Differential Pressure Calculator - dP, Velocity, and Flow Rate

A differential pressure calculator is a fluid-mechanics tool that turns two pressure readings and fluid density into the pressure drop dP, then derives velocity, flow rate, and equivalent head of water.

• • Filter and HVAC monitoring: Compute pressure drop across a clogged or clean filter, coil, or damper.
• • Pitot-static airspeed: Convert the impact-to-static pressure difference from a pitot probe into a true airspeed reading.
• • Orifice and Venturi flow metering: Back out the volume flow rate through an orifice plate, Venturi tube, or nozzle from a measured dP.
• • Tank level and pump head: Translate the dP at the bottom of a tank into a liquid column height or compare pump suction and discharge pressures.

Differential pressure is the same quantity that drives Bernoulli's equation, so when a fluid speeds up through a constriction or loses height, the static pressure on either side shifts by the dynamic pressure 1/2 rho v^2.

This calculator is built around two pressures and one density, which is the minimum data needed for dP, velocity, and orifice flow rate.

If you are working in air rather than water, the air density calculator returns rho for sea level or a custom temperature and altitude in one step.

The calculator evaluates dP = P_high - P_low, then applies three downstream formulas: the pitot-static velocity, the ISO 5167 orifice flow rate, and the water-column conversion. Velocity and orifice flow rate use the user-entered rho. The water-column output is always the equivalent head of water at rho = 1000 kg/m^3, which keeps the same numerical meaning in HVAC and filter work regardless of the working fluid. Standard gravity is g = 9.80665 m/s^2.

• P_high, P_low: Higher- and lower-side pressures in pascals. Use absolute or consistent gauge on both.
• rho: Mass density of the working fluid in kg/m^3.
• d, D: Orifice throat d and upstream pipe D, in metres. Beta = d / D must stay below 1.
• Cd: Discharge coefficient. Sharp-edged orifice uses Cd near 0.61.
• g: Gravitational acceleration, fixed at 9.80665 m/s^2.

The velocity formula is the pitot-static inversion of Bernoulli's equation: the impact-to-static pressure difference equals the dynamic pressure 1/2 rho v^2.

The orifice flow equation follows ISO 5167 for a concentric thin-plate orifice. The discharge coefficient lumps the velocity-of-approach, expansion factor, and tap-location effects; the same form applies to Venturi tubes, flow nozzles, and pitot tubes with appropriate Cd.

According to Engineering Toolbox, the ISO-style orifice, Venturi, and nozzle flow equations all follow Q = Cd * A2 * sqrt(2 dP / (rho * (1 - beta^4))), with discharge coefficients of about 0.61 (sharp-edged orifice) and 0.97 to 0.99 (Venturi tube).

According to Engineering Toolbox, fresh water near 4 deg C has a density of about 1000 kg/m^3, so 1 kPa of pressure difference corresponds to roughly 0.102 m of water column.

The pitot-static velocity derivation here is the same algebra the Bernoulli equation calculator solves in its most general form, including elevation head and a Solve For menu for any of the six Bernoulli variables.

Four ideas worth understanding before you trust the dP, velocity, and flow rate the calculator returns.

These four ideas reappear in fluid-mechanics coursework alongside Bernoulli, the Reynolds number, and dP-to-head conversions.

Hand the same rho, v, and pipe diameter to the Reynolds number calculator to check whether the flow is laminar or turbulent before trusting the discharge coefficient you chose.

Use the differential pressure calculator in six steps, from picking a fluid to reading the velocity and flow rate.

1. 1 Choose the fluid and density: Use 1000 kg/m^3 for water, 1.225 kg/m^3 for sea-level air, or the actual density for a process fluid.
2. 2 Enter the higher-side pressure: Type the upstream or higher-side pressure in pascals in the P_high field. 101325 Pa is standard sea-level atmosphere.
3. 3 Enter the lower-side pressure: Type the downstream or lower-side pressure in pascals in the P_low field. P_low must be <= P_high for forward flow.
4. 4 Set the orifice and pipe diameters: Enter the orifice throat diameter d and the upstream pipe diameter D in metres. For ISO 5167, beta = d / D should stay between 0.3 and 0.7.
5. 5 Pick the discharge coefficient Cd: Use 0.61 for a sharp-edged orifice, 0.97-0.99 for a Venturi tube, 0.96-0.98 for a flow nozzle, 0.98-1.0 for an averaging pitot probe.
6. 6 Read the dP, velocity, and flow rate: The result panel reports dP in Pa, kPa, bar, and psi, the pitot-static velocity in m/s, the orifice flow rate in m^3/s, and the equivalent water-column height in metres.

For a 250 Pa HVAC pre-filter at sea level, set rho = 1.225, P_high = 101575 Pa, P_low = 101325 Pa, leave the orifice defaults, and read the result. dP = 250 Pa, about 20.2 m/s equivalent velocity, and roughly 2.5 cm of water column head.

If the pressure gauges you have on hand read in bar or psi, the bar to psi conversion is the fast way to convert each pressure to pascals before you type it into P_high or P_low.

Practical reasons to use this calculator instead of working the formulas by hand.

• • Three outputs from one pair of inputs: Enter P_high and P_low once and read dP in four units, the pitot velocity, the orifice flow rate, and the equivalent liquid column height.
• • Built-in ISO 5167 form: The flow equation already includes the (1 - beta^4) velocity-of-approach correction, so you do not have to remember the expansion factor.
• • Works for any incompressible fluid: Set rho to water (1000), air (1.225), oil (about 900), or a custom density.
• • Auditable unit conversion: The same dP is reported in Pa, kPa, bar, and psi so you can hand-check against a manifold gauge.
• • Edge-friendly validation: Beta = 1, zero density, and equal pressures are surfaced as inline notices instead of being silently swallowed.

Use this tool whenever a measurement or homework problem gives you two pressures, a fluid, and a pipe, and you need the velocity or flow rate without re-deriving the Bernoulli or ISO 5167 form.

If the same pressure difference acts on a body in the flow rather than across a meter, the drag equation calculator converts the dynamic pressure into a drag force using the same rho and v the differential pressure calculator returns.

What changes the answer, and what the calculator does not capture.

• • Steady, incompressible, single-phase flow is assumed. Compressible gases at high pressure ratios, pulsating flow, and two-phase mixtures need a dedicated compressible or multiphase model.
• • The orifice equation assumes ISO 5167 thin-plate geometry with corner taps. Custom tap locations and very small Reynolds numbers require a calibrated Cd curve instead of a fixed 0.61.
• • The velocity from a pitot-static probe assumes the probe is aligned with the streamline and the flow is subsonic. At transonic speeds the local static pressure no longer matches the freestream static pressure.

Convert psi, kPa, bar, or inches of water column to pascals first; a 1 percent unit error in P_high or P_low propagates straight through to dP, v, and Q.

Heads of liquid such as mmH2O and inH2O are defined against water at the reference density of 1000 kg/m^3, so the calculator reports dP in pascals plus the equivalent head of water in metres.

According to NIST Special Publication 811, 1 bar is exactly 100000 Pa and 1 psi equals approximately 6894.757 Pa, while mmH2O and inH2O are heads of liquid rather than strict SI pressure units.

When the factory transducer is calibrated in kPa but your downstream report needs psi, the kPa to psi conversion calculator converts the differential pressure output without re-running the entire calculation.