# Valve Flow Coefficient Calculator (Liquids and Gases)

URL: https://speedycalculator.com/calculators/physics/valve-flow-coefficient/
Last updated: 2026-10-30

> The valve flow coefficient calculator finds the Cv needed for a given flow, or the flow through a valve of known Cv, for liquids and for gases in subcritical or choked flow.

## Inputs

- Fluid
- Find
- Specific gravity (water = 1, air = 1 for gases)
- Inlet pressure P₁ (absolute) (psi, bar, kPa)
- Outlet pressure P₂ (absolute) (psi, bar, kPa)
- Gas temperature (K, °C, °F)
- Liquid flow rate (US gpm, m³/h, L/min)
- Gas flow rate (scfh)
- Flow coefficient C_v

## Results

- Flow condition (gas)
- Required C_v
- Flow rate
- Equivalent K_v

## Formula

```
Liquid: Q = C_v·√(ΔP/SG) (gpm, psi) · Gas, subcritical (P₂ > P₁/2): Q = 1360·C_v·√(ΔP·P₂/(SG·T))
Gas, critical: Q = 660·C_v·P₁/√(SG·T)  (Q in scfh, P absolute psia, T in °R)
```

## Explanation

Valve sizing differs for liquids and gases. Gases expand as pressure drops, and once the outlet falls below about half the inlet pressure the flow chokes – it no longer increases as the outlet pressure drops further.

### How to use the Valve Flow Coefficient Calculator

- **Fluid**
- **Find**
- **Specific gravity (water = 1, air = 1 for gases)**
- **Inlet pressure P₁ (absolute)**
- **Outlet pressure P₂ (absolute)**
- **Gas temperature**
- **Liquid flow rate**
- **Gas flow rate (scfh)**
- **Flow coefficient C_v**

Results update as you type, every field has its own unit menu, and everything is calculated in your browser.

### How it works

Choose the fluid type and what to calculate, then enter the values. Pressures are absolute.

### Inputs explained

FieldWhat to enterFluidChoose one: Liquid, GasFindChoose one: Flow coefficient C_v, Flow rateSpecific gravity (water = 1, air = 1 for gases)A numberInlet pressure P₁ (absolute)Units: psi, bar, kPaOutlet pressure P₂ (absolute)Units: psi, bar, kPaGas temperatureUnits: K, °C, °FLiquid flow rateUnits: US gpm, m³/h, L/minGas flow rate (scfh)A numberFlow coefficient C_vA number

### Example values

How the main result changes when **Specific gravity** changes and everything else stays at the example values above:

Specific gravity (water = 1, air = 1 for gases)Required C_v0.515.81140.7519.3649122.36071.25251.527.3861231.6228

## Worked example

Inputs — Fluid: Liquid; Find: Flow coefficient C_v; Specific gravity (water = 1, air = 1 for gases): 1; Inlet pressure P₁ (absolute): 100 psi; Outlet pressure P₂ (absolute): 80 psi; Liquid flow rate: 100 US gpm.

Results — **Required C_v = 22.3607**; Equivalent K_v = 19.342.

## Key terms

- **Choked flow**: Flow limited by sonic velocity.

## FAQ

**What is choked flow?**
When gas reaches sonic speed in the valve, flow stops increasing as P₂ falls.

**Why absolute pressure?**
Gas density depends on absolute pressure.

**What is scfh?**
Standard cubic feet per hour at 60 °F and 14.7 psia.

**How much margin should a control valve have?**
Size so the valve is 60–80% open at normal flow.


## Sources

- [The Engineering ToolBox](https://www.engineeringtoolbox.com/)
- [ISA-75.01.01 – Flow equations for sizing control valves](https://www.isa.org/)