Cv Flow Calculator: Valve Flow Coefficient for Liquids and Gases
The Cv flow calculator finds the valve flow coefficient (Cv) needed to pass a target flow rate at a given pressure drop, or back-solves for flow rate when Cv is known. Choose liquid or gas mode, pick a preset fluid or enter your own specific gravity, set inlet and outlet pressures, and get instant results with step-by-step working. Gas mode automatically detects subcritical versus choked (critical) flow and applies the correct formula.
What is the valve flow coefficient Cv?
The valve flow coefficient Cv is the volume of water at 60 F (in US gallons) that flows through a valve in one minute when the pressure drop across it is exactly 1 psi. It was defined by ANSI/ISA to give engineers a single, reproducible number to compare valves of different designs, sizes, and manufacturers. A higher Cv means a less restrictive valve. For liquids, the Cv scales directly with flow rate and with the square root of the specific gravity divided by the pressure drop. For gases, two formulas apply depending on whether the flow is subcritical (outlet pressure above half the inlet) or choked/critical (outlet below half the inlet, where further reducing pressure cannot increase flow).
Liquid vs. gas: which formula applies?
For incompressible liquids the ISA formula is Cv = Q * sqrt(SG / dP), where Q is flow in GPM, SG is specific gravity relative to water, and dP is the pressure drop in psi. For compressible gases the fluid expands as it drops in pressure, so the formula accounts for both pressures rather than just their difference. In the subcritical regime (P2 greater than P1/2) the formula is Cv = (Q / 962) * sqrt(SG * T / (P1 squared minus P2 squared)), with Q in SCFH and T in Rankine. When the valve is choked (P2 less than P1/2), the formula simplifies to Cv = Q * sqrt(SG * T) / (816 * P1) because mass flow is limited by sonic velocity at the vena contracta and does not increase no matter how low P2 drops. This calculator detects the regime automatically from your inputs.
Cv and its metric counterpart Kv
The metric equivalent of Cv is Kv, defined as cubic metres of water per hour at a 1 bar pressure drop. The conversion is simply Kv = Cv / 1.156. European valve data sheets almost always list Kv; North American sheets use Cv. If you are specifying a valve from a European supplier for an imperial-unit system, multiply the Kv rating by 1.156 to get the equivalent Cv. This calculator outputs both so you can compare directly against either type of data sheet.
Selecting a valve from the Cv result
The calculated Cv is the minimum required for your operating conditions. When choosing a valve from a catalogue, add a margin of 10 to 25 percent above the calculated value to allow for wear over time, manufacturing tolerances, and any future increase in flow demand. Oversizing beyond 50 to 100 percent can cause control valves to operate near their closed position where control is poor, leading to instability. For on-off valves such as ball valves or gate valves, a larger Cv simply means a lower pressure drop and is usually acceptable. Use the reference table below for typical Cv ranges by valve type and size as a starting point.
Common valve Cv values by valve type and size
| Valve type | Size | Typical Cv range |
|---|---|---|
| Ball valve (full bore) | 1/4 in / DN8 | 0.5 - 2 |
| Ball valve (full bore) | 1/2 in / DN15 | 5 - 15 |
| Ball valve (full bore) | 1 in / DN25 | 25 - 60 |
| Ball valve (full bore) | 2 in / DN50 | 120 - 250 |
| Globe valve | 1/2 in / DN15 | 3 - 8 |
| Globe valve | 1 in / DN25 | 12 - 30 |
| Globe valve | 2 in / DN50 | 55 - 120 |
| Gate valve (full open) | 1 in / DN25 | 50 - 80 |
| Gate valve (full open) | 2 in / DN50 | 200 - 350 |
| Butterfly valve | 2 in / DN50 | 50 - 120 |
| Butterfly valve | 4 in / DN100 | 250 - 600 |
| Check valve | 1/2 in / DN15 | 2 - 6 |
| Check valve | 1 in / DN25 | 10 - 25 |
| Needle valve | 1/4 in / DN8 | 0.02 - 0.5 |
| Solenoid valve (direct acting) | 1/4 in / DN8 | 0.1 - 2 |
Typical published Cv ranges for standard valve types. Always verify against the manufacturer data sheet for the exact valve model.
Frequently asked questions
What does a Cv of 1.0 mean?
A Cv of 1.0 means the valve will pass 1 US gallon per minute of water with a 1 psi pressure drop across it. It is the fundamental definition of the flow coefficient. A Cv of 10 passes 10 GPM at 1 psi, or about 3.16 GPM at 10 psi (because flow scales with the square root of pressure drop).
How is Cv different from Kv?
Cv (US) and Kv (metric) measure the same thing in different unit systems. Kv is cubic metres per hour of water at a 1 bar pressure drop; Cv is US gallons per minute at 1 psi. The conversion is Cv = Kv x 1.156, or Kv = Cv / 1.156. European valve data sheets use Kv; North American data sheets use Cv.
What is choked or critical flow?
For a compressible gas, once the outlet pressure drops below half the inlet pressure (P2 less than P1/2), the gas reaches sonic velocity at the narrowest point of the valve (the vena contracta). At this point the flow rate cannot increase further no matter how much the downstream pressure is reduced - the flow is "choked." A different formula applies in this regime. The calculator detects the condition automatically and reports the flow regime in the results.
Can I use this calculator for steam?
Steam is a gas and follows the gas flow formulas. For saturated steam you need its specific gravity relative to air at standard conditions, which varies with temperature and pressure. At 100 psia the specific gravity of steam relative to air is approximately 0.62. For high-accuracy steam sizing, use dedicated steam tables to find the correct density and enter it as a custom specific gravity. Note that for two-phase or wet steam, additional corrections (the Ys steam expansion factor) are needed that go beyond this calculator.
Why does the calculator ask for absolute pressure rather than gauge pressure?
The gas flow formulas use absolute pressures in the ratio P2/P1 to determine the flow regime. Gauge pressure readings (which show pressure above atmospheric) must be converted to absolute by adding atmospheric pressure (14.696 psia at sea level, or 1.01325 bara). Using gauge pressures directly would produce errors in the regime check and in the formula itself. If your gauges read in psig, add 14.7 to convert to psia before entering.
How do I size a control valve versus an on-off valve?
For on-off (isolation) valves, select a valve whose rated Cv at full open is at least 10-20% above your calculated required Cv. For control valves, the story is more nuanced: you need the valve to operate between about 20% and 80% of its travel at your normal flow, which means the valve's maximum Cv at full open should be roughly 1.5 to 3 times the required Cv. Operating a control valve near its closed position causes instability; operating near fully open removes controllability.