How this instrument works
Differential pressure is the arithmetic difference between two pressures measured at two points: ΔP = P₁ − P₂. A sensor built for this job ignores either value's size — connect it across a filter, an orifice plate, or the two sides of a diaphragm, and it reports only the gap. That is why a transmitter rated in kilopascals can sit in a line carrying several bar of static load: the two large signals cancel internally before the electronics see a number anywhere near their working range.
The formula's shape follows from how these sensors are built. A thin diaphragm sits between two ports, P₁ pushing one way and P₂ the other, and its deflection is proportional to the net force — proportional to P₁ − P₂ when the ports are equal area. Bernoulli's principle is what makes the reading useful for flow: forcing fluid through a constriction like an orifice plate speeds it up, trading static pressure for velocity, so the drop across the plate grows with the square of flow rate. A square root of that drop gives an estimate of flow, the working idea behind most mechanical flow meters installed before digital mass-flow sensors took over.
Sign matters more here than in most subtractions: swap which port is P₁ and which is P₂ and the answer flips sign, and on a real transmitter wired backwards it flips which way the needle moves. There is also a physical limit a subtraction on paper does not have. Every real sensor carries a maximum working differential far below either individual pressure it can withstand statically, so a unit rated for 500 kPa differential can still rupture from a 50 kPa gap if the line pressure on one side spikes past its overrange rating.
- Enter Pressure 1 — the reading from the reference or high-pressure side, such as upstream of a filter or the high port on a transmitter.
- Enter Pressure 2 — the reading from the other side, in the same or a different unit; the instrument converts internally before subtracting.
- Read Differential pressure — the result field shows P₁ − P₂, positive whenever Pressure 1 is the larger of the two.
- Switch units on any field between Pa, kPa, atm, or psi to match your gauge or transmitter datasheet.
Worked example — 150 kPa against 100 kPa across a sensor
A transmitter sits across a process line, reading Pressure 1 at 150,000 Pa (150 kPa) on the upstream port and Pressure 2 at 100,000 Pa (100 kPa) on the downstream port. The instrument computes ΔP = 150,000 − 100,000 = 50,000 Pa, a 50 kPa differential — the figure the transmitter's display and its 4-20 mA output actually carry, not either absolute reading on its own.
That 50 kPa gap is exactly the kind of number an orifice-plate flow meter or a filter-clog alarm is built around. A clean air filter typically drops only a few kilopascals across it, so a steady 50 kPa reading on a filter that started life at 5 kPa is a loud signal to swap the element before it collapses or starves downstream equipment of flow.
Questions
What is the difference between differential and gauge pressure?
Gauge pressure is measured against local atmosphere, so it is really a differential reading with P₂ fixed at ambient. A dedicated differential instrument generalizes this: P₂ can be any second point, not just the atmosphere — the far side of a filter, the other leg of a manometer, or the base of a second tank. Every gauge reading is a special case of ΔP = P₁ − P₂ where P₂ happens to equal atmospheric pressure.
Why do orifice-plate flow meters read differential pressure instead of flow directly?
Because Bernoulli's equation ties flow speed to a pressure drop, not to a pressure by itself. Forcing fluid through the constriction of an orifice plate raises its velocity and lowers its static pressure downstream, and the resulting ΔP grows with the square of volumetric flow rate. A transmitter reading P₁ − P₂ across the plate, combined with a square-root extraction, is how flow was metered industrially for decades before mass-flow sensors became common.
Can differential pressure come out negative?
Yes — it just means Pressure 2 is the larger of the two. Swap 150,000 Pa and 100,000 Pa in this calculator and ΔP flips from 50,000 Pa to −50,000 Pa. On a physical transmitter, wiring the ports backwards produces the same sign flip, which is why installation manuals are explicit about which port is high side and which is low side.
Why does a clogging filter show a rising differential pressure?
A filter's pores narrow as debris builds up, so pushing the same volume of air or fluid through it needs a larger pressure drop to keep the flow rate steady. Facilities often set an alarm at two to three times the clean-filter reading, so a climbing ΔP flags replacement before the restriction gets severe enough to damage a fan or starve a process of flow.
What units does this calculator support?
Pascals internally, with kPa, atm, and psi available on the unit menus for both pressure fields and the result. Enter Pressure 1 and Pressure 2 in whichever unit matches your gauge or datasheet — the calculator converts to a shared unit before subtracting, so mixing psi on one field and kPa on the other still returns a correct differential.