Metered history
A series mA reading on the correct range, the 250-ohm sampling voltage, and the DCS trend for the same minute. Estimates end where the calibrator begins.
Methodology
Explicit-input models with visible formulas, instrument-grade unit conventions, machine-checked test cases, and a stated verification boundary. Screening-grade arithmetic for loop checks and calibrations, not custody transfer.
The principle
Each calculator is a fixed formula over labeled inputs. There are no hidden scores, no black-box adjustments, and no location lookups: the numbers you type, plus the stated defaults, fully determine the outputs. Every calculator page shows its formula, and every calculator ships with automated test cases that fixed inputs must reproduce before publication.
Units and conventions
4-20 mA maps linearly: I = 4 + 16 x fraction. 0-10 V maps as V/10 of span unless the transmitter is 2-10 V live-zero. PLC raw counts always pass through the module profile first (for example 4 mA is 5530 counts on the S7-1200 4-20 mA range, not zero). Percent of span is (I - 4)/16 on current loops.
Temperatures stay in Celsius internally; Fahrenheit and Kelvin are display conversions only. Resistance stays in ohms with full precision through the Callendar-Van Dusen and Beta equations; rounding happens once, at display. Tolerances are %FS (percent of span) unless the input label says otherwise.
Copper lead resistance uses 0.0172 ohm·mm2/m at 20 C with a 0.393 %/C temperature coefficient. Loop supply margin is computed at the design current (20 mA plus alarm over-range, typically 21-22 mA), not at 4 mA. Encoder counts use PPR x decode mode (X1/X2/X4) as effective CPR everywhere.
Outputs are screening-grade: good enough to size a first pass, pick a wire or resistor, or check a field reading. They are not calibration certificates and do not replace a calibrator, a DCS trend, or a metered loop test.
Method by category
Linear scaling EU = low + fraction x span, both directions: mA/V/counts to engineering units and back. Wire-break (below 3.6 mA, NAMUR NE43) and over-range (above 20.5 mA) flags ride alongside every conversion, plus the 250-ohm sampling voltage for DCS mismatch checks.
Supply minus 20 mA x total resistance minus barrier drop minus transmitter minimum equals margin. Cable drop uses 2 x I x rho x L / S with temperature correction. The 250-ohm resistor dissipates 0.1 W at 20 mA and carries a derating plus tolerance-band check.
PT100/PT1000 use the Callendar-Van Dusen quadratic above 0 C; below 0 C the page says table, not extrapolation. Two-wire error is lead ohms / (R0 x A), about 2.5 C per ohm on PT100. Type K/J/T/N thermocouples convert through a stated Seebeck coefficient with explicit cold-junction compensation.
Effective CPR = PPR x decode mode. RPM = frequency x 60 / CPR; the counter frequency limit back-calculates maximum usable RPM. Linear axes use lead-screw pitch / CPR for um-per-count resolution and counts-per-mm for electronic gearing.
Two-point trim solves gain = (std2 - std1)/(raw2 - raw1), offset = std1 - gain x raw1, verified against a third check reading. Span error and hysteresis are %FS against the accuracy class (0.1/0.25/0.5). ADC resolution is span / 2^bits in engineering units, checked against the required tolerance.
Table segments interpolate linearly with slope and fraction shown; out-of-range readings raise an extrapolation flag instead of silently extending. dP flow uses Q = Qmax x sqrt(dP/dPmax) with a low-flow cutoff band. NTC thermistors use 1/T = 1/T0 + ln(R/R0)/B in Kelvin with the part-number Beta.
Sources and baselines
Coefficients are named, not hidden: Callendar-Van Dusen A = 3.9083e-3, B = -5.775e-7; copper rho = 0.0172 ohm·mm2/m at 20 C, alpha = 0.00393/C; NAMUR NE43 thresholds 3.6/20.5 mA; PLC profiles per Siemens S7 and Allen-Bradley manuals. Defaults carry their source; a yearly review checks them against current manufacturer tables.
Where loop practice is discussed, manufacturer installation manuals and NAMUR recommendations are cited as context for why a rule exists, never as installation instruction. The site procedure and the instrument engineer always govern.
Typical Seebeck values (K 41, J 51, T 41, N 39 uV/C), NTC Beta anchors, and encoder PPR examples are labeled as starting points. Nameplate data and manufacturer sheets replace them during verification.
Verification protocol
A series mA reading on the correct range, the 250-ohm sampling voltage, and the DCS trend for the same minute. Estimates end where the calibrator begins.
Module profile and range card: S7 or AB, 0-20 vs 4-20 mA, raw low/high counts exactly as configured this shift.
Nameplate facts: transmitter range, RTD type and wiring (2/3/4-wire), resistor tolerance and rating, encoder PPR and decode mode.
Lead length and gauge, ambient temperature, barrier drops, and supply voltage that no generic model can see.
A qualified instrument engineer confirms the conclusion before a loop is commissioned or a transmitter is trimmed.
Coefficients are stated starting points, not live process data. Calculator results are screening outputs, not calibration certificates, loop approvals, or guarantees.
Known limits
Nothing here determines whether a loop is fit for service. Barrier selection, area classification, and SIL ratings are field decisions under the site procedure.
Scaling tools assume a linear transmitter characteristic. Bent curves need segmented calibration, which these tools flag but do not fit.
Interpolation inputs project arithmetic, not the process. They show sensitivity to table spacing; they do not predict drift, fouling, or sensor aging.
Default profiles never describe your module. Two channels on different range cards can legitimately disagree on the same loop current.