Froude Number Calculator - Subcritical and Supercritical Flow

A froude number calculator is a fluid mechanics tool that turns a flow velocity, a characteristic length, and gravity into a single dimensionless ratio called the Froude number, then labels the flow as subcritical, critical, or supercritical. It is the standard way to compare gravity-driven flows in open channels, spillways, and ship hulls.

• • Open channel flow classification: Tell whether a channel, river, or spillway is subcritical (slow, deep, calm) or supercritical (fast, shallow, with standing waves) before sizing the cross-section.
• • Ship hull and model towing: Compare a ship or a scale model at the same Froude number so wave-making resistance, sinkage, and trim scale correctly between the prototype and the lab.
• • Hydraulic jump and energy dissipation: Spot the Froude number on each side of a hydraulic jump so you can size a stilling basin or riprap apron that absorbs the energy difference.

The Froude number is dimensionless, so the same value comes out of metric and imperial inputs once the gravity field is converted to ft/s^2 inside the script.

For the inertial-to-viscous counterpart of this ratio, the Reynolds number calculator returns the matching flow regime using density, velocity, length, and viscosity.

It applies the standard open-channel Froude number formula to the velocity, characteristic length, and gravity you enter, then assigns a flow regime label using the 1.0 threshold that every fluid mechanics textbook uses.

• V (velocity): Average flow speed in the direction of travel. In metric mode the unit is m/s; in imperial mode it is ft/s.
• L (characteristic length): The length scale that matches the problem. For open channel flow this is the flow depth or hydraulic depth; for ship work it is the length at the waterline.
• g (gravitational acceleration): Local gravity. Defaults to 9.80665 m/s^2 and is editable so the calculator can be used in lab centrifuges or on other planets.
• Vc (critical velocity): The flow velocity that produces Fr = 1 with the same g and L. Computed as sqrt(g * L) and shown alongside the Froude number.

The dimensionless nature of the ratio is also why the imperial inputs produce the same Froude number as the metric inputs: the gravity field is converted to ft/s^2 internally (1 m/s^2 = 3.28084 ft/s^2), so the same 9.80665 m/s^2 default returns the correct answer in either system.

According to the Engineering ToolBox Froude number reference, the Froude number is the dimensionless ratio of inertia force to the weight of a fluid element, and the threshold of 1 marks the velocity at which downstream pressure disturbances can no longer travel upstream

When you also need the energy, pressure, and elevation split along a streamline, the Bernoulli equation calculator uses the same velocity and length inputs to compute the Bernoulli head.

Four ideas explain every number the result panel shows:

These four ideas are also the reason the Froude number is paired with the Reynolds number in most fluid mechanics courses. The Reynolds number captures the inertial-to-viscous ratio, while the Froude number captures the inertial-to-gravitational ratio.

For the wave-propagation side of supercritical flow, the harmonic wave equation calculator solves the standard wave equation with wavelength, period, and wave speed inputs.

Five short steps are enough to get a trustworthy Froude number for an open channel or a ship hull.

1. 1 Pick a unit system: Choose metric for meters and m/s, or imperial for feet and ft/s. Gravity always stays in m/s^2; the calculator converts it to ft/s^2 internally so the same default returns the correct Froude number in either system.
2. 2 Select the characteristic length type: Pick channel depth, ship length at the waterline, hydraulic radius, or custom. The label on the length field updates to match the preset.
3. 3 Enter the flow velocity: Type the average flow velocity V in the active unit. Use 0 if you only need the critical velocity.
4. 4 Enter the characteristic length: Type the depth, ship length at the waterline, or hydraulic radius L. For ship work, the waterline length is the standard L.
5. 5 Adjust gravity and read the result: Leave gravity at 9.80665 m/s^2 for Earth. Edit the field for lab or planetary g, and the result panel updates with the Froude number and the regime label.

Practical example: a 1.5 m channel at 1.0 m/s on Earth returns Fr = 0.2608 (Subcritical), and the critical velocity of 3.8347 m/s shows how fast the same channel would have to flow before the surface breaks into standing waves.

If your channel ends in a broad-crested weir, the broad crested weir calculator takes the same depth and gravity inputs and returns the discharge over the crest.

A dedicated Froude number tool removes the unit-conversion and threshold-checking steps that usually slow down an open channel or ship calculation.

• • Removes unit-conversion errors: Metric and imperial inputs return the same Froude number because gravity stays in m/s^2 and is converted to ft/s^2 automatically.
• • Surfaces the regime label immediately: The result panel says Subcritical, Critical, or Supercritical next to the number, so you do not have to remember whether Fr is above or below 1.
• • Returns the critical velocity for free: Critical velocity is computed as sqrt(g * L) and shown on the result panel, so you can see how close the actual flow is to the threshold without running a second tool.
• • Pairs with the length-type preset: The length-type preset names the right L for open channel flow, ship hulls, or hydraulic radius work, and the help text reminds you which length to enter.

The result panel matches the other dimensionless-number tools in this category, so a user who switches between the Froude number and the Reynolds number only has to learn one layout.

Once the froude number is in the supercritical range, the drag equation calculator pairs the same velocity and length with density and drag coefficient to size the resistance force.

Three variables drive the Froude number, and two limitations tell you when to treat the result as a screening number rather than a final design value.

• • The Froude number is a single-ratio screening tool that omits viscous losses, sediment transport, and air entrainment, so a subcritical open channel may still erode for other reasons.
• • For ship hulls, the Froude number uses the waterline length, not the rule length. Mixing the two is the most common reason a Froude number disagrees with a towing-tank measurement.

The regime label is the easiest signal to read: Subcritical means gravity waves can travel upstream, while Supercritical means waves cannot travel upstream and the surface is rough.

According to the NIST CODATA standard acceleration of gravity, the conventional reference value g_n is 9.80665 m/s^2, which is the default this calculator pre-fills

According to the Engineering ToolBox Manning's Formula and Gravity Flow reference, the Froude number is the key non-dimensional parameter that separates subcritical open channel flow from supercritical flow, and it pairs directly with Manning's equation for routine gravity-flow design work

For the floatation side of the same ship hull, the buoyant force calculator uses displaced volume, fluid density, and gravity to return the upward buoyant force.