Valve flow coefficient (Cv) describes how much flow a valve can pass for a defined pressure drop. A Cv of 10 means that 10 US gallons of water at 60°F can pass through the valve each minute with a 1 psi pressure drop under the reference test condition.
At the same pressure drop and with the same fluid, a higher Cv means more flow capacity. It does not mean better control in every system. A valve can have enough maximum capacity and still be too large for stable operation at normal load.
This guide shows how to calculate Cv for a simple liquid duty, convert Cv to flow rate, compare Cv with Kv, and recognise when a full sizing method is required. For the wider calculation path, see MacoTango’s valve sizing and calculation resources.
What Does Cv Mean on a Valve?
Cv is a capacity coefficient, not a valve size. Two valves with the same DN or NPS connection can have different Cv values because their body shape, bore, trim and flow path are different.
Three Cv values are often involved in a control-valve decision:
- Required Cv: the coefficient calculated from one operating case.
- Rated Cv: the valve manufacturer’s stated coefficient at a defined travel, commonly full travel.
- Cv at a given travel: the coefficient available at a particular valve position, taken from the valve’s inherent characteristic data.
A higher rated Cv can pass more flow at the same test pressure drop. However, if the required Cv is only a small part of the rated value, the valve may work close to its seat at normal load and give limited usable travel.
Valve Cv Formula for Liquid Flow
For a turbulent, single-phase liquid that is not choked, the basic formula is:
Cv = Q × √(SG / ΔP)
- Cv = valve flow coefficient
- Q = liquid flow rate in US gallons per minute (gpm)
- SG = liquid specific gravity, where water is about 1.0
- ΔP = pressure drop across the valve in psi
This equation is useful for a first liquid check. It does not include every correction needed for viscous flow, attached reducers, cavitation, flashing or choked flow.
Worked Cv Example
A clean liquid must flow at 150 US gpm. Its specific gravity is 0.85, and the available pressure drop across the valve is 5 psi.
Cv = 150 × √(0.85 / 5)
Cv = 150 × 0.412
Required Cv ≈ 61.8
The result is the required Cv for this one operating case. It is not yet a final valve size. Minimum, normal and maximum flow cases still need to be compared with the candidate valve’s Cv-versus-travel data.
How Do You Convert Cv to GPM?
Rearrange the liquid equation to calculate flow:
Q = Cv × √(ΔP / SG)
For water with SG = 1.0, a valve with Cv 10 passes about 10 gpm at a 1 psi pressure drop, or 14.1 gpm at a 2 psi pressure drop, within the simple formula’s limits. You can also rearrange the equation as ΔP = SG × (Q / Cv)2 when flow and Cv are known.
For a quick calculation, use the Cv to GPM calculator. For liquid, gas or steam inputs and minimum, normal and maximum cases, use the full control valve Cv calculator.
Use matching flow, pressure, temperature and fluid data for each operating case.
Cv vs Kv: Conversion and Unit Basis
Cv and Kv describe the same type of valve capacity, but they use different reference units. Cv uses US gpm and psi. Kv uses cubic metres per hour and bar.
- Cv = 1.156 × Kv
- Kv = 0.865 × Cv
For example, Cv 50 is about Kv 43.3. Always confirm which coefficient a catalogue or sizing sheet uses before comparing numbers. The symbols are not interchangeable without conversion.
Required Cv, Rated Cv and Valve Opening
Required Cv comes from the process duty. Rated Cv comes from a particular valve and trim. The selection step is to find a valve whose Cv curve covers the required capacity across the operating range, not merely to choose the first rated Cv above one maximum-flow result.
The valve’s inherent characteristic shows how Cv changes with travel under a constant test pressure drop. Once installed, the pressure drop across the valve usually changes with flow because the rest of the piping system also consumes pressure. The resulting flow-versus-travel curve can therefore differ from the catalogue curve.
This is why a control valve should be checked at minimum, normal and maximum conditions. MacoTango’s guide to control valve installed characteristic explains this system effect in more detail.
When the Simple Cv Formula Is Not Enough
The basic liquid equation is an estimate, not a universal sizing method. Move to a full calculation when any of these conditions applies:
- High viscosity or low Reynolds number: the turbulent-flow assumption may no longer hold.
- Cavitation, flashing or liquid choking: pressure recovery and vapour pressure can limit capacity and create noise or damage risk.
- Gas or steam service: compressibility, temperature, expansion and choking must be included, using absolute pressure inputs.
- Reducers, expanders or restrictive fittings near the valve: attached piping can change the effective sizing coefficients.
- Large pressure drop or severe service: velocity, noise, vibration, trim design, material and actuator demand need separate checks.
The official IEC 60534-2-1 publication page covers the standardised sizing framework for incompressible and compressible fluids. The Fluid Controls Institute sizing guide also explains why the simple equation needs correction for some valve and piping conditions.
For practical examples of the capacity limit, see choked flow in control valves.
How to Use Cv Without Oversizing the Valve
Use Cv without oversizing by calculating the requirement at matched minimum, normal and maximum conditions, then comparing all three results with valve-specific Cv-versus-travel data.
- Define the real operating cases. Record minimum, normal and maximum flow with matching inlet pressure, outlet pressure, temperature and fluid properties.
- Choose the correct calculation branch. Use the simple equation only for a suitable liquid duty; use compressible or corrected methods where required.
- Calculate required Cv for every case. Do not size from maximum flow while keeping normal-case pressures or properties.
- Match the result to valve-specific data. Compare each required Cv with the manufacturer’s Cv curve, trim options and stated test basis.
- Check the installed duty. Review travel, rangeability, pressure recovery, choking or cavitation, velocity, noise, piping effects and actuator demand before freezing the selection.
The control valve sizing guide develops this workflow beyond the first Cv result.
Bottom line: Cv is a capacity index, not a complete valve selection. Calculate the duty, compare it with the valve’s Cv-versus-travel data, and then verify the limits that the simple formula leaves out before comparing suitable control valves.