Valve Cv Calculator (Flow Coefficient & Cv/Kv Sizing)

Valve sizing determines the flow coefficient needed for a valve to pass the required flow rate at a given pressure drop. An undersized valve cannot deliver enough flow; an oversized valve operates near its seat, causing poor control, noise, and accelerated wear.

Cv and Kv — Flow Coefficients

The flow coefficient quantifies how much flow a valve can pass. Two conventions exist:

• Cv (US) — US gallons per minute of water at 60 °F with a 1 psi pressure drop
• Cv (UK) — imperial (UK) gallons per minute of water with a 1 psi pressure drop. Because a UK gallon is larger than a US gallon, Cv (UK) is about 17% smaller than Cv (US) for the same valve (Kv = 1.039 × Cv UK)
• Kv — cubic metres per hour of water at a 1 bar pressure drop

Throughout this page, “Cv” means Cv (US) — the most common convention — unless stated otherwise.

The conversion is: $C_v = 1.156 \times K_v$. There is also Cv (UK) which uses imperial gallons: $K_v = 1.039 \times C_v\text{(UK)}$.

Cv to Kv Converter

To convert Cv to Kv, multiply by 0.865 (Kv = 0.865 × Cv US); to convert Kv to Cv (US), multiply by 1.156. For imperial gallons, Kv = 1.039 × Cv (UK). The Cv/Kv Converter tab above applies all three instantly, so this control valve Cv calculator also works as a standalone Cv-to-Kv conversion tool for an already-installed valve.

Liquid Valve Sizing

For incompressible (liquid) flow, the basic sizing equation relates flow rate to Kv and pressure drop:

• $Q$ — volumetric flow rate
• $K_v$ — valve flow coefficient
• $\Delta P$ — pressure differential across the valve
• $SG$ — specific gravity of the fluid relative to water

Gas Valve Sizing (IEC 60534)

Compressible flow through valves is more complex. The IEC 60534 standard introduces the expansion factor $Y$, which accounts for the change in gas density as pressure drops across the valve:

• $x$ — pressure ratio ($\Delta P / P_1$)
• $F_k$ — ratio of specific heats factor
• $x_T$ — critical pressure drop ratio factor (≈0.7 for globe valves; lower for rotary ball and butterfly valves — see the table below)

Choked Flow

Choked flow occurs when the pressure ratio $x$ reaches the critical value $x_{choked} = F_k \cdot x_T$. Beyond this point, increasing the downstream pressure drop does not increase flow — the expansion factor $Y$ cannot fall below its limiting value of 2/3. This calculator detects choking automatically and displays a warning when the valve is at maximum capacity.

Cavitation, Vena Contracta & Pressure Recovery

Cavitation occurs when the local pressure inside a valve drops below the fluid's vapor pressure, forming vapor bubbles that collapse violently as the flow recovers downstream — causing noise, vibration, and rapid erosion of the trim. The lowest pressure occurs at the vena contracta: the point of minimum flow area, and maximum velocity, just past the valve restriction. The liquid pressure recovery factor F_L captures how much pressure recovers from the vena contracta back to the valve outlet. A low F_L (e.g. butterfly valves around 0.55) means a deeper pressure dip at the vena contracta and easier cavitation; a high F_L (e.g. globe valves around 0.9) recovers less aggressively and resists it.

Inherent Flow Characteristic

The inherent flow characteristic describes how flow changes with valve travel (stem position) at a constant pressure drop. Published Cv/Kv is the fully open value; the characteristic governs how capacity builds between closed and open. Three are common:

• Linear — flow is proportional to valve opening — suited to systems where most of the pressure drop stays across the valve and is roughly constant.
• Equal-percentage — each equal increment of travel changes flow by an equal percentage of the current flow. It is the most common throttling characteristic because, as the valve's own share of pressure drop falls when it opens, the installed characteristic ends up close to linear.
• Quick-opening — most of the flow capacity is reached early in the travel — used for on/off and relief service rather than throttling.

For a deeper guide to IEC 60534 valve sizing, see our blog post: Understanding Control Valve Sizing with IEC 60534. New to flow coefficients? Start with Cv vs Kv explained.

Related calculators & references

• Cv to Kv conversion reference
• Relief valve sizing calculator (API 520)
• Orifice plate sizing calculator
• Pipe friction loss calculator

The standard's own sizing examples, worked with the equations above. Example 1: 360 m³/h of water at 363 K (ρ 965.4 kg/m³) through a globe valve from 680 kPa to 220 kPa abs. Examples 3 and 4: 3,800 Nm³/h of CO₂ (M 44.01, γ 1.297 from the CO₂ preset — the standard rounds it to 1.30) at 433 K through a rotary valve with xT = 0.60 from 680 kPa abs to 450 kPa abs, then to 250 kPa abs.

1. Liquid (Ex 1): SG = 965.4/998.2 = 0.9671, ΔP = 4.60 bar. Kv = 360 · √(0.9671 / 4.60) = 165.1 m³/h, i.e. Cv (US) = 190.8. The standard sizes it at Kv = 165 — the 0.1 is its 999 kg/m³ reference density.
2. Gas, sub-critical (Ex 3): x = (680 − 450)/680 = 0.338; Fk = 1.297/1.40 = 0.926, so the choke limit is Fk·xT = 0.926 × 0.60 = 0.556. x is below it — the flow is sub-critical.
3. Expansion factor Y = 1 − x/(3·Fk·xT) = 0.797; inlet compressibility Z = 0.990 (Peng-Robinson). Kv = Q / (N9 · Y · P1 · √(x / (M·T·Z))) with N9 = 24.6 for Nm³/h, kPa and K: Kv = 67.3 m³/h. The standard sizes it at Kv = 67.2 (with Z = 0.991).
4. Gas, choked (Ex 4): with the outlet at 250 kPa abs, x = 0.632 exceeds 0.556, so the valve is choked — Y floors at 2/3 and x is held at the limit. Kv = 62.8 m³/h; the standard sizes it at Kv = 62.6. The residual on both gas examples is only the γ rounding and the Z evaluation; the equations are the standard's. The gas tab raises the choked-flow flag for these inputs.
5. Deep choke, US units (Fisher Control Valve Handbook, compressible sizing problem 1): 6.0 × 10⁶ SCFH of natural gas (M 17.38, γ 1.31, ideal Z) from 200 psig to 50 psig at 60 °F through an 8″ ball valve with xT = 0.137. x = 0.70 against a choke limit of 0.128 — about 5.4× critical — so Y sits at its 2/3 floor: Cv = 1514. The handbook's result at the rated xT is Cv = 1515 (it then refines xT at the actual travel).

These figures are computed by the same functions the tabs above run. Entering Example 1 in the Liquid tab, or Example 3 / 4 in the Gas tab (Carbon Dioxide preset, 160 °C, xT 0.60, pressures in gauge: 578.68 and 348.68 / 148.68 kPa), reproduces them; the Fisher problem needs SCFH (60 °F), psi and °F selected with the custom-gas fields set to γ 1.31, M 17.38.