Thermocouple & RTD uncertainty calculator
Build a measurement-uncertainty budget for a comparison calibration of a thermocouple or RTD. Enter each contributor in °C, pick its distribution, and get the combined standard uncertainty and the expanded uncertainty at k = 2 using the GUM (JCGM 100) method. Everything runs in your browser.
Your contributors
For labeling only. The budget is the same; uncertainty is reported at this point.
Contributors (each in °C)
Leave any at 0 to exclude it. Pick the distribution that matches the source.
Uncertainty budget
Combined standard uncertainty u_c = sqrt(Σ u_i²); expanded uncertainty U = k·u_c with k = 2 (≈ 95%).
Temperature uncertainty budgets, in plain terms
What goes in a temperature uncertainty budget
When you calibrate a temperature sensor by comparison — sitting the unit under test next to a reference in a bath, dry block, or furnace — the difference you record is not perfect. A budget lists every source that adds scatter or bias and converts each one to a comparable number. The usual terms are the reference standard (from its certificate), the readout or indicator accuracy, the readout resolution, repeatability of the comparison, the bath or block uniformity and stability, the unit-under-test resolution, and — for thermocouples only — the reference-junction (cold-junction) compensation. Entering them all in °C keeps the budget consistent and avoids the trap of converting microvolts through a Seebeck coefficient that changes with temperature.
Why RSS / combined uncertainty
Each raw value first becomes a standard uncertainty by dividing by the divisor for its distribution: a certificate value at k = 2 is divided by 2, a manufacturer accuracy or tolerance band (rectangular) by √3, a digital resolution by 2√3, a triangular quantity by √6, and a standard deviation from repeats is already k = 1. Because these sources are independent, the GUM combines them as the root sum of squares, u_c = sqrt(u_1² + u_2² + …), rather than adding them linearly. Linear addition would assume every error peaks together, an unrealistic worst case that overstates the result. Multiplying the combined value by a coverage factor k = 2 gives the expanded uncertainty U at roughly 95% — the form quoted on calibration certificates.
Thermocouple vs RTD contributors
The budgets are mostly the same, with one difference. A thermocouple generates a small voltage that depends on the temperature difference between its measuring junction and a reference junction, so the reference-junction (cold-junction) compensation is a real, often significant contributor. An RTD such as a Pt100 measures resistance directly and has no thermoelectric junction, so that term simply does not exist — this tool removes it when you select an RTD. Thermocouples also tend to have larger inhomogeneity and drift, so their repeatability and reference-standard terms are usually larger than a comparable RTD's. For the standard methods and worked examples behind these budgets, see the GUM (JCGM 100:2008), EURAMET cg-8 for temperature, and ASTM E220 for thermocouple calibration by comparison.
Common questions
-
How do I calculate thermocouple measurement uncertainty?
List every contributor that adds scatter or bias to the reading — the reference standard from its certificate, the readout accuracy and resolution, repeatability, the bath or block uniformity and stability, the unit-under-test resolution, and the reference-junction (cold-junction) compensation. Convert each one to a standard uncertainty by dividing by the divisor for its distribution (k = 2 normal divides by 2, rectangular by √3, and so on). Combine them in quadrature, u_c = sqrt(Σ u_i²), then expand with k = 2 to get U at about 95%. That is the GUM (JCGM 100) method this calculator follows.
-
What is k = 2 (expanded uncertainty)?
The combined standard uncertainty u_c is a one-sigma value: roughly a 68% coverage interval. To report a 95% interval you multiply by a coverage factor k. For an approximately normal result k = 2 gives about 95% coverage, and U = k·u_c = 2·u_c is the expanded uncertainty. Calibration certificates almost always quote U at k = 2, so this tool defaults to k = 2.
-
Do I include reference-junction uncertainty for an RTD?
No. The reference-junction (cold-junction) term applies only to thermocouples, where the measuring circuit needs a known temperature at the junction with the readout. RTDs such as a Pt100 are resistance sensors with no thermoelectric junction to compensate, so there is no reference-junction contributor. This calculator hides that input when you select an RTD.
-
Why combine the contributors in quadrature instead of just adding them?
The contributors are independent sources of error, so they do not all push the reading the same way at the same time. Adding them linearly would assume a worst case that almost never happens and would overstate the uncertainty. The GUM combines independent standard uncertainties as the root sum of squares — u_c = sqrt(u_1² + u_2² + …) — which is the statistically correct way to propagate independent variances.
-
What distribution divisor should I use for each input?
Use a value from a calibration certificate at k = 2 with the k = 2 setting (÷2). Use rectangular (÷√3) for a manufacturer accuracy spec or a tolerance band where any value in the range is equally likely. Use the resolution setting (÷(2√3)) for a digital display least-significant digit. A standard deviation from repeated readings is already a standard uncertainty, so use k = 1 (÷1). Triangular (÷√6) suits a quantity more likely to sit near the middle of its range.
-
Is this a substitute for a full uncertainty budget or accredited procedure?
No. It is an estimator that applies the standard GUM combination to the contributors you enter, so you can size a budget and see which term dominates. A rigorous budget may need sensitivity coefficients, correlation between sources, a proper type-A analysis with enough degrees of freedom, and the effective coverage factor from the Welch–Satterthwaite equation. Treat the result as a working estimate and validate it against your documented procedure (EURAMET cg-8, ASTM E220) before reporting.
This calculator is an uncertainty-budget estimator that applies the standard GUM (JCGM 100:2008) root-sum-of-squares combination to the contributors you enter. It is not a full type-A and type-B analysis and does not include sensitivity coefficients, correlation between sources, effective degrees of freedom, or your accredited calibration and measurement capability. It does not replace the GUM, EURAMET cg-8, or ASTM E220, or your laboratory’s documented procedure. Treat the result as a working estimate and validate it against your own quality system before reporting.
Keep the uncertainty with the record
Axiospec keeps every calibration, uncertainty budget, and certificate in one tamper-evident ledger built for ISO/IEC 17025. See it on real calibration data, no signup.