# Froude Number Calculator

URL: https://speedycalculator.com/calculators/physics/froude-number/
Last updated: 2026-10-30

> The Froude number calculator finds the Froude number of open-channel flow from the flow velocity and the hydraulic depth (cross-section area divided by top width), and classifies the flow.

## Inputs

- Flow velocity v (m/s, km/h, mph, ft/s, knots)
- Cross-section area A (m², cm², mm², km², in², ft²)
- Top width T (m, cm, mm, km, in, ft, yd, mi)
- Gravitational acceleration g (m/s², ft/s², g, cm/s²)

## Results

- Hydraulic depth
- Froude number
- Flow type

## Formula

```
D_h = A/T,  Fr = v / √(g·D_h)
```

## Explanation

The Froude number compares flow speed with the speed of surface waves. Below 1 (subcritical) waves can travel upstream; above 1 (supercritical) they can't – and the transition back produces a hydraulic jump.

### How to use the Froude Number Calculator

- **Flow velocity v**
- **Cross-section area A**
- **Top width T**
- **Gravitational acceleration g**

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

### How it works

Enter the flow velocity, the wetted cross-section area and the water surface (top) width.

### Inputs explained

FieldWhat to enterFlow velocity vUnits: m/s, km/h, mph, ft/s, knotsCross-section area AUnits: m², cm², mm², km², in², ft²Top width TUnits: m, cm, mm, km, in, ft …Gravitational acceleration gUnits: m/s², ft/s², g, cm/s²

### What each result means

- **Hydraulic depth** = [Cross-section area A]÷[Top width T]
- **Froude number** = [Flow velocity v]÷sqrt([Gravitational acceleration g]×[Cross-section area A]÷[Top width T])

### Example values

How the main result changes when **Flow velocity v** changes and everything else stays at the example values above:

Flow velocity v (m/s)Froude number1.50.67742.251.016131.35483.751.69354.52.032262.7096

## Worked example

Inputs — Flow velocity v: 3 m/s; Cross-section area A: 2 m²; Top width T: 4 m; Gravitational acceleration g: 9.80665 m/s².

Results — Hydraulic depth = 0.5 m; **Froude number = 1.3548**; Flow type = Supercritical (rapid).

## Key terms

- **Hydraulic depth**: Flow area divided by surface width.

## FAQ

**What does Fr = 1 mean?**
Critical flow – the flow speed equals the shallow-water wave speed.

**Where does supercritical flow occur?**
Down steep spillways and chutes.

**What happens when supercritical flow slows?**
A hydraulic jump forms.

**Is the Froude number used for ships?**
Yes – with hull length, to predict wave resistance.


## 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/)