Froude Number Calculator

The Froude number is a dimensionless ratio that compares fluid inertia with the restoring effect of gravity. It is especially important in open-channel hydraulics, spillways, rivers, ship design, wave studies, and other flows with a free surface. This calculator uses Fr = v/√(gL), where v is representative velocity, g is gravitational acceleration, and L is a characteristic length. Standard gravity is taken as 9.80665 meters per second squared. Choosing characteristic length depends on the problem. For rectangular open-channel flow, hydraulic depth is typically flow area divided by top width and equals physical depth for a wide rectangular channel. Naval architects often use waterline length when comparing vessel wave-making behavior. The velocity and length must use compatible units so that the final ratio remains dimensionless. A Froude number below one describes subcritical flow. Surface disturbances can travel both upstream and downstream, and downstream controls may influence upstream water level. At Fr equal to one, wave speed and mean flow speed match, producing critical flow and minimum specific energy for a given discharge. Above one, flow is supercritical: disturbances cannot propagate upstream, the flow tends to be shallow and fast, and a hydraulic jump may occur when it transitions to subcritical conditions. Hydraulic jumps dissipate substantial energy and are often deliberately contained in engineered stilling basins downstream of gates or spillways. The simple classification is most directly applicable to open-channel flow when hydraulic depth is used. Real channels may have nonuniform velocity, irregular geometry, bed slope, turbulence, and rapidly varied regions that require more detailed analysis. For vessels, the Froude number provides a useful similarity condition for scale models because wave patterns depend strongly on gravity. It does not replace Reynolds-number matching for viscous effects. Use this calculator for quick checks, model scaling, flume experiments, and preliminary hydraulic interpretation, then apply geometry-specific equations and local standards for final engineering decisions.