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Physics calculator

Cavitation Number Calculator

Compute the cavitation number σ = (p − p_v) / (½ ρ v²). Runs locally. Not NPSH, not Thoma NPSH/H, not Weber, and not Euler Eu=Δp/(ρ v²).

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
Cavitation number σ = (p − p_v) / (½ ρ v²). Invert p, p_v, or v.
Scope
Cavitation number σ = (p − p_v) / (½ ρ v²); default ρ=1000 kg/m³; p and p_v absolute Pa
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) @ 2026-09-17T13:12:27.589Z
Semantic contract
PASS

Formulas

Core equations used by this calculator.

Cavitation numberσ = (p − p_v) / (½ ρ v²)
Pressurep = p_v + σ · ½ ρ v²
Vapor pressurep_v = p − σ · ½ ρ v²
Velocityv = √(2(p − p_v) / (ρ σ))
iSI. p and p_v absolute Pa; ρ in kg/m³; v in m/s; σ dimensionless. This page is not NPSH, not Thoma σ_Th=NPSH/H, not Weber We=ρv²L/σ, and not Euler Eu=Δp/(ρ v²).

How to use

1

Enter p

Absolute reference pressure in Pa. Invert for p on the p tab.

2

Enter p_v

Absolute vapor pressure in Pa. Water at 20 °C is about 2339 Pa. Invert on the p_v tab.

3

Enter v

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

4

Read σ

σ = (p − p_v) / (½ ρ v²). Default ρ=1000 kg/m³. REST may send v; the query layer uses v_m_s.

Example calculations

Common configurations with formula and result.

ϟ

σ = 2

p=150000 Pa, p_v=50000 Pa, ρ=1000 kg/m³, v=10 m/s

σ = (150000 − 50000) / (½ × 1000 × 10²)
σ = 2
ϟ

Invert p

σ=2, p_v=50000 Pa, v=10 m/s

p = p_v + σ · ½ ρ v²
p = 150000 Pa

Cavitation Number calculator specification

Version 1.0.0 · Engine tested

Calculation status

Review policy · Evidence

Definition
Cavitation number σ = (p − p_v) / (½ ρ v²). Reference pressure minus vapor pressure, over dynamic pressure. Not NPSH head.
What it calculates
Cavitation number σ = (p − p_v) / (½ ρ v²). Invert p, p_v, or v.
Inputs
  • mode?
  • p|sigma
  • p_v|sigma
  • v|sigma
  • rho?
Outputs
  • sigma
  • p
  • p_v
  • rho
  • v
  • mode
  • model
Formula
σ = (p − p_v) / (½ ρ v²)
Assumptions
  • Cavitation number σ = (p − p_v) / (½ ρ v²); default ρ=1000 kg/m³; p and p_v absolute Pa
  • Not NPSH head, not Thoma σ_Th=NPSH/H, not Weber We=ρv²L/σ, not Euler Eu=Δp/(ρ v²)
  • Not Reynolds, not capillary Ca=μv/σ, not Q=Av
Units
  • SI; p and p_v in Pa; ρ in kg/m³; v in m/s; σ dimensionless
Boundary conditions
  • missing p, p_v, v, or σ when required → MISSING_REQUIRED_INPUT
  • p, v, ρ, or σ ≤ 0 → VALUE_MUST_BE_POSITIVE
  • p ≤ p_v → VALUE_OUT_OF_RANGE
  • NPSH/z/hf/H/g, We/L, Re/μ, Eu/Δp, A/Q → MIXED_INPUT_ENCODING
  • npsh, thoma, weber, or euler as mode → INVALID_MODE
Example
p=150000 p_v=50000 v=10 → σ=2
Validation cases

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

  • p=150000 p_v=50000 v=10 → sigma=2
  • mode=pressure sigma=2 p_v=50000 v=10 → p=150000
  • p=150000 p_v=50000 v=10 NPSH=10 → MIXED_INPUT_ENCODING
Sources
  • ISO 80000-11 — Characteristic numbers — Cavitation number
    Supports: σ = (p − p_v) / (½ ρ v²); inertia vs vapor-pressure deficit, not NPSH head
  • ISO 80000-4 — Mechanics — Pressure
    Supports: p and p_v are absolute pressures; ½ ρ v² is a dynamic pressure
Calculation version
1.0.0

Background

Interpretation and common distinctions.

Compute the cavitation number from reference pressure, vapor pressure, density, and speed.

Supported and not supported

Supported — σ from p, p_v, ρ, v · invert p, p_v, or v · API physics.fluid.cavitation

Not supported — NPSH head, Thoma σ_Th=NPSH/H, Weber We, Euler Eu=Δp/(ρv²), Reynolds, capillary Ca, Q=Av

Agent / API notes

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

{ "p": 150000, "p_v": 50000, "v": 10 }

Modes: number (default), pressure, vapor, velocity. Errors: MISSING_REQUIRED_INPUT, INVALID_NUMBER, VALUE_MUST_BE_POSITIVE, VALUE_OUT_OF_RANGE, MIXED_INPUT_ENCODING, INVALID_MODE.

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

Other calculators in this family: NPSH, Weber number, Reynolds number, Pitot tube .

H NPSH › We Weber number › Re Reynolds number › v Pitot tube ›
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Frequently asked questions

Key distinctions behind the calculation.

Is this NPSH?

No. NPSHa is a head in metres at /calc/physics/npsh. Sending NPSH, z, hf, H, p_s, p_atm, or g is MIXED_INPUT_ENCODING.

Is this the Thoma number?

No. Thoma σ_Th = NPSH/H is a pump-similarity ratio. This page is the flow cavitation number (p−p_v)/(½ρv²).

Is this Weber number?

No. We = ρ v² L / σ with σ as N/m is /calc/physics/weber-number. Sending We, L, or σ in N/m is MIXED_INPUT_ENCODING.

Is this Euler number?

No. Eu = Δp / (ρ v²). Send p and p_v separately. A single Δp is MIXED_INPUT_ENCODING.

Where does this run?

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