Calculate Froude Number Instantly
Use this tool to compute the Froude number (Fr) for open-channel flow, ship hydrodynamics, and gravity-wave problems.
V = flow velocity (m/s), g = gravitational acceleration (m/s2), L = characteristic length (m), often hydraulic depth.
What Is the Froude Number?
The Froude number is a dimensionless ratio that compares inertial effects to gravitational effects in a moving fluid. It helps engineers and scientists understand whether flow behavior is wave-dominated, tranquil, rapid, or near a transition point.
You will see it often in river hydraulics, spillway design, ship resistance studies, and physical scale modeling. Because it is dimensionless, it is very useful for comparing different systems that have different sizes, speeds, and flow depths.
Froude Number Formula
Standard expression
The most common form is:
Fr = V / √(gL)
- Fr: Froude number (no units)
- V: characteristic velocity (m/s)
- g: gravitational acceleration (m/s2)
- L: characteristic length (m)
In open channel flow, L is often taken as hydraulic depth. In naval architecture, it may be a waterline length or another relevant length scale.
How to Use This Froude Number Calculator
- Enter fluid velocity in meters per second.
- Enter the characteristic length in meters.
- Confirm gravity (default is 9.81 m/s2).
- Click Calculate to get Fr and flow classification.
The result panel will display the numerical value and an interpretation: subcritical, critical, or supercritical flow.
How to Interpret the Result
Subcritical flow (Fr < 1)
Gravitational effects dominate. Disturbances can travel upstream, and the flow is generally slower and deeper.
Critical flow (Fr ≈ 1)
The flow is near a transition. This condition is important in control sections, weirs, and hydraulic structures.
Supercritical flow (Fr > 1)
Inertial effects dominate. Flow is faster and shallower, and disturbances typically cannot travel upstream.
Worked Example
Suppose a channel has velocity V = 4.0 m/s, hydraulic depth L = 1.5 m, and g = 9.81 m/s2.
√(gL) = √(9.81 × 1.5) = √14.715 ≈ 3.836
Fr = 4.0 / 3.836 ≈ 1.04
Since Fr is slightly above 1, the flow is supercritical (very close to critical).
Where Engineers Use Froude Number
- Open channel hydraulics: channels, culverts, spillways, and rivers
- Hydraulic jumps: identifying and analyzing transition zones
- Ship hydrodynamics: evaluating wave-making resistance
- Physical modeling: preserving dynamic similarity between model and prototype
- Flood routing and control structures: checking flow regimes and stability
Common Input Mistakes to Avoid
- Mixing units (for example, feet with meters).
- Using zero or negative values for velocity or length.
- Using the wrong characteristic length for the problem type.
- Ignoring local gravity if you are doing high-precision work.
Final Thoughts
The Froude number is one of the most practical and widely used indicators in fluid mechanics. A quick calculation can immediately tell you the likely behavior of flow and help guide design decisions. Use the calculator above whenever you need a fast, reliable Fr estimate.