Groundwater flows from higher to lower hydraulic head. The hydraulic gradient – the head drop per unit distance – drives the flow and, multiplied by hydraulic conductivity, gives the Darcy flux.
How to use the Hydraulic Gradient Calculator
- Head at point 1 h₁
- Head at point 2 h₂
- Distance L
- Hydraulic conductivity (optional)
Results update as you type, every field has its own unit menu, and everything is calculated in your browser.
How it works
Enter the hydraulic heads at the two points and the distance between them.
Inputs explained
| Field | What to enter |
|---|---|
| Head at point 1 h₁ | Units: m, cm, mm, km, in, ft … |
| Head at point 2 h₂ | Units: m, cm, mm, km, in, ft … |
| Distance L | Units: m, cm, mm, km, in, ft … |
| Hydraulic conductivity (optional) | Units: m/s, cm/s, m/day |
What each result means
- Hydraulic gradient i = ([Head at point 1 h₁] – [Head at point 2 h₂])÷[Distance L]
- In percent = ([Head at point 1 h₁] – [Head at point 2 h₂])÷[Distance L]×100
- Darcy flux K·i = [Hydraulic conductivity (optional)]×([Head at point 1 h₁] – [Head at point 2 h₂])÷[Distance L]
Example values
How the main result changes when Head at point 1 h₁ changes and everything else stays at the example values above:
| Head at point 1 h₁ (m) | Hydraulic gradient i |
|---|---|
| 12.5 | -0.105 |
| 18.75 | -0.0425 |
| 25 | 0.02 |
| 31.25 | 0.0825 |
| 37.5 | 0.145 |
| 50 | 0.27 |
Formula
i = (h₁ − h₂) / L
Worked example
Inputs — Head at point 1 h₁: 25 m; Head at point 2 h₂: 23 m; Distance L: 100 m; Hydraulic conductivity (optional): 0.0001 m/s.
Results — Hydraulic gradient i = 0.02; In percent = 2 %; Darcy flux K·i = 0.1728 m/day.
Key terms
- Hydraulic head
- Height a water column rises to at a point.
Frequently asked questions
Which way does groundwater flow?
From high to low hydraulic head.
Is the gradient dimensionless?
Yes – metres per metre.
What is hydraulic head?
Elevation head plus pressure head.
What gradients are typical?
0.001–0.01 in regional aquifers.