A "±0.1% accurate" transmitter is never the real accuracy of the measurement. This builds the full error budget across the loop and combines the terms properly — by root-sum-square, not by adding them up.
Standard method — stated scope limits apply
Range & Operating Point
Enter the range and the process value you want the uncertainty evaluated at. "% of reading" terms change with the reading; "% of span" terms don't.
Error Terms
Enter the loop’s error terms and calculate.
About This Calculation
Every instrument in a measurement loop — the primary sensor, the transmitter, any signal conditioning, the receiving DCS/PLC input card — contributes its own accuracy error, and these don't simply add together: independent, random errors combine in quadrature (root-sum-of-squares), meaning a loop's total uncertainty is meaningfully smaller than the sum of all the individual component errors, though larger than any single one. This calculator combines the individual accuracy specifications from a real instrument loop into the total measurement uncertainty the loop actually delivers — the number that matters for deciding whether a measurement is good enough for its intended use (custody transfer, control, or just monitoring).
Frequently Asked Questions
Why do independent errors add in quadrature (root-sum-of-squares) instead of simply adding up?
Independent random errors are statistically very unlikely to all be at their maximum, in the same direction, simultaneously — quadrature combination correctly reflects that a loop’s TOTAL uncertainty is dominated by its largest individual contributor, not inflated by naively summing every source as if they always align.
When should errors be added directly (worst-case) instead of in quadrature?
When errors are NOT independent — for example, if a single environmental factor (like ambient temperature) affects both the sensor and the transmitter’s accuracy simultaneously and in a correlated way, quadrature combination would understate the real combined effect, and a more conservative worst-case addition may be appropriate for that shared factor.
Which single component usually dominates total loop uncertainty?
It depends on the loop, but the primary sensor (RTD, thermocouple, orifice plate discharge coefficient uncertainty) is very often the largest single contributor — transmitters and receiving instrumentation have typically become accurate enough that the physical sensing element itself is usually the limiting factor in overall loop accuracy.
Does loop uncertainty include installation effects like straight-run requirements?
Not directly — this calculation combines the STATED accuracy specifications of the instruments themselves. Installation-related errors (inadequate straight run for a flow element, poor thermal contact for an RTD) are real but separate sources of error not captured in a manufacturer’s accuracy specification, and should be checked independently.