Valve Cv Calculator (flow coefficient Cv/Kv, flow rate or pressure drop for liquids)

Understanding the valve Cv calculator — concept and principle

The flow coefficient tells you how much liquid a valve lets through for a given pressure drop. This calculator works with Cv (US gallons per minute at 1 psi) and Kv (m³/h at 1 bar). It can find the coefficient from a flow and pressure drop, the flow from a coefficient, or the pressure drop from a coefficient and flow, for any liquid of known specific gravity.

Passing 10 m³/h of water with a 0.5 bar drop needs Kv 14.1, or Cv 16.4.

How it is calculated

Q = Kv × √(Δp ÷ SG) (m³/h, bar)

Q = Cv × √(Δp ÷ SG) (US gpm, psi)

Kv = Q × √(SG ÷ Δp); Δp = SG × (Q ÷ Kv)²

Cv = 1.156 × Kv (from 1 US gal = 3.785411784 L and 1 psi = 6,894.757 Pa)

Q flow rate, Δp pressure drop across the valve, SG specific gravity relative to water.
The first row shows the solved quantity in your chosen units.

The principle

A valve is a restriction. Pushing liquid through it turns pressure into velocity, and Bernoulli's principle says the pressure drop grows with the square of velocity. So flow rises only with the square root of the pressure drop: doubling Δp gives about 41 % more flow. Heavier liquids need more pressure to reach the same speed, which is why SG sits under the square root. The coefficient lumps the valve's size and internal shape into one number measured with water, so different valves can be compared directly.

Worked example

Default inputs: solve for Cv and Kv, metric, Q = 10 m³/h, Δp = 0.5 bar, SG = 1.0.

Kv = 10 × √(1.0 ÷ 0.5) = 10 × 1.4142 = 14.142.
Cv = 1.156 × 14.142 = 16.35 (also the result in your units).
Flow in US gpm = 10 × 4.403 = 44.029 gpm.
Pressure drop = 0.5 bar = 7.252 psi = 50 kPa.

Each point is the calculator re-run with only “Flow rate (m³/h or US gpm)” changed; the gold point is the default example. Change the inputs above and this chart follows your numbers.

Flow rate (m³/h or US gpm)	Result in your units
2.5	4.087
5	8.175
7.5	12.26
10	16.35
12.5	20.44
15	24.52
20	32.7

How to read the result

Pick a valve whose rated Cv is comfortably above the calculated value, so it can control flow without running nearly wide open. Many control-valve guidelines aim for the normal operating point well within the valve's travel, leaving room for regulation in both directions. A valve with far too large a Cv will operate near closed, where control is poor and wear is higher.

Common mistakes

Mixing metric Kv with US Cv; they differ by about 16 %.
Using total system pressure instead of the drop across the valve.
Applying the liquid equation to gases or steam.
Ignoring cavitation or flashing at large pressure drops, which limits flow (choked flow).

Keep in mind: These equations are valid for turbulent, non-choked liquid flow. Gases, flashing or cavitating liquids, viscous fluids and valves with reducers need the full IEC 60534 / ISA-75.01 sizing method and the valve maker's data.

Frequently asked questions

What does Cv = 1 mean?

The valve passes 1 US gallon per minute of 60 °F water at a 1 psi pressure drop.

How do I convert Kv to Cv?

Multiply Kv by about 1.156; to go back, multiply Cv by about 0.865.

Why does flow rise with the square root of pressure drop?

Pressure drop is proportional to velocity squared, so velocity and flow follow the square root.

Does temperature matter?

Indirectly, through the liquid's density (SG) and its vapour pressure, which affects cavitation.

Sources: IEC 60534-2-1 / ANSI/ISA-75.01.01, Industrial-process control valves: flow capacity sizing equations · NIST Special Publication 811 (unit conversion factors)

Checked 9 Nov 2026. Liquid flow-coefficient equations C_v = Q√(SG/ΔP) (US gpm, psi) and K_v = Q√(SG/ΔP) (m³/h, bar), K_v = 0.8646·C_v: Neutrium, “Pressure loss: Cv and Kv method” (secondary summary of IEC 60534-2-1 / ISA-75.01 practice). Cv/Kv factor recomputed here from exact unit definitions (NIST SP 811 conversion factors).

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