Weber Number Calculator

Calculate the Weber Number — a dimensionless ratio of inertial to surface tension forces — by entering fluid density (ρ), velocity (v), characteristic length (L), and surface tension (σ). You can also work in reverse: enter a known Weber Number to solve for any one of the four variables. Results include the computed value plus a visual breakdown of the contributing force components. Also try the use the Hydraulic Gradient Calculator.

Required when solving for density, velocity, length, or surface tension

kg/m³

Mass per unit volume of the fluid

m/s

Speed of the fluid flow

m

Relevant length scale (e.g. droplet diameter)

N/m

Surface tension coefficient of the fluid (water ≈ 0.072 N/m at 25°C)

Results

Result

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Inertial Force Component (ρv²L)

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Surface Tension Component (σ)

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Flow Regime

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What is the Weber Number?

The Weber Number (We) is a dimensionless quantity in fluid mechanics that represents the ratio of inertial forces to surface tension forces acting on a fluid. It is used to analyze phenomena involving fluid interfaces, such as droplet formation, liquid jets, and spray atomization. A high Weber Number indicates that inertia dominates, leading to droplet breakup, while a low value means surface tension keeps the fluid together. See also our Reynolds Number Calculator.

What is the formula for the Weber Number?

The Weber Number is calculated as We = ρv²L / σ, where ρ is the fluid density (kg/m³), v is the fluid velocity (m/s), L is the characteristic length (m) such as droplet diameter, and σ is the surface tension coefficient (N/m). Each variable can also be isolated and solved if the Weber Number and other values are known.

How do I calculate the Weber Number step by step?

First, square the fluid velocity (v²). Then multiply by density (ρ) and characteristic length (L) to get the inertial force component (ρv²L). Finally, divide that product by the surface tension (σ). For example, with ρ = 12, v = 18, L = 32, σ = 43: We = (12 × 324 × 32) / 43 = 124416 / 43 ≈ 2893.4.

What does a high Weber Number indicate?

A high Weber Number (We >> 1) means that inertial forces significantly outweigh surface tension forces. In practice, this leads to fluid instability, droplet breakup, or atomization of liquid jets. This is relevant in spray nozzle design, fuel injection systems, and inkjet printing. You might also find our calculate Surface Tension (γ), Surface Tension (mN/m) & Formula Applied — Surface Tension useful.

What does a low Weber Number indicate?

A low Weber Number (We << 1) indicates that surface tension dominates over inertial forces. The fluid tends to maintain a coherent shape, resisting breakup into droplets. This regime is common in microfluidics and slow-moving liquid streams.

What are the units of the Weber Number?

The Weber Number is dimensionless — it has no units. This is because the units of ρv²L (kg/m³ × m²/s² × m = N/m²·m = N/m) cancel exactly with the units of surface tension σ (N/m), leaving a pure numeric ratio.

Can I use this calculator to find density, velocity, or surface tension from a known Weber Number?

Yes. Using the 'I want to calculate' dropdown, you can select any of the five variables as the unknown. The calculator rearranges the formula accordingly: for example, density ρ = We·σ / (v²·L), velocity v = √(We·σ / (ρ·L)), and so on.

What is a typical Weber Number for water droplets?

For water droplets in air, Weber Numbers typically range from near 0 for slow dripping conditions to well over 100 for high-speed spray jets. Critical breakup of droplets generally begins around We ≈ 12, though the exact threshold depends on droplet size, fluid properties, and surrounding gas conditions.