Process Instrumentation
Differential Pressure Flow Transmitter Calibration: 5-Point Procedure
A DP flow transmitter converts a differential pressure signal from an orifice plate, flow nozzle, or Venturi tube into a flow rate output.
Calibrating it correctly requires understanding two separate outputs: the raw DP in mbar or inH₂O, and the derived flow rate in engineering units.
This guide covers the complete 5-point DP flow transmitter calibration procedure, the square root relationship between DP and flow, as-found and as-left recording, and a 5-point error calculator.
DP Input vs Flow Output
Square Root Relationship
As-Found and As-Left
±0.5% Acceptance Limit
The critical difference in a DP flow transmitter calibration is the square root relationship.
Flow is proportional to the square root of DP, not to DP directly. A 1% DP error produces only a 0.5% flow error.
DP Flow Transmitter: What You Are Actually Calibrating
Hello! Today we are covering the complete calibration procedure for a DP flow transmitter connected to a differential pressure primary element. This is a common source of confusion in the field: technicians sometimes calibrate the DP input correctly but forget to verify the square-root-extracted flow output. Both must be checked — and both must be recorded in the calibration record.
A DP flow transmitter contains two functional blocks that must both be calibrated.
The first block is the DP measurement section: it converts differential pressure into a raw DP value in mbar, inH₂O, or kPa.
The second block is the square root extractor: it converts raw DP into a 4-20 mA flow output using Q ∝ √ΔP.
DP to Flow Conversion (Square Root)
Q / Q_max = √(ΔP / ΔP_max)
Q: actual flow rate
Q_max: maximum flow rate (at DP_max, corresponding to 20 mA output)
ΔP: measured differential pressure
ΔP_max: maximum DP (calibrated span, corresponding to 100% flow)
Output current: I = 4 + 16 × √(ΔP / ΔP_max)
Example: ΔP_max = 250 mbar. At ΔP = 100 mbar:
I = 4 + 16 × √(100/250) = 4 + 16 × 0.632 = 14.11 mA
This corresponds to 63.2% of maximum flow — not 40% (which would be the linear value).
Q_max: maximum flow rate (at DP_max, corresponding to 20 mA output)
ΔP: measured differential pressure
ΔP_max: maximum DP (calibrated span, corresponding to 100% flow)
Output current: I = 4 + 16 × √(ΔP / ΔP_max)
Example: ΔP_max = 250 mbar. At ΔP = 100 mbar:
I = 4 + 16 × √(100/250) = 4 + 16 × 0.632 = 14.11 mA
This corresponds to 63.2% of maximum flow — not 40% (which would be the linear value).
Did You Know? Because of the square root relationship, a DP flow transmitter has very poor accuracy at low flows.
At 10% of maximum flow, the DP is only 1% of the maximum DP. A transmitter with a DP accuracy of ±0.075% of span produces a flow error of approximately ±0.75% of span at 10% flow.
This is why most DP flow loops have a low-flow cutoff (typically at 10 to 25% of maximum flow) below which the flow reading is forced to zero. Without this cutoff, noise in the DP signal becomes noise in the square root output, producing wildly oscillating low-flow readings.
At 10% of maximum flow, the DP is only 1% of the maximum DP. A transmitter with a DP accuracy of ±0.075% of span produces a flow error of approximately ±0.75% of span at 10% flow.
This is why most DP flow loops have a low-flow cutoff (typically at 10 to 25% of maximum flow) below which the flow reading is forced to zero. Without this cutoff, noise in the DP signal becomes noise in the square root output, producing wildly oscillating low-flow readings.
√ΔP
Flow is proportional to the square root of DP — not to DP directly
±0.5%
Typical acceptance limit for a DP flow transmitter calibration at each calibration point
5 points
0%, 25%, 50%, 75%, 100% of DP span — same as level transmitter calibration
4 mA
Output at zero flow (0% DP). Not 4 mA at minimum flow — 4 mA always corresponds to zero DP.
Before You Start: Calibration Equipment and Checks
A DP flow transmitter calibration requires a calibrated DP source, a reference DP standard (digital indicator, ±0.025% accuracy), and a calibrated mA meter or loop calibrator.
Before applying any pressure, complete these pre-calibration checks.
Tip: Verify the transmitter range before touching anything.
Connect the HART communicator and read the configured DP span. If the transmitter is ranged for 250 mbar but the primary element was sized for a 500 mbar span, every calibration point will be applied at the wrong DP input.
Confirm the span against the instrument data sheet before proceeding.
Connect the HART communicator and read the configured DP span. If the transmitter is ranged for 250 mbar but the primary element was sized for a 500 mbar span, every calibration point will be applied at the wrong DP input.
Confirm the span against the instrument data sheet before proceeding.
Tip: Check the square root extractor setting.
Some DP transmitters have the square root extraction disabled — they output a linear 4-20 mA proportional to DP, with the square root done externally in the DCS or flow computer.
Calibrate the transmitter in the mode it actually operates in. If the square root is in the DCS, calibrate the transmitter as a linear DP device (like a pressure transmitter) and verify the DCS output separately.
Some DP transmitters have the square root extraction disabled — they output a linear 4-20 mA proportional to DP, with the square root done externally in the DCS or flow computer.
Calibrate the transmitter in the mode it actually operates in. If the square root is in the DCS, calibrate the transmitter as a linear DP device (like a pressure transmitter) and verify the DCS output separately.
5-Point DP Flow Transmitter Calibration Procedure
1
Isolate and equalise the transmitter.
Close the high-side and low-side root valves. Open the equalising valve to bring both sides of the DP transmitter to the same pressure. This sets the true zero differential pressure condition. Verify the transmitter output is at 4.00 mA (±0.05 mA) at zero DP. If not, this is an as-found zero error — record it before making any adjustment.
2
Connect the calibration source to the high-pressure side.
Vent the low-pressure side to atmosphere (or maintain the reference pressure used during the original calibration). Connect the precision DP source to the high-pressure side. Apply DP inputs corresponding to 0%, 25%, 50%, 75%, and 100% of the calibrated DP span.
3
Record as-found readings at all five DP points — do not adjust yet.
At each point, allow the reading to stabilise, then record both the actual mA output and the indicated flow reading (if the square root extractor is internal). Calculate the error at each point. If any point exceeds the acceptance limit, raise a non-conformance before adjusting. See the correction factor guide.
4
Adjust zero and span if required.
For a HART smart transmitter, use sensor trim (lower and upper trim) via HART communicator to correct the DP input side. Use output trim to correct the 4 mA and 20 mA endpoints if needed. See the sensor trim and output trim guide for the step-by-step trim procedure.
5
Record as-left readings at all five points and verify the square root output.
After adjustment, re-apply all five DP inputs and record the as-left mA values. For a transmitter with internal square root extraction, also verify the flow output at each point using the formula I = 4 + 16 × √(DP/DP_max). Sign and date the calibration record. Restore all valves to normal service position.
Expected mA at Each Calibration Point
Expected mA — Linear DP Mode (no internal square root)
I = 4 + (DP% / 100) × 16
0% DP: 4.00 mA (zero flow)
25% DP: 8.00 mA
50% DP: 12.00 mA
75% DP: 16.00 mA
100% DP: 20.00 mA
25% DP: 8.00 mA
50% DP: 12.00 mA
75% DP: 16.00 mA
100% DP: 20.00 mA
Expected mA — Square Root Mode (internal √DP extraction)
I = 4 + 16 × √(DP%/100)
0% DP: 4.00 mA (0% flow)
25% DP: 4 + 16 × √0.25 = 4 + 8.00 = 12.00 mA (50% flow)
50% DP: 4 + 16 × √0.50 = 4 + 11.31 = 15.31 mA (70.7% flow)
75% DP: 4 + 16 × √0.75 = 4 + 13.86 = 17.86 mA (86.6% flow)
100% DP: 20.00 mA (100% flow)
25% DP: 4 + 16 × √0.25 = 4 + 8.00 = 12.00 mA (50% flow)
50% DP: 4 + 16 × √0.50 = 4 + 11.31 = 15.31 mA (70.7% flow)
75% DP: 4 + 16 × √0.75 = 4 + 13.86 = 17.86 mA (86.6% flow)
100% DP: 20.00 mA (100% flow)
The 25% DP point is 12.00 mA in square root mode — the same as the 50% point in linear mode. This confuses many technicians on first calibration. Always confirm which mode the transmitter is operating in before interpreting the output readings.
Did You Know? Most modern DP flow transmitters output the square root of DP as the primary variable (PV) on the HART protocol, while simultaneously transmitting the raw DP as a secondary variable (SV) on the same loop.
A HART communicator can display both values simultaneously. This lets you verify the square root extraction in the transmitter without needing to calculate it manually.
If the SV (raw DP) reads correctly but the PV (flow output) does not match the expected √DP value, the square root extraction setting or the DP span configuration is incorrect in the transmitter — not a sensor error.
A HART communicator can display both values simultaneously. This lets you verify the square root extraction in the transmitter without needing to calculate it manually.
If the SV (raw DP) reads correctly but the PV (flow output) does not match the expected √DP value, the square root extraction setting or the DP span configuration is incorrect in the transmitter — not a sensor error.
5-Point Error Calculator
5-Point As-Found / As-Left Error Calculator
Enter actual mA readings to calculate error at each calibration point. Select linear or square root mode.
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Watch: How to Calibrate a DP Flow Transmitter
Calibration Questions
What is the difference between calibrating a DP flow transmitter versus a standard pressure transmitter?
A DP flow transmitter with internal square root outputs mA proportional to √DP, not DP. At 25% DP, the expected output is 12.00 mA in square root mode versus 8.00 mA in linear mode.
Why is a 5-point calibration needed for a DP transmitter on a flow loop?
The square root function is non-linear, so endpoint checks alone are insufficient. The 5-point procedure catches mid-range linearity errors in the square root extraction at 0%, 25%, 50%, 75%, and 100% of DP span.
What causes a low-flow reading error in a DP flow transmitter?
At 10% flow, DP is only 1% of maximum. Small DP errors and noise are amplified by the square root function at these low values. Most DP flow loops apply a low-flow cutoff at 10 to 25% of maximum to prevent false readings.
What is the correct zero DP condition for calibration?
Zero DP is when both sides of the transmitter are at exactly the same pressure. Open the equalising valve on the 3-valve or 5-valve manifold with both root valves closed. Output should read 4.00 mA at this condition.
How do I check if the square root extractor is active in my DP flow transmitter?
Connect a HART communicator and check the output mode configuration: linear or square root. Alternatively, apply 25% of DP span: if the output is 12.00 mA, the square root is active. If 8.00 mA, the output is linear.
External References
- DP Flow Measurement: Transmitter Selection and Calibration | Emerson Rosemount
- How to Calibrate a DP Flow Transmitter | Yokogawa (2025)
What We Learn Today
- A DP flow transmitter outputs 4-20 mA proportional to √DP (not DP). At 25% DP, the expected output in square root mode is 12.00 mA — not 8.00 mA.
- Always confirm whether the square root extraction is internal (in the transmitter) or external (in the DCS/flow computer) before calibrating. The expected mA values at each point are completely different.
- Apply a low-flow cutoff (typically 10 to 25% of maximum flow) to prevent DP noise from being amplified by the square root function at low flows.
“Calibrating a DP flow transmitter without checking the square root output is like calibrating a thermometer in Celsius and not verifying the Fahrenheit display. The sensor may be right and the output still wrong.”