Strouhal Number Calculator

The Strouhal number is a dimensionless ratio that tells you how often vortices peel off an object sitting in a fluid stream. Czech physicist Vincenc Strouhal worked it out in 1878 while studying why wires vibrate in wind. The same number explains why power lines hum, why slender chimneys sometimes shake themselves apart, and why fish and birds tend to flap at a particular rhythm when they want to move efficiently. When fluid runs past a blunt object, it sheds alternating swirls behind it in a pattern called a Von Kármán vortex street, and the Strouhal number ties the frequency of that shedding to the flow speed and the size of the object.

What the Strouhal number measures

The Strouhal number (St) compares how fast vortices are shedding from an object to how fast fluid is moving past it. For a plain circular cylinder in cross-flow, the value sits near 0.21 across a Reynolds number range from roughly 300 to 200,000. That stability is useful: if you know the geometry and the flow speed, you can predict the shedding frequency without measuring it.

A low Strouhal number means vortices are spaced far apart, so shedding is slow. A high value means they come thick and fast. The frequency matters because if it happens to match a structure's natural frequency, energy keeps pumping into the oscillation on every cycle and the whole thing can shake itself apart.

How to use this calculator

Enter any three of the four values and the fourth fills in automatically. Plug in the shedding frequency, the diameter, and the flow speed to get the Strouhal number. Or, if you already know the Strouhal number for your geometry and want the shedding frequency at a given flow speed and object size, enter those instead.

Unit conversions are handled for you. Frequency works in hertz or cycles per minute; length in meters, centimeters, feet, or inches; velocity in m/s, ft/s, mph, or knots. The output is always dimensionless because the units cancel.

Understanding the formula

The Strouhal number is the product of vortex shedding frequency and characteristic length divided by fluid velocity:

St = \frac{f \cdot L}{v}

Here $f$ is the vortex shedding frequency, $L$ is the characteristic length (diameter for a cylinder, width for a plate), and $v$ is the fluid velocity. A worked example helps.

Take a power line about 2 cm thick (L = 0.02 m) with a steady 10 m/s wind hitting it broadside. Experimental data puts St at around 0.21 for a circular cylinder, so the shedding frequency works out to:

f = \frac{St \cdot v}{L} = \frac{0.21 \times 10}{0.02} = 105 \text{ Hz}

The wire vibrates at 105 Hz, roughly a low G note, and on a quiet windy night you can sometimes hear it. The vortices pop off alternately from either side, pushing the wire one way then the other on each cycle. If that frequency lines up with the wire's natural frequency, the oscillation grows until something gives.

Where it shows up

Structural engineers care about this because vortex-induced vibration sways bridge decks, rattles offshore platforms, and has brought down more than one steel chimney. The classic fix on a tall stack is to wrap helical strakes around the top third. They break up the regular shedding pattern so no single frequency dominates.

Biologists noticed something more surprising. Efficient swimmers and flyers cruise at Strouhal numbers between 0.2 and 0.4 almost regardless of species. Dolphins, tuna, sharks, hummingbirds, geese on migration: when they're moving at their preferred speed, the combination of flapping rate, body width, and travel speed lands in that narrow band. It seems to be the most efficient point for thrust per unit of muscle work, and the observation has shaped how engineers design flapping-wing drones and bio-inspired underwater vehicles.

Acoustics runs on the same principle. Whistling kettles, the tone you get blowing across a bottle, the hum of a fence wire in a gale: all of them come down to vortex shedding at a Strouhal-defined frequency. HVAC engineers, auto designers, and architects use the relationship to predict and quiet down unwanted noise.

Tips for accurate results

Pick the right characteristic length. For a cylinder it's the diameter; for a flat plate normal to flow it's the width; for anything more complex you'll need to dig into experimental data. The standard St ≈ 0.21 only applies to a circular cylinder in the subcritical Reynolds range (about 300 to 200,000). Outside that band, or for other shapes, the number shifts: square cylinders land around 0.13 to 0.18, and a flat plate broadside to flow sits closer to 0.16.

For structural design, run the calculation, then compare the predicted shedding frequency against the structure's natural frequency. If they fall within about 20% of each other, you have a resonance risk and need to either change the geometry, add damping, or stiffen the structure to move the natural frequency out of the way.

Frequently asked questions

What's a typical Strouhal number value?

For a circular cylinder in cross-flow, St ≈ 0.21 is the standard figure, valid from Reynolds numbers around 300 up to 200,000. Square cylinders run lower at 0.13 to 0.18. A flat plate normal to flow comes in around 0.16. Cruising animal locomotion clusters between 0.2 and 0.4.

Why is the Strouhal number dimensionless?

Frequency times length divided by velocity is (1/s)(m)/(m/s), and the units cancel to give a pure number. That's what lets the same Strouhal number describe a 1-meter bridge pier and a 1-centimeter wind tunnel model, as long as the flow regimes match. It's the basis of scale-model testing.

When should I worry about resonance?

Once the calculated shedding frequency falls within roughly 20% of a structure's natural frequency. Tall, slim structures in steady wind are the usual suspects: chimneys, antenna masts, slender bridges. Standard mitigations are damping devices, geometry changes like spoilers or strakes, or shifting the natural frequency by adding mass or stiffness.

Can I use this for turbulent flow?

Yes. The Strouhal concept applies through both laminar and turbulent regimes, though the value drifts a bit with Reynolds number. For a circular cylinder the 0.21 figure holds well across the subcritical turbulent range. Push past Re ≈ 200,000 into supercritical flow and the boundary layer transitions, which jolts the Strouhal number. If you need precision at very high Reynolds numbers, check experimental data or CFD for your specific geometry instead of relying on the standard value.