# Hydraulic Conductivity Calculator

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

> The hydraulic conductivity calculator finds the hydraulic conductivity of a soil from the Hazen or Kozeny–Carman grain-size formulas, or from constant-head, falling-head or Darcy flow test data.

## Inputs

- Method
- Effective grain size d₁₀ (mm, cm, m, in, µm)
- Hazen coefficient C
- Porosity n
- Flow rate (mL/s, L/s, L/min)
- Sample length L (cm, mm, m, in, ft)
- Sample area A (cm², m²)
- Head difference h (cm, mm, m, in, ft)
- Standpipe area a (cm², mm²)
- Initial head h₁ (cm, mm, m, in, ft)
- Final head h₂ (cm, mm, m, in, ft)
- Elapsed time t (s, ms, min, h, days)

## Results

- Hydraulic conductivity K
- Intrinsic permeability (water, 20 °C)
- Typical of

## Formula

```
Hazen: K (cm/s) = C·d₁₀² (cm) · Kozeny–Carman: K = (ρg/μ)·n³/(1 − n)²·d₁₀²/180
Constant head: K = Q·L/(A·h) · Falling head: K = (a·L/(A·t))·ln(h₁/h₂)
```

## Explanation

Hydraulic conductivity tells how easily water moves through soil or rock – gravel drains quickly, clay barely at all. It is needed for well design, drainage, landfills and dam seepage.

### How to use the Hydraulic Conductivity Calculator

- **Method**
- **Effective grain size d₁₀**
- **Hazen coefficient C**
- **Porosity n**
- **Flow rate**
- **Sample length L**
- **Sample area A**
- **Head difference h**
- **Standpipe area a**
- **Initial head h₁**
- **Final head h₂**
- **Elapsed time t**

Results update as you type, every field has its own unit menu, and everything is calculated in your browser.

### How it works

Choose the method and enter the values.

### Inputs explained

FieldWhat to enterMethodChoose one: Hazen (grain size), Kozeny–Carman (grain size & porosity), Constant-head test, Falling-head testEffective grain size d₁₀Units: mm, cm, m, in, µmHazen coefficient CA numberPorosity nA numberFlow rateUnits: mL/s, L/s, L/minSample length LUnits: cm, mm, m, in, ftSample area AUnits: cm², m²Head difference hUnits: cm, mm, m, in, ftStandpipe area aUnits: cm², mm²Initial head h₁Units: cm, mm, m, in, ftFinal head h₂Units: cm, mm, m, in, ftElapsed time tUnits: s, ms, min, h, days

### Example values

How the main result changes when **Effective grain size d₁₀** changes and everything else stays at the example values above:

Effective grain size d₁₀ (mm)Hydraulic conductivity K (cm/s)0.10.010.150.02250.20.040.250.06250.30.090.40.16

## Worked example

Inputs — Method: Hazen (grain size); Effective grain size d₁₀: 0.2 mm; Hazen coefficient C: 100.

Results — **Hydraulic conductivity K = 0.04 cm/s**; Intrinsic permeability (water, 20 °C) = 41.48643 darcy; Typical of = Clean sand.

## Key terms

- **Hydraulic conductivity**: Darcy flux per unit hydraulic gradient.

## FAQ

**What is d₁₀?**
The grain size than which 10% of the soil (by mass) is finer.

**When is Hazen's formula valid?**
For clean sands with d₁₀ between 0.1 and 3 mm.

**Which lab test should I use?**
Constant head for sands and gravels; falling head for finer soils.

**How does K relate to permeability?**
K = k·ρg/μ – it also depends on the fluid.


## 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/)
- [USGS – Groundwater basics](https://www.usgs.gov/special-topics/water-science-school)