HomeCalculatorsPhysicsWeber Number Calculator
Physics calculator

Weber Number Calculator

Compute the Weber number We = ρ v² L / σ. Runs locally. Not Reynolds, not Froude, not Manning, not Q=Av, and not capillary Ca=μv/σ.

Instant result
Result
—

Enter values to calculate.

Inputs—
Mode—
Formula—
Trust summary Engine tested · Source checked · 17/17 tests · Production surface contract 3/3 · v1.0.0
Input interpretation
Enter values to calculate.
Result
—
Model
Weber number We = ρ v² L / σ. Invert v, L, or σ.
Scope
Weber We = ρ v² L / σ
Verification
Engine tested · 17/17 tests · Production surface contract 3/3 · Source checked · v1.0.0
Named expert review
Optional · Not performed
Sources
Sources
Evidence
2 golden · 10 boundary · 5 property · Production surface contract 3/3 · Artifact integrity PASS
Production
Embedded snapshot: STALE · Last attested schema matched 1.0.0 snapshot / local build · Semantic contract ✓ · Last attestation PASS · current evidence changed · re-attestation required · Public/cache ✓ · Origin ✓ · Live production status PASS (0 stale; 163 CURRENT) @ 2026-09-17T09:03:11.906Z
Semantic contract
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Formulas

Core equations used by this calculator.

Weber numberWe = ρ v² L / σ
Velocityv = √(We σ / (ρ L))
LengthL = We σ / (ρ v²)
Surface tensionσ = ρ v² L / We
iSI. ρ in kg/m³, v in m/s, L in m, σ in N/m. This page is not Reynolds Re=ρvL/μ, not Froude Fr=v/√(gL), not Manning, not Q=Av, and not capillary Ca=μv/σ.

How to use

1

Enter density ρ

Fluid density in kg/m³. Water is 1000.

2

Enter speed v

Characteristic speed in m/s. Invert for v on the v tab. URL field is v_m_s.

3

Enter length L

Characteristic length, often droplet diameter, in metres.

4

Enter σ

Interfacial tension in N/m. Water–air at 20 °C is about 0.0728 N/m. Invert on the σ tab.

Example calculations

Common configurations with formula and result.

ϟ

We = 1000

ρ=1000 kg/m³, v=1 m/s, L=0.072 m, σ=0.072 N/m

We = 1000 × 1² × 0.072 / 0.072
We = 1000
ϟ

Invert v

We=1000, same ρ, L, σ

v = √(We σ / (ρ L))
v = 1 m/s

Weber Number calculator specification

Version 1.0.0 · Engine tested

Calculation status

Review policy · Evidence

Definition
Weber number We = ρ v² L / σ. Inertia versus surface tension. σ is interfacial tension, not viscosity.
What it calculates
Weber number We = ρ v² L / σ. Invert v, L, or σ.
Inputs
  • mode?
  • v|We
  • L|We
  • rho
  • sigma|We
Outputs
  • We
  • v
  • L
  • rho
  • sigma
  • mode
  • model
Formula
We = ρ v² L / σ
Assumptions
  • Weber We = ρ v² L / σ
  • Inertia vs surface tension; σ is interfacial tension, not viscosity μ
  • Not Reynolds, not Froude, not Manning, not Q=Av, not capillary Ca=μv/σ
Units
  • SI; ρ in kg/m³; v in m/s; L in m; σ in N/m; We dimensionless
Boundary conditions
  • missing ρ, v, L, σ, or We when required → MISSING_REQUIRED_INPUT
  • ρ, v, L, σ, or We ≤ 0 → VALUE_MUST_BE_POSITIVE
  • Re/μ/ν, Fr/g, n, C/R/S, A/Q → MIXED_INPUT_ENCODING
  • reynolds, froude, or manning as mode → INVALID_MODE
Example
rho=1000 v=1 L=0.072 sigma=0.072 → We=1000
Validation cases

3 published on this page · 17/17 tests · Production surface contract 3/3 · View evidence

  • rho=1000 v=1 L=0.072 sigma=0.072 → We=1000
  • mode=velocity We=1000 rho=1000 L=0.072 sigma=0.072 → v=1
  • v=1 L=0.072 rho=1000 sigma=0.072 Re=200000 → MIXED_INPUT_ENCODING
Sources
  • ISO 80000-11 — Characteristic numbers — Weber number We
    Supports: We = ρ v² l / σ; inertia/surface-tension, not viscous Reynolds, not gravity Froude
  • ISO 80000-4 — Mechanics — Surface tension
    Supports: σ has dimension force/length; v length/time; L length; ρ mass/volume
Calculation version
1.0.0

Background

Interpretation and common distinctions.

Compute the Weber number from density, speed, characteristic length, and interfacial tension.

Supported and not supported

Supported — We from ρ, v, L, σ · invert v, L, or σ · API physics.fluid.weber

Not supported — Reynolds Re/μ/ν, Froude Fr/g, Manning n, Chezy C, Q=Av, capillary Ca=μv/σ

Agent / API notes

Capability id: physics.fluid.weber · tool id: weber-number · pin 1.0.0.

{ "rho": 1000, "v": 1, "L": 0.072, "sigma": 0.072 }

Modes: We (default), velocity, length, sigma. Errors: MISSING_REQUIRED_INPUT, INVALID_NUMBER, VALUE_MUST_BE_POSITIVE, MIXED_INPUT_ENCODING, INVALID_MODE.

Calculator URL stays /calc/physics/weber-number. There is no /calc/fluid.

Other calculators in this family: Reynolds number, Froude number, Hydraulic diameter, Flow rate .

Re Reynolds number › Fr Froude number › D Hydraulic diameter › Q Flow rate ›
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Frequently asked questions

Key distinctions behind the calculation.

Is this Reynolds number?

No. Re = ρ v L / μ is /calc/physics/reynolds. Sending Re, μ, or ν is MIXED_INPUT_ENCODING. Density ρ is required here; viscosity is not.

Is this Froude number?

No. Fr = v / √(g L) is /calc/physics/froude-number. Sending Fr or g is MIXED_INPUT_ENCODING.

Is this capillary number?

No. Ca = μ v / σ is viscous/surface-tension. Sending μ is MIXED_INPUT_ENCODING.

Is this Q = A·v?

No. Volumetric flow from area and velocity is /calc/physics/flow-rate. Sending A or Q is MIXED_INPUT_ENCODING.

Where does this run?

Locally in the browser by default. REST and MCP call the same fluid-engine weberNumber wrapper.