Calculate the Froude number from flow velocity and characteristic length, and read whether the flow is subcritical, critical or supercritical.
For open channels use flow depth as the length; for ships and models use hull length. g is taken as 9.81 m/s².
Froude number
How to use this tool
Type the flow velocity in metres per second.
For open channels use the flow depth; for a ship or model use its length.
Fr = v / √(gL). Below 1 is subcritical, 1 is critical, above 1 is supercritical.
Subcritical flow is deep and slow; supercritical flow is shallow and fast, as in a steep chute.
Formula & worked example
Water flowing at 5 m/s with a depth of 10 m has Fr = 5 / √(9.81 × 10) ≈ 0.505 — subcritical flow.
Limitations — read this before you rely on it
The Froude number describes the balance of inertia and gravity only. It does not capture viscosity, turbulence, friction losses or channel shape, which also affect real flows.
Frequently asked questions
A dimensionless ratio comparing flow inertia to gravity: Fr = v / √(gL). It classifies open-channel and ship flows.
Fr below 1: deep, slow, tranquil flow where surface waves can travel upstream.
Fr above 1: shallow, fast flow where waves cannot travel upstream, seen in steep chutes and spillways.
Critical flow: the wave speed equals the flow speed, the boundary between subcritical and supercritical.
Yes — with hull length as L, it governs wave-making resistance and is used to scale model tests to full-size ships.