Field Formulas
The relationships behind the calculators, each with a worked example. When you want the math itself, not the tool, it lives here.
Percent of span
Where the value sits on the range. 75 on a 0–100 range is 75%.
Percent from mA
12 mA reads 50%. A live 4 mA is 0%, not a dead loop.
Linear scaling
Any span to any span. 50 °C on 0–100 °C maps to 12 mA on 4–20.
3–15 psi (pneumatic)
The old standard. 50% is 9 psi; 0% = 3 psi, 100% = 15 psi.
Square-root extraction
Flow follows the root of differential pressure. 50% DP is 70.7% flow. Extraction tool →
Flow signal from DP signal
12 mA of linear DP becomes 15.31 mA of flow.
Flow vs differential pressure
Double the flow, quadruple the DP. Why a DP cell needs the root taken before it reads flow.
Error, percent of span
Reads 12.1 mA where ideal is 12 on a 4–20 loop: +0.625% of span. Worksheet →
Turndown (rangeability)
A cell good from 10 to 250 inH2O has a 25:1 turndown.
Zero & span
Zero moves the LRV up or down; span sets how wide the range is. Adjust zero first, then span, then re-check zero.
RTD, Pt100 (IEC 60751)
A = 3.9083×10⁻³, B = −5.775×10⁻⁷, R0 = 100 Ω. At 100 °C, 138.51 Ω. RTD tool →
Thermocouple, cold junction
The meter reads the difference. Type K hot 300 °C, terminals 25 °C ≈ 11.2 mV. TC tool →
Celsius & Fahrenheit
100 °C = 212 °F. A 1 °C step is a 1.8 °F step.
Ohm's law & power
Across a 250 Ω HART resistor, 12 mA drops 3.0 V. Loop powered, two wires, one signal.
Loop burden
At full 20 mA, every 250 Ω needs 5 V of headroom. Add the wiring and the sense resistors before you trust the supply.
Examples are rounded for reading. The calculators carry full precision. Confirm against your facility's procedure and reference standard.