Field Pocket Guide

Field Formulas

The relationships behind the calculators, each with a worked example. When you want the math itself, not the tool, it lives here.

01 Signals & scaling

Percent of span

% = (X − LRV) ÷ (URV − LRV) × 100

Where the value sits on the range. 75 on a 0–100 range is 75%.

mA from percent

mA = 4 + (% ÷ 100) × 16

50% of span is 12 mA. 0% = 4 mA, 100% = 20 mA. Scaling tool →

Percent from mA

% = (mA − 4) ÷ 16 × 100

12 mA reads 50%. A live 4 mA is 0%, not a dead loop.

Linear scaling

Out = OutLRV + (In − InLRV) ÷ (InURV − InLRV) × (OutURV − OutLRV)

Any span to any span. 50 °C on 0–100 °C maps to 12 mA on 4–20.

3–15 psi (pneumatic)

psi = 3 + (% ÷ 100) × 12

The old standard. 50% is 9 psi; 0% = 3 psi, 100% = 15 psi.

02 Flow & square root

Square-root extraction

%Flow = √(%DP)

Flow follows the root of differential pressure. 50% DP is 70.7% flow. Extraction tool →

Flow signal from DP signal

mA_flow = 4 + √((mA_DP − 4) ÷ 16) × 16

12 mA of linear DP becomes 15.31 mA of flow.

Flow vs differential pressure

Q ∝ √(ΔP)

Double the flow, quadruple the DP. Why a DP cell needs the root taken before it reads flow.

03 Calibration

Error, percent of span

Err% = (Measured − Ideal) ÷ (URV − LRV) × 100

Reads 12.1 mA where ideal is 12 on a 4–20 loop: +0.625% of span. Worksheet →

Turndown (rangeability)

TD = URV_max ÷ URV_min

A cell good from 10 to 250 inH2O has a 25:1 turndown.

Zero & span

Span = URV − LRV

Zero moves the LRV up or down; span sets how wide the range is. Adjust zero first, then span, then re-check zero.

04 Temperature

RTD, Pt100 (IEC 60751)

R = R0 (1 + A·t + B·t²),  t ≥ 0

A = 3.9083×10⁻³, B = −5.775×10⁻⁷, R0 = 100 Ω. At 100 °C, 138.51 Ω. RTD tool →

Thermocouple, cold junction

V_meter = E(hot) − E(reference)

The meter reads the difference. Type K hot 300 °C, terminals 25 °C ≈ 11.2 mV. TC tool →

Celsius & Fahrenheit

°F = °C × 9⁄5 + 32

100 °C = 212 °F. A 1 °C step is a 1.8 °F step.

05 Electrical

Ohm's law & power

V = I × R  ·  P = V × I

Across a 250 Ω HART resistor, 12 mA drops 3.0 V. Loop powered, two wires, one signal.

Loop burden

V_available ≥ 0.020 A × R_total

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.