Valve flow coefficient calculator
Water flowing at 20 gallons per minute through a 4 psi drop needs a valve rated Cv 10. Enter the flow, the pressure drop and the specific gravity to get the coefficient to look for in a manufacturer's catalog. Free in your browser.
- Free
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- Your data stays on your device
Run — free
Worked example
- Flow rate
- 20
- Pressure drop
- 4
- Specific gravity
- 1
- Cv
- 10 Cv
The valve flow coefficient calculator recovers catalog Cv from a measured or specified liquid flow rate in US gallons per minute, a strictly positive pressure drop in pounds per square inch, and the fluid specific gravity relative to water at sixty degrees Fahrenheit. The engine inverts the incompressible liquid identity: Cv equals Q times the square root of G over ΔP — the same relation that defines Cv as the water flow, in gallons per minute at sixty degrees Fahrenheit, that produces a one-psi drop through the valve. Water has G equal to one, so twenty gallons per minute across a four-psi drop yields Cv of ten exactly; denser brines raise the required coefficient and lighter hydrocarbons lower it for the same drop and flow.
What catalog Cv is and how this calculator recovers it
The valve flow coefficient Cv is defined in US customary units as the number of US gallons per minute of water at sixty degrees Fahrenheit that will pass through a valve with a pressure drop of one pound per square inch. Manufacturers publish that rating for each body size, trim, and opening, but engineers in the field more often start from a required throughput and a known station drop and need the Cv they must specify, not the gallons per minute that a given rating would pass.
Inverting the incompressible liquid identity is therefore the everyday sizing step: volumetric flow Q in gallons per minute equals Cv times the square root of ΔP over G, so Cv equals Q times the square root of G over ΔP, where ΔP is the pressure drop across the valve in psi and G is the fluid specific gravity relative to water at sixty degrees Fahrenheit.
For water, G equals one, so Cv collapses to Q divided by the square root of ΔP; twenty gallons per minute through a four-psi drop therefore needs a valve rated Cv equals ten. A heavier liquid such as concentrated brine with G greater than one raises the required Cv for the same drop and flow, because more mass must be driven through the vena contracta; a lighter hydrocarbon with G less than one lowers the required Cv.
This calculator evaluates that textbook inverse with no piping-geometry factor Fp, no Reynolds-number factor FR, and no liquid-pressure-recovery or choked-flow limit from ISA-75 or IEC 60534. Those installed-condition corrections belong in a full control-valve sizing package once the adjacent fittings, vapor pressure, and recovery factor FL are known. Use this page when you already have Q, ΔP, and G and need the corresponding unchoked liquid Cv, and treat flashing, cavitating, or two-phase service as out of scope for this identity.
Where recovering Cv from flow is used in design, labs, and software
Process and mechanical engineers use the inverse liquid Cv identity to turn a required gallons-per-minute throughput at a known station drop into a catalog coefficient before they open a full ISA-75 worksheet. A first-pass estimate of Cv from Q, ΔP, and G sizes a globe, ball, or butterfly valve for water, glycol, or light oil service, and it is honest about omitting choked-flow and piping-geometry corrections until those data exist.
Teaching labs ask students to recover Cv from a measured GPM and a manometer drop and to discuss why a real installed valve may need a larger catalog rating than the identity when adjacent reducers add resistance; a deterministic oracle lets instructors generate keys for arbitrary Q, ΔP, and G without a commercial sizing suite. Software tests for control-valve modules need a frozen expected Cv for water and for a non-unity specific gravity so that a refactor of a hydraulics library cannot silently change the inverted square-root formula.
Field technicians checking a control valve during a water-balance or hydrostatic test can turn a measured volume per time and the upstream and downstream pressures into a catalog Cv when the liquid is subcooled. Keep requests small, pin the rounded cv in tests, and you get reproducible valve coefficients for homework, LMS plugins, and edge workers without standing up a valve-sizing solver of your own.
What you can do with it
Catalog valve sizing from required GPM
Turn a required liquid throughput and a station pressure drop into the catalog Cv to specify for water, glycol, or light oil before opening a full ISA-75 worksheet.
Hydraulics homework and lab keys
Generate deterministic Cv answers for arbitrary GPM, ΔP, and specific gravity so students can check the inverted square-root identity against manometer data.
FAQ
What formula does the valve flow coefficient calculator use?
The inverted incompressible liquid catalog identity Cv = Q · √(G / ΔP), with Q in US gallons per minute, ΔP in psi, and G the fluid specific gravity relative to water at 60 °F. Piping-geometry, Reynolds, and choked-flow factors are not applied.
Why must pressure drop and specific gravity be positive?
Both sit under the square root in Cv = Q · √(G / ΔP).
Which units should I use for Q, ΔP, G, and Cv?
Flow rate is in US gallons per minute. Pressure drop is in psi. The returned cv is the US customary coefficient (GPM of water at 1 psi).
Does a denser liquid need a higher Cv?
Yes. For the same flow and pressure drop, a liquid heavier than water, such as concentrated brine, needs a higher Cv, while a lighter hydrocarbon needs a lower one. Water itself has a specific gravity of exactly one.
Does the result account for choked flow or nearby fittings?
No. It is the textbook liquid formula with no piping geometry factor, no Reynolds-number factor and no pressure-recovery or choked-flow limit from ISA-75 or IEC 60534. Those corrections belong in a full control-valve sizing once the fittings and vapor pressure are known.
Related tools
For developers — API access
Everything on this page is available programmatically. This section is for teams who want to wire it into their own systems; everyone else can just use the tool above.
API endpoint
Prefer to automate it? One authenticated POST creates the task; the result comes back by webhook or a signed link. The same capability also runs here on the web, by email and from Telegram — and soon from our app too.
Call it from your stack
curl -X POST https://api.kit.forhosting.com/phys/valve-flow-coefficient \
-H "Authorization: Bearer $KIT_KEY" \
-H "Content-Type: application/json" \
-d '{"flow_rate":20,"pressure_drop":4,"specific_gravity":1}'const res = await fetch("https://api.kit.forhosting.com/phys/valve-flow-coefficient", {
method: "POST",
headers: {
"Authorization": `Bearer ${process.env.KIT_KEY}`,
"Content-Type": "application/json"
},
body: JSON.stringify({
"flow_rate": 20,
"pressure_drop": 4,
"specific_gravity": 1
})
});
const { task_id } = await res.json();import os, requests
res = requests.post(
"https://api.kit.forhosting.com/phys/valve-flow-coefficient",
headers={"Authorization": f"Bearer {os.environ['KIT_KEY']}"},
json={
"flow_rate": 20,
"pressure_drop": 4,
"specific_gravity": 1
},
)
task_id = res.json()["task_id"]<?php
$res = file_get_contents("https://api.kit.forhosting.com/phys/valve-flow-coefficient", false, stream_context_create([
"http" => [
"method" => "POST",
"header" => "Authorization: Bearer " . getenv("KIT_KEY") . "\r\nContent-Type: application/json",
"content" => '{"flow_rate":20,"pressure_drop":4,"specific_gravity":1}',
],
]));
$task = json_decode($res, true);body := bytes.NewBufferString(`{"flow_rate":20,"pressure_drop":4,"specific_gravity":1}`)
req, _ := http.NewRequest("POST", "https://api.kit.forhosting.com/phys/valve-flow-coefficient", body)
req.Header.Set("Authorization", "Bearer "+os.Getenv("KIT_KEY"))
req.Header.Set("Content-Type", "application/json")
res, _ := http.DefaultClient.Do(req)Example request
{
"flow_rate": 20,
"pressure_drop": 4,
"specific_gravity": 1
}Example response
{
"task_id": "tsk_a1b2c3d4e5f6a1b2c3d4e5f6",
"type": "phys.valve_flow_coefficient",
"status": "queued",
"_links": {
"result": "/tasks/tsk_…/result"
}
}The API is asynchronous: the call returns a task_id immediately and the result arrives by webhook. Polling is capped at 1 req/s per task.
Pricing
Published price — no tokens, no invented credits. A failed task is never charged.
Limits
max_abs_flow_rate | 1000000000000 |
max_abs_pressure_drop | 1000000000000 |
max_abs_specific_gravity | 1000000000000 |
Errors
| HTTP | Code | Meaning |
|---|---|---|
401 | unauthorized | Missing or invalid API key. |
402 | insufficient_balance | Your balance doesn't cover the task price. |
404 | unknown_type | That task type doesn't exist. |
429 | rate_limited | Too many requests. Use the webhook instead of polling. |
Technical notes
Pressure drop or specific gravity that is not strictly positive is rejected as invalid_input and is not billed. Successful API calls cost $0.002.
Inputs, units, response fields, and invalid values
Specific gravity must be strictly positive because G sits under the square root; a non-positive G would make Cv undefined or imaginary. Flow rate must be a finite non-negative number; a negative GPM is non-physical, while zero flow yields Cv equal to zero. Magnitudes above one trillion are rejected as outside the supported range. Failed validation is not billed. POST a JSON body with three required finite numbers: flow_rate, the volumetric liquid flow in US gallons per minute; pressure_drop, the upstream-minus-downstream pressure drop in psi; and specific_gravity, the fluid specific gravity G relative to water at sixty degrees Fahrenheit. Preferred names are those canonical fields; aliases Q, q, flow, gpm, volumetric_flow, and flow_gpm are accepted for the flow, aliases delta_p, dp, dP, pressure_diff, delta_p_psi, and dp_psi for the drop, and aliases sg, G, gf, fluid_sg, and specific_g for specific gravity, so spreadsheets and typed forms can reuse the same contract. Each value may arrive as a JSON number or as a decimal numeric string, including scientific notation; booleans, objects, arrays, empty strings, NaN, and infinities are rejected. Pressure drop must be strictly positive: zero and negative ΔP fail with invalid_input because the catalog liquid formula is defined for a driving drop in the forward direction and dividing by the square root of ΔP would be undefined or imaginary. On success the body echoes the three inputs rounded to twelve decimal places, plus cv, unit Cv, a formula string, and method isa_liquid_cv.
Integration use cases
Control-valve software fixtures
Pin expected unchoked liquid Cv in unit tests for water (G = 1) and for non-unity specific gravity without embedding a commercial valve-sizing library.
Technical questions
How is this different from converting Cv to Kv or from computing GPM from Cv?
This page recovers Cv from flow, drop, and gravity. Unit conversion among Cv, Kv, and Av is a separate converter. Computing liquid GPM from a published Cv is the inverse identity and a separate calculator.
What does the valve flow coefficient calculator cost?
The browser tool is free. API requests use prepaid KIT balance at $0.002 per successful call; invalid input is not billed.