-Calculate Editorial Team. (2026). Hydraulic Gradient Calculator [Online calculator]. TG we-Calculate. https://we-calculate.com/calculator/hydraulic-gradient-calculator
TG we-Calculate Editorial Team. "Hydraulic Gradient Calculator." TG we-Calculate. 2026. https://we-calculate.com/calculator/hydraulic-gradient-calculator.
TG we-Calculate Editorial Team, "Hydraulic Gradient Calculator," TG we-Calculate, 2026. [Online]. Available: https://we-calculate.com/calculator/hydraulic-gradient-calculator
@misc{wecalculate_hydraulic_gradient_calculator, title = {Hydraulic Gradient Calculator}, author = {{TG we-Calculate Editorial Team}}, howpublished = {\url{https://we-calculate.com/calculator/hydraulic-gradient-calculator}}, year = {2026}, note = {TG we-Calculate} }
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