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
| Field | What to enter |
|---|---|
| Flow velocity v | Units: m/s, km/h, mph, ft/s, knots |
| Cross-section area A | Units: m², cm², mm², km², in², ft² |
| Top width T | Units: m, cm, mm, km, in, ft … |
| Gravitational acceleration g | Units: 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 number |
|---|---|
| 1.5 | 0.6774 |
| 2.25 | 1.0161 |
| 3 | 1.3548 |
| 3.75 | 1.6935 |
| 4.5 | 2.0322 |
| 6 | 2.7096 |
Formula
D_h = A/T, Fr = v / √(g·D_h)
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.
Frequently asked questions
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.