Thermocouple Calculator

A thermocouple produces an emf from the difference between its measuring junction and its reference junction. The published reference functions assume that reference junction is held at 0 °C — an ice bath, historically. Real instruments terminate at a block sitting at room temperature instead, so the voltage arriving at the input is smaller than the tables expect by exactly the emf of the block's own temperature. Adding that back before inverting is cold-junction compensation, and getting it wrong shifts every reading by roughly the room temperature.

Neither direction is a single formula. Going from temperature to voltage, each sub-range is a polynomial E = Σ cᵢ·tⁱ in °C, and type K carries an extra exponential term above 0 °C: a₀·exp(a₁·(t − a₂)²) with a₀ = 0.1185976 mV, a₁ = −1.183432×10⁻⁴ and a₂ = 126.9686. That term is not a rounding detail — at 100 °C it contributes 108.82 µV, so dropping it returns 3987.41 µV instead of the tabulated 4096.2 µV, about 2.7 °C low while still looking entirely plausible. The inverse direction is a separate fit, t = Σ dᵢ·Eⁱ, rather than an exact reversal of the forward polynomial — for type K NIST publishes it in three pieces, −5.891…0 mV, 0…20.644 mV and 20.644…54.886 mV, each with its own residual band. So this tool reports which sub-range applied and the band NIST publishes for it, instead of presenting a number as if it were exact.

Thermoelectric voltage against temperature, reference junction at 0 °C, in millivolts rounded to 0.1 µV. Type K spans the widest range, so it sets the rows; types J and T appear at the temperatures their own tables publish. These are the values the calculator above returns — if your meter terminates at room temperature rather than in an ice bath, subtract the cold junction's own voltage from the table figure to get what the meter will actually show.

Two things the rows make visible. Type J produces more voltage than type K at every temperature the two tables share — 5.2689 against 4.0962 mV at 100 °C — which is why a J couple on a K-configured input reads high rather than merely noisy. And the spacing is not constant: type K averages 41.0 µV per °C over its first 100 °C but only 34.4 µV per °C between 1300 and 1372 °C, so the sensitivity a two-point calibration assumes near room temperature is not the sensitivity you get at the top of the range. Type J is printed to 1 µV rather than 0.01 µV above 760 °C in the source tables, so the 800, 1000 and 1200 °C rows carry one fewer digit. Types R and S are charted in the next section; E, N and B are in the calculator above but not charted here.

The platinum-rhodium types read differently enough from the base-metal ones that charting them on the same rows would be misleading: at 1000 °C a type R couple produces 10.50596 mV where type K produces 41.2756 mV, about a quarter of the output. Values below are thermoelectric voltage against temperature with the reference junction at 0 °C, printed to the digit the source tables publish, at the temperatures those tables list.

Type R sits above type S at every temperature the two tables share, and the gap widens with temperature — 0.6474 against 0.64591 mV at 100 °C is a 1.5 µV difference, while 21.10148 against 18.69251 mV at 1768 °C is 2.4 mV. The two are not interchangeable at the top of the range even though their ranges and alloys are usually quoted together. The 1064 °C row is where NIST switches inverse sub-range: above 11.361 mV for type R, and above 10.332 mV for type S, the mV-to-°C fit changes and its published residual band tightens to −0.0005…+0.001 °C for R and ±0.0002 °C for S, the narrowest bands NIST publishes for any type — then widens again to about ±0.002 °C in the final sub-range above 1664.5 °C. All of those are far below any sensor tolerance, so it is the thermocouple and not the arithmetic that limits you there.

Coefficients from the NIST ITS-90 Thermocouple Database, cross-checked against NIST Monograph 175 (Burns et al., 1993). Wire colour codes and tolerance classes belong to ANSI/ASTM E230 and IEC 60584 and are deliberately not published here.

If you are sizing an input stage or sanity-checking a reading, the useful question is not the temperature span but the voltage span. Below is the millivolt range over which NIST publishes an inverse — that is, the range this calculator will convert back to temperature, with the temperature span it corresponds to. Reference junction at 0 °C throughout.

Two consequences worth reading off the table. First, the span is not proportional to the temperature range: type E covers 1200 degrees in 85.198 mV while type S covers 1818 degrees in 18.928 mV, so an input range chosen for a type E couple leaves a type S couple using about a fifth of it — and with it, a fifth of the resolution. Second, these voltage bounds are narrower at the cold end than the reference functions themselves. The forward functions for types K, E, N and T reach −270 °C — type K produces −6.4577 mV there, type N −4.3451 mV — but NIST publishes no inverse below −200 °C for them, and none below 250 °C for type B, so this calculator refuses those voltages rather than extrapolating a plausible-looking number.