The valve Cv calculator above relates three quantities for a liquid flowing through a valve: the flow rate, the pressure drop across the valve, and the valve's flow coefficient. Fix any two and the third follows. It reports the answer in both conventions in use, the US Cv and the metric Kv, and it flags the pressure drop beyond which the liquid chokes and the relationship stops holding at all.
Arb Digital builds free tools that name the standard they follow rather than presenting a formula with no provenance. The relations here are the standard incompressible-flow sizing equations for control valves, and the choked-flow limit uses the liquid pressure recovery factor in the same form the sizing standard defines. The model is turbulent, single-phase, fully developed liquid flow through the valve alone. Gases, flashing service, viscous liquids and two-phase mixtures each need a different equation, and each is named below rather than quietly ignored.
What This Valve Cv Calculator Does
A valve's flow coefficient is a deliberately practical definition. Cv is the number of US gallons per minute of water at 60 °F that the valve passes with one pound per square inch of pressure drop across it. Kv is the same idea in metric units: cubic metres per hour of water with one bar of drop. A valve with a Cv of 57.8 passes 57.8 gpm of water at 1 psi, and because flow scales with the square root of the drop, it passes twice that at 4 psi.
That square-root behaviour is the single most important thing about the coefficient, and it is where intuition goes wrong. Doubling the flow through a fixed valve opening does not double the pressure drop; it quadruples it. A pump that had margin at half flow can be badly short of it at full flow, and the shortfall appears suddenly rather than gradually.
Cv and Kv are two units for one physical quantity, related by a fixed conversion of about 1.156 Cv per Kv. Neither is a size in millimetres or inches. Two valves with the same nominal bore can have coefficients differing by a factor of three, because the coefficient depends on the internal trim geometry and not on the pipe connection.
How to Use It
- Choose which quantity you are missing. Sizing a new valve means solving for the coefficient. Checking an existing one means solving for flow or for pressure drop.
- Enter the flow and drop in whatever units you have. The menus convert internally, so a metric flow with an imperial pressure is handled correctly.
- Set the specific gravity for the actual liquid. Water is 1.0. The coefficient scales with the square root of specific gravity, so a liquid 20 per cent denser needs about 10 per cent more coefficient.
- Use the coefficient at your expected opening. Published tables give Cv against percentage travel. A control valve running at 90 per cent open has almost no room to correct upward, and one running at 10 per cent controls badly.
- Check the choked limit before trusting the answer. If the drop you entered exceeds it, the flow through the valve is capped by cavitation and the square-root relation no longer applies.
The Formula and a Worked Example
For turbulent liquid flow, Cv = Q √(G/ΔP), with Q in US gallons per minute, ΔP in psi and G the specific gravity. Rearranged, Q = Cv√(ΔP/G) and ΔP = G(Q/Cv)2. The metric form is identical in structure: Kv = Q√(G/ΔP) with Q in m³/h and ΔP in bar.
Work the defaults through. Fifty cubic metres per hour is 50 × 4.402868 = 220.14 US gallons per minute, and one bar is 14.5038 psi. For water, G = 1, so Cv = 220.14 ÷ √14.5038 = 220.14 ÷ 3.8084 = 57.80. The metric coefficient is 0.865 × 57.80 = 50.0, which is exactly the metric definition read straight off the inputs: 50 m³/h at 1 bar is a Kv of 50. That agreement between the two routes is a useful check that the units have not been mangled.
The choked limit uses ΔPchoked = FL2(P1 − FFPv), where FF is the liquid critical pressure ratio factor, taken as 0.96 − 0.28√(Pv/Pc). With a 5 bar absolute inlet, a vapour pressure of 0.0234 bar and FL = 0.9, that gives 0.81 × (5 − 0.957 × 0.0234) = 4.03 bar. The 1 bar drop in the example is comfortably below it.
Why Choked Flow Ends the Relationship
Liquid speeds up as it squeezes through the restriction in a valve, and its static pressure falls as it does so. Downstream of the narrowest point the flow slows again and some of that pressure is recovered. The lowest pressure in the whole valve is therefore not the outlet pressure but the pressure at the vena contracta, and it is lower than either end.
If that minimum falls to the liquid's vapour pressure, the liquid boils locally. Vapour bubbles form, then collapse violently as the pressure recovers downstream. That is cavitation, and it does two things. It caps the flow, so increasing the downstream pressure drop no longer increases the flow at all. And it erodes the trim, because bubble collapse against a metal surface removes material.
The recovery factor FL quantifies how much pressure a particular valve recovers. A globe valve with a tortuous path recovers little and has a high FL, around 0.9, so it tolerates a large drop before choking. A butterfly valve recovers a great deal and may have an FL near 0.6, choking at less than half the drop. This is why a butterfly valve substituted for a globe valve on the same duty can cavitate when the globe valve did not, at identical pressures, with the coefficient calculation looking perfectly healthy.
The Assumptions and Where They Stop Holding
This calculation assumes a single-phase liquid in turbulent flow, no flashing, no cavitation, and no correction for the pipe fittings immediately either side of the valve.
Viscosity is the first assumption to fail. In laminar or transitional flow the square-root relation breaks down and a Reynolds number factor has to be applied, which can change the required coefficient substantially for a heavy oil. The Reynolds number calculator tells you which regime you are in before you rely on the answer here.
Piping geometry is the second. Reducers, expanders or a close-coupled elbow change the effective coefficient, and the sizing standard handles them with a piping geometry factor. A valve installed between reducers passes less than its published coefficient implies.
Gases and vapours are the third and largest departure. A compressible fluid expands as it passes through the valve, so density is not constant, and above a critical pressure ratio the flow chokes at sonic velocity. The compressible sizing equations use an expansion factor and a specific heat ratio factor, and applying the liquid formula to steam or air gives an answer that is wrong rather than approximate.
How This Differs From the Adjacent Flow Tools
The boundary matters, because three tools on this site all produce a pressure drop and they are not interchangeable. The pipe flow calculator computes frictional loss along a length of straight pipe using the Darcy-Weisbach equation and a friction factor from the pipe roughness and Reynolds number. That is distributed loss over distance. This page computes the loss across a single valve using an empirically measured coefficient for that specific valve, which is a lumped loss at a point, measured on a test rig rather than derived from geometry.
The orifice flow calculator sits between the two: it is also a lumped restriction, but it uses a discharge coefficient tied to a defined geometry rather than a manufacturer's published figure for a variable opening. Use the flow rate calculator for the relationship between velocity, bore and volumetric flow, the flow rate converter and pressure converter to rescale units, and the specific gravity calculator if you have a density and need the ratio this page asks for.
Where the Standards Live
The sizing equations for control valves are internationally standardised. IEC 60534-2-1:2011, Industrial-process control valves — Part 2-1: Flow capacity, sizing equations for fluid flow under installed conditions, contains the equations for predicting the flow of both compressible and incompressible fluids through control valves. In the United States the corresponding work is maintained by the ISA75 control valve standards committee, whose scope covers all ISA standardisation work related to valves. The default vapour pressure offered above is for water near room temperature; vapour pressures for other liquids and temperatures can be obtained from the Antoine equation parameters published in the NIST Chemistry WebBook phase change data.
Arb Digital builds free tools like this one because useful pages earn attention. If you want tools, calculators or content built for your own audience, we can help.
Browse All Free Tools Talk to Arb DigitalCommon Mistakes to Avoid
- Using the fully open coefficient — a control valve is sized to run part open, and the coefficient at 40 per cent travel is a fraction of the wide-open figure.
- Confusing Cv with valve size — the coefficient describes the trim, not the connection. Two valves of the same nominal bore can differ several-fold.
- Assuming flow is proportional to pressure drop — it goes as the square root, so four times the drop gives twice the flow.
- Applying the liquid equation to a gas — compressible flow needs an expansion factor and its own choked-flow treatment.
- Ignoring the recovery factor when changing valve type — a high-recovery valve cavitates at a drop a low-recovery valve handles without complaint.
Related Free Tools From Arb Digital
For friction along the pipe rather than across the valve, use the pipe flow calculator, and for a fixed restriction the orifice flow calculator. The flow rate calculator converts between velocity, bore and volume, the Reynolds number calculator checks the flow regime the equations assume, and the Bernoulli equation calculator covers the pressure and velocity trade the vena contracta depends on. Rescale inputs with the pressure converter or the flow rate converter, and browse the full free online tools hub for everything else.
Frequently Asked Questions
It is the number of US gallons per minute of water at 60 degrees Fahrenheit that the valve passes with a pressure drop of one pound per square inch across it. It is measured on a test rig for a given valve at a given opening, not calculated from the valve's dimensions.
Multiply Cv by 0.865 to get Kv, or multiply Kv by about 1.156 to get Cv. They describe the same physical capacity in different units, Kv being cubic metres per hour of water at one bar of drop.
No. The coefficient depends on the internal trim, so two valves with identical pipe connections can have coefficients that differ by a factor of three. A reduced-trim valve is deliberately built with a much lower coefficient than its bore suggests.
Because the drop is proportional to the square of the flow at a fixed opening. That is the same square-root relation read the other way, and it is why a system with adequate margin at part flow can be badly short at full flow.
It is the condition where the pressure at the narrowest point falls to the liquid's vapour pressure. The liquid boils locally, the flow stops responding to further increases in pressure drop, and the collapsing vapour bubbles erode the trim.
How much of the pressure lost at the vena contracta the valve gets back downstream. A globe valve recovers little and has a high factor near 0.9; a butterfly valve recovers a lot and may sit near 0.6, so it chokes at a much smaller pressure drop.
No. Compressible fluids expand through the valve and require the compressible sizing equations, with an expansion factor and a specific heat ratio factor. Applying the liquid formula to a gas gives a wrong answer, not a rough one.
Yes, once the flow is no longer fully turbulent. In laminar and transitional flow a Reynolds number factor must be applied, and for viscous oils the correction can be large enough to change the valve selected.
This tool is provided for educational and estimating use only. It uses the turbulent, single-phase liquid sizing relation and does not apply piping geometry, Reynolds number, flashing, two-phase or compressible corrections. Valve selection for a real process, and any duty involving pressure, temperature or hazardous fluids, must be specified and verified by a qualified engineer against the applicable standard and the manufacturer's published data.
