Home › Tools › Flow Rate from Pressure Calculator
This calculator estimates volumetric flow rate from a pressure measurement in three common situations: a differential pressure reading across an orifice or similar restriction, rescaling an existing DP flow reading with the square-root law, and flow through a valve with a published Cv. It solves the same equations we use when sizing DP flow elements for customers, with the velocity-of-approach factor included.
One thing the calculator cannot do, because physics does not allow it: turn a single line-pressure number into a flow. Pressure only maps to flow through a known geometry. If you are not sure which pressure you have, start with the guide on the flow rate and pressure relationship.
Calculator
Pressure to flow calculator
Liquids only. Gases and steam are compressible: density changes with pressure and temperature, so these formulas need an expansibility correction and density at operating conditions. Results are engineering estimates, not a calibration.
How the calculation works
| Mode | Formula | Use when |
|---|---|---|
| Orifice / DP element | Q = C·E·A·√(2ΔP/ρ), E = 1/√(1−β⁴) | You have a DP reading across a known bore in a known pipe |
| Square-root rescale | Q2 = Q1·√(ΔP2/ΔP1) | You know one flow-DP pair for the element and have a new DP reading |
| Valve Cv | Q (GPM) = Cv·√(ΔP/SG) | Flow through a valve with a published Cv, drop in psi |
The discharge coefficient C defaults to 0.61, the typical ISO 5167 value for a standard concentric orifice plate at moderate beta ratios and turbulent Reynolds numbers. Venturi tubes run much higher: ISO 5167-4 lists 0.995 for a classical venturi with a machined convergent section and 0.984 for a rough-cast one. If you know your element type, adjust C accordingly. The velocity-of-approach factor E corrects for the fluid already moving in the approach pipe; at β = 0.6, skipping E understates flow by about 7 percent.
Worked example
A DN80 water line has an orifice with a 40 mm bore, and the transmitter reads 16 kPa. Then β = 40/80 = 0.5, E = 1/√(1 − 0.5⁴) = 1.033, bore area A = 1.257 × 10⁻³ m², and the velocity term is √(2 × 16000/1000) = 5.66 m/s. Flow: Q = 0.61 × 1.033 × 1.257×10⁻³ × 5.66 = 4.48 × 10⁻³ m³/s, which is 16.1 m³/h, about 71 US GPM. Type those numbers into the first tab and you get the same answer.
Limitations
- Liquids only. Gases and steam are compressible: density changes along the element, so the calculation needs an expansibility factor and density at operating pressure and temperature. For steam, use a meter with built-in compensation; see the steam flow meter options.
- The result is an estimate, not a calibration. Real installations follow ISO 5167 coefficients for the exact bore, pipe, tap arrangement, and Reynolds number, plus straight-run requirements upstream and downstream.
- Line pressure is not enough. All three modes need either a differential pressure or a known coefficient. A single gauge reading cannot give you flow.
Related guides and products
- Flow rate and pressure relationship: formulas and worked examples
- Orifice plate flow meter
- Differential pressure transmitters
- Product selector: find an instrument by your parameters
FAQ
Can you convert psi to flow rate?
Only through a known geometry. A psi value across a valve with a published Cv converts directly with Q = Cv·√(ΔP/SG). A psi value across an orifice converts with the orifice equation. A psi value on its own, with no defined restriction, cannot be converted to flow.
How do you calculate flow rate from pressure and diameter?
You need two diameters, not one: the pipe inside diameter and the restriction bore. Their ratio (beta) sets the velocity-of-approach factor, the bore sets the area, and the differential pressure and fluid density do the rest. The first tab of the calculator takes exactly these inputs.
How do you calculate air flow rate from pressure?
Air is compressible, so the liquid formulas here only hold as a rough estimate at very low differential pressures. For real air and gas work, the calculation needs gas density at operating conditions plus an expansibility factor per ISO 5167, or skip the inference entirely and measure mass flow directly with a thermal mass flow meter.
Request a quote
If the numbers point to a DP flow measurement, send us the pipe size, fluid, pressure, temperature, and flow range. We size the bore, select the transmitter range, and return a documented configuration with the calculation sheet.