# Hydraulic Gradient Calculator

URL: https://speedycalculator.com/calculators/physics/hydraulic-gradient/
Last updated: 2026-10-30

> The hydraulic gradient calculator finds the slope of the hydraulic head between two points – in groundwater or pipe flow – from the two heads and the distance between them.

## Inputs

- Head at point 1 h₁ (m, cm, mm, km, in, ft, yd, mi)
- Head at point 2 h₂ (m, cm, mm, km, in, ft, yd, mi)
- Distance L (m, cm, mm, km, in, ft, yd, mi)
- Hydraulic conductivity (optional) (m/s, cm/s, m/day)

## Results

- Hydraulic gradient i
- In percent
- Darcy flux K·i

## Formula

```
i = (h₁ − h₂) / L
```

## Explanation

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

FieldWhat to enterHead at point 1 h₁Units: m, cm, mm, km, in, ft …Head at point 2 h₂Units: m, cm, mm, km, in, ft …Distance LUnits: 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 i12.5-0.10518.75-0.0425250.0231.250.082537.50.145500.27

## 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.

## FAQ

**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.


## Sources

- [Fluid Mechanics (F. M. White) – reference text](https://www.mheducation.com/highered/product/fluid-mechanics-white-chul/M9781260258318.html)
- [The Engineering ToolBox](https://www.engineeringtoolbox.com/)