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Instrumentation

Square Root Extraction Calculator

In differential-pressure (DP) flow measurement, the differential pressure across a flow element is proportional to the square of flow, so flow is proportional to the square root of differential pressure. This calculator converts between differential-pressure percent (of calibrated DP span) and flow percent (of calibrated flow range) in either direction, and flags whether the result sits below an optional low-flow cutoff. It is the square-root signal relationship only — not orifice sizing, density compensation, or custody-transfer metering.

TypeInteractive engineering calculator

Calculator

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Results
Differential-pressure %25%
Flow fraction0.5
Flow %50%

Formulas

DP across element
ΔP ∝ flow²
Flow percent from ΔP percent
flow% = √(ΔP% / 100) × 100
ΔP percent from flow percent
ΔP% = (flow% / 100)² × 100

Diagram

Square-root extraction: flow% = √(ΔP% / 100) × 100100%0flow %differential-pressure %25%50%

Worked example

A DP transmitter on an orifice plate reads 25% of its calibrated differential-pressure span. What flow does that represent?

  1. 01flow fraction = √(ΔP% / 100) = √(25 / 100) = √0.25 = 0.5
  2. 02flow% = 0.5 × 100 = 50%
  3. 03Reverse check: ΔP% = (50 / 100)² × 100 = 25%
Result

25% of differential pressure corresponds to 50% of flow; 50% flow maps back to 25% differential pressure.

FAQ

Why does 25% differential pressure give 50% flow?
Differential pressure rises with the square of flow, so flow is the square root of differential pressure. √0.25 = 0.5, which is 50% flow. The two percentages are equal only at 0% and 100%.
Where is square-root extraction applied?
It can be done in the transmitter (square-root output mode), in the DCS or PLC, or in a local indicator. The rule is that it must be applied exactly once — never doubled and never missed.
What does the low-flow cutoff do?
Near zero differential pressure the square root amplifies noise, so the flow reading can become unstable. A low-flow cutoff forces the output to zero below a set flow percent to keep the reading steady and avoid totalising noise.
Does this size the orifice plate?
No. This is only the square-root signal relationship. Sizing the orifice, nozzle, or venturi is a separate flow-element design task requiring datasheets and standards.

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