Froude Number Calculator
Written by Thierno Sadou Diallo, formula verified per our methodology • Last checked on 9/9/2026
The Froude number is calculated with Fr = velocity ÷ √(9.81 × characteristic length). A value below 1 indicates a subcritical (fluvial) regime, above 1 a supercritical (rapid) regime.
Explanation
The Froude number compares a flow's kinetic energy to its gravitational potential energy, in situations where a free surface exists (a river, a channel, a ship's hull) — unlike the Reynolds number, which instead compares inertial forces to viscous forces, with no reference to gravity. A Froude number below 1 characterizes a fluvial (or subcritical) regime: the flow is relatively slow and calm, and a disturbance can propagate upstream. Above 1, the regime becomes supercritical (or rapid/torrential): the flow is fast, disturbances can no longer travel back upstream, somewhat like a shock wave in air once speed exceeds that of sound (a direct parallel with the Mach number, which plays an analogous role for compressible flows). This number is central to river hydraulics (channel design, flood forecasting), naval engineering (a ship hull's resistance to forward motion, where the Froude regime strongly influences bow wave formation), and meteorology for certain atmospheric flows.
Example: 3 m/s velocity, 1 m depth
Inputs
Velocity: 3 m/s. Characteristic length: 1 m.
Calculation
Froude number = 3 ÷ √(9.81 × 1) = 3 ÷ 3.132 ≈ 0.958.
Result
With a Froude number of about 0.96 (close to 1, just below the critical threshold), this flow is subcritical but close to the transition to supercritical.
Frequently asked questions
What exactly happens at a Froude number of 1?
A Froude number of 1 corresponds to the critical regime: the flow's velocity exactly equals the propagation speed of surface waves in that medium. It's an unstable transition point, comparable to breaking the sound barrier in aerodynamics (Mach number 1), where the flow's behavior changes qualitatively.
Which characteristic length should be used for a ship?
For a vessel, the characteristic length is generally the waterline length (the hull's length at the water's surface). The resulting Froude number is a key indicator of wave resistance: naval architects often try to design a hull and cruising speed that stay within a favorable Froude range, to limit the bow wave formation that consumes energy.
Why use 9.81 m/s² and not a different value of gravity?
9.81 m/s² is the standard acceleration of gravity at Earth's surface, the relevant value for the vast majority of hydraulic and naval engineering applications. This calculator uses it as a fixed constant, consistent with the site's hydrostatic pressure calculator.