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Physics calculator

Pitot Tube Calculator

Compute incompressible pitot-static speed v = C √(2 Δp / ρ). Default C=1. Runs locally. Not a venturi, not an orifice, not Q=Av, and not two-station Bernoulli.

Instant result
Result
—

Enter values to calculate.

Inputs—
Mode—
Formula—
Trust summary CVP VERIFIED · CVP protocol 1.0.0-proposed · Engineering assurance · v = C √(2 Δp / ρ), default C=1, plus pressure and C solves, + O3 mpmath tabulated velocity.
Input interpretation
Enter values to calculate.
Result
—
Verified scope
v = C √(2 Δp / ρ), default C=1, plus pressure and C solves, + O3 mpmath tabulated velocity.
Assurance
Engineering
Declared partition coverage
PASS · 5/5 declared partitions (velocity, solve, alias, awkward, invalid-domain) · Matrix
Deferred
Not venturi, not orifice, not Q=Av, and not two-station Bernoulli.
Numerical scope
O2: pitot vs a separate-module identity (≤2 ULP). Not venturi, not orifice, not Q=Av, and not two-station Bernoulli. ≤2 ULP vs O3 applies only to the published tabulated pitot vectors. Not venturi, not orifice, not Q=Av, and not Bernoulli.
Known limitations
  • Core CVP does not include live graph, viewport, or pointer interaction.
Model
Incompressible pitot-static speed from dynamic pressure. Invert Δp or C. Default C=1.
Scope
Incompressible pitot-static; v = C √(2 Δp / ρ); default C=1
Verification
Engine tested · Source checked · v1.0.0 · CVP VERIFIED · CVP protocol 1.0.0-proposed · Engineering assurance · v = C √(2 Δp / ρ), default C=1, plus pressure and C solves, + O3 mpmath tabulated velocity.· View Manifest · CVP overview · Specification
Versions
Calculation 1.0.0 · CVP protocol 1.0.0-proposed · Evidence 2026-09-26.o2-o3
Verification revision
2026-09-26.o2-o3 · 1/1 property · digest eb8c62b1fc3e
Legacy regression
17/17 tests · Production surface contract 5/5
Trust layers
Verification VERIFIED · Production CURRENT · Overall CVP state: VERIFIED under CVP 1.0.0-proposed
Reference
O1 model · O3 expected_values · O3 numerical_behavior · O2 expected_values · O2 numerical_behavior
Interfaces
PASS · UI (SSR) / REST / MCP — ui-ssr is query-result HTML, not a live browser session. Error-path engine·REST·MCP 1/1 (status, code, calculation_version). SSR compared on URL-canonical requested calculations; empty query is idle (not an error) and JSON-typed object/array inputs are REST/MCP-only.
Supplemental domain review
Not performed
Named expert review
Not performed
CVP suite
4/4 golden · 9/9 CVP boundary · 10/10 invalid · 1/1 property · 1/1 metamorphic · 8/8 O3 · 2/2 cross-interface · 5/5 CVP contract · Manifest
Sources
  • ISO 3966 — Measurement of fluid flow in closed conduits — Velocity area method using Pitot static tubes — Pitot-static probes
  • ISO 80000-4 — Mechanics — Pressure and velocity
Sources
Evidence
2 legacy golden · 10 legacy boundary · legacy regression suite · 4/4 oracle-backed golden · 10/10 invalid · Artifact integrity PASS
This calculator CURRENT · Public schema 1.0.0 matches · Semantic contract ✓ · Production attested · Public/cache ✓ · Origin ✓
Semantic contract
PASS
Full verification

Manifest identity, reference classes, interfaces, suite, and production records.

Formulas

Core equations used by this calculator.

Velocityv = C √(2 Δp / ρ)
Dynamic pressureΔp = ρ (v / C)² / 2
CoefficientC = v / √(2 Δp / ρ)
iSI. Δp in Pa, ρ in kg/m³, v in m/s. Default C=1 (ideal). This page is not a venturi, not an orifice plate, not Q=Av, and not two-station Bernoulli.

How to use

1

Enter Δp

This is the pitot-static difference P0 − P_static, in pascals. Invert for Δp on the Δp tab.

2

Enter density ρ

Use the fluid density at the static port. Water is 1000 kg/m³. Air at 15 °C is about 1.225 kg/m³.

3

Optional C

Leave blank for ideal C=1. Probe coefficients are typically near 1. Do not send orifice C_d.

4

Read v

v = C √(2 Δp / ρ). Invert velocity uses the v field (v_m_s in the URL).

Example calculations

Common configurations with formula and result.

ϟ

Water, Δp=5000 Pa

ρ=1000 kg/m³, C=1

v = √(2 × 5000 / 1000)
v = √10 ≈ 3.162 m/s
ϟ

C=0.98

Same Δp and ρ

v = 0.98 √10
v ≈ 3.099 m/s

Pitot Tube calculator specification

Version 1.0.0 · Engine tested

Calculation status

Review policy · Evidence

Definition
Incompressible pitot-static: v = C √(2 Δp / ρ). Δp = P0 − P_static. Default C = 1.
What it calculates
Incompressible pitot-static speed from dynamic pressure. Invert Δp or C. Default C=1.
Inputs
  • mode?
  • dP|v
  • rho
  • C?
Outputs
  • v
  • dP
  • rho
  • C
  • mode
  • model
Formula
v = C √(2 Δp / ρ)
Assumptions
  • Incompressible pitot-static; v = C √(2 Δp / ρ); default C=1
  • Δp is P0 − P_static at the probe
  • Not compressible, not a venturi, not an orifice, not Q=Av, not two-station Bernoulli
Units
  • SI; Δp in Pa; ρ in kg/m³; v in m/s; C dimensionless
Boundary conditions
  • missing Δp, ρ, or v when required → MISSING_REQUIRED_INPUT
  • Δp, ρ, v, or C ≤ 0 → VALUE_MUST_BE_POSITIVE
  • D1/D2, C_d, A, Q, P1/v1/h1, n, K, Kv → MIXED_INPUT_ENCODING
  • bernoulli, venturi, or orifice as mode → INVALID_MODE
Example
dP=5000 rho=1000 → v=√10
Validation cases

3 published on this page · 17/17 tests · Production surface contract 5/5 · View evidence

  • dP=5000 rho=1000 → v=√10
  • C=0.98 dP=5000 rho=1000 → v=0.98√10
  • dP=5000 rho=1000 P1=101325 → MIXED_INPUT_ENCODING
Sources
  • ISO 3966 — Measurement of fluid flow in closed conduits — Velocity area method using Pitot static tubes — Pitot-static probes
    Supports: Local velocity from dynamic pressure; C is a probe coefficient near 1
  • ISO 80000-4 — Mechanics — Pressure and velocity
    Supports: Dynamic pressure has the dimension of pressure; v has dimension length/time
Calculation version
1.0.0

Background

Interpretation and common distinctions.

Compute incompressible pitot-static speed from dynamic pressure.

Supported and not supported

Supported — v from Δp and ρ · invert Δp or C · optional C (default 1) · API physics.fluid.pitot

Not supported — venturi D1/D2, orifice C_d, Q=Av, two-station Bernoulli P1/v1/h1, compressible/subsonic corrections

Agent / API notes

Capability id: physics.fluid.pitot · tool id: pitot-tube · pin 1.0.0.

{ "dP": 5000, "rho": 1000 }

With a probe coefficient: { "dP": 5000, "rho": 1000, "C": 0.98 }. Modes: velocity (default), pressure, C. Errors: MISSING_REQUIRED_INPUT, INVALID_NUMBER, VALUE_MUST_BE_POSITIVE, MIXED_INPUT_ENCODING, INVALID_MODE.

Calculator URL stays /calc/physics/pitot-tube. There is no /calc/fluid.

Other calculators in this family: Alternate Depth Calculator, Bernoulli Equation Calculator, Broad-Crested Weir Calculator, Cavitation Number Calculator, Chezy Formula Calculator, Colebrook Friction Factor Calculator, Concentric Reducer Calculator, Critical Depth Calculator . Explore all Fluid Mechanics.

→ Alternate Depth Calculator Compute both rectangular depths at the same specific energy from E, Q, and width b. Runs locally. Not specific energy from y+v; not specific force M; not hydraulic jump y2; not critical depth yc as the product. › → Bernoulli Equation Calculator Incompressible Bernoulli along a streamline: solve P2, v2, or h2. Runs locally in your browser. › → Broad-Crested Weir Calculator Compute rectangular broad-crested weir discharge Q = C_d (2/3)^{3/2} b √g H^{3/2}. Default C_d=0.85. Runs locally. Not a thin-plate weir, not Manning, not Q=Av, and not an orifice. › → 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). › → Chezy Formula Calculator Compute open-channel mean velocity V = C √(R S). Runs locally. Not Manning n, not Q=Av, not Hazen–Williams, and not Darcy. › → Colebrook Friction Factor Calculator Solve the Colebrook–White equation for Darcy friction factor f from Re and ε/D. Turbulent pipes Re≥4000. Runs locally. Not laminar 64/Re and not a Moody-chart lookup. › → Concentric Reducer Calculator Compute concentric-reducer loss h = K v₂² / (2g) with K = 0.5 (1 − A₂/A₁) referenced to the downstream speed. Runs locally. Not sudden expansion, not gradual contraction α, not vena-contracta C_c, not catalog K, and not Q=Av. › → Critical Depth Calculator Compute rectangular critical depth yc = (q²/g)^{1/3}. Runs locally. Not a Froude wrap, not specific energy, not a hydraulic jump, and not Q=Av. ›

Frequently asked questions

Key distinctions behind the calculation.

Is this a venturi meter?

No. A converging–throat Bernoulli meter is /calc/physics/venturi. Sending D1 or D2 is MIXED_INPUT_ENCODING.

Is this an orifice?

No. Tank or plate Q=C_d… is /calc/physics/orifice-discharge. Sending C_d or A is MIXED_INPUT_ENCODING.

Is this the Bernoulli equation?

No. Two-station P/ρ + v²/2 + g h is /calc/physics/bernoulli. Sending P1, v1, or h1 is MIXED_INPUT_ENCODING. This page takes only the pitot-static Δp.

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 pitotTube wrapper.