Enter the upstream hydraulic head (h₁), downstream hydraulic head (h₂), and the flow path length (L) to calculate the hydraulic gradient — the rate of head change per unit distance. The result tells you the magnitude and direction of groundwater flow between two points in an aquifer. Also try the Reynolds Number Calculator.
Hydraulic Gradient (hg)
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Head Difference (h₁ − h₂)
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Flow Direction
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Hydraulic Gradient (%)
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The hydraulic gradient is the ratio of the difference in hydraulic head between two points to the distance between those points. It describes how steeply the hydraulic head changes over a given length and drives the direction and rate of groundwater flow through porous media. See also our use the Weber Number Calculator.
The hydraulic gradient (hg) is calculated using the formula hg = (h₁ − h₂) / L, where h₁ is the upstream hydraulic head, h₂ is the downstream hydraulic head, and L is the flow path length between the two points. The result is dimensionless (m/m or ft/ft).
A positive hydraulic gradient means h₁ is greater than h₂, indicating that the hydraulic head decreases in the direction of flow — the natural situation for groundwater moving downgradient. A negative gradient would indicate reverse flow, where water moves from the lower-head point toward the higher-head point.
Using the formula hg = (h₁ − h₂) / L = 5 / 10 = 0.5 m/m. This means the hydraulic head drops by 0.5 metres for every metre of horizontal distance, which is a relatively steep gradient indicating vigorous groundwater flow. You might also find our find Water Density with Water Density Calculator useful.
Because the hydraulic gradient is a ratio of length (head) to length (distance), it is dimensionless — expressed as m/m or ft/ft. It is sometimes also written as a percentage or as a pure decimal number between 0 and 1 for gentle gradients.
The hydraulic gradient is a fundamental parameter in Darcy's Law, which quantifies groundwater flow through porous media. Together with hydraulic conductivity, it allows engineers and hydrogeologists to calculate groundwater discharge, track contaminant plumes, and design remediation systems.
Natural hydraulic gradients in unconfined aquifers typically range from about 0.0001 to 0.05 m/m (0.01% to 5%). Flat sedimentary basins tend to have very low gradients near 0.001, while hilly or mountainous terrain can produce much steeper gradients exceeding 0.01.
According to Darcy's Law, the groundwater flux (q) equals hydraulic conductivity (K) multiplied by the hydraulic gradient (hg): q = K × hg. A steeper gradient drives faster flow through a given material. The actual pore velocity also depends on the porosity of the aquifer material.