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RTD & Thermocouple Calculator (PT100/PT1000 IEC 60751, K/J/T/N/E/S/R/B NIST ITS-90)

RTD: R = R₀(1 + AT + BT² [+ C(T−100)T³]) · TC: V(T) NIST ITS-90 polynomials Ω, mV, °C, °F, K, µV/°C

RTDs use IEC 60751 Callendar-Van Dusen coefficients (α = 0,00385): A = 3,9083×10⁻³, B = −5,775×10⁻⁷, C = −4,183×10⁻¹² (C used only below 0°C). Thermocouples use NIST ITS-90 polynomials for both directions. Inverse polynomial approximations introduce small errors (up to ±0,05°C typical) — well within thermocouple accuracy classes. For calibration-grade measurements consult the primary NIST tables and your sensor\'s individual calibration certificate.

Two ways of measuring temperature in industry

Industrial temperature measurement is dominated by two sensor families. RTDs (Resistance Temperature Detectors) — mostly PT100 and PT1000 — measure temperature by the change in resistance of a platinum element. Thermocouples generate a voltage across a junction of two dissimilar metals. Both convert temperature into an electrical signal, but the physics, math, and practical trade-offs are very different. This calculator handles both — accurately, using the internationally-standardized equations rather than the linear approximations that most online calculators default to.

How to use this calculator

  • RTD mode — pick sensor type (PT100, PT1000, PT200, or PT500), choose direction (temperature → resistance for design, or resistance → temperature for troubleshooting), enter the value. Uses the IEC 60751 Callendar-Van Dusen equation, which is accurate to ±0,01 Ω across the full range.
  • Thermocouple mode — pick TC type (K, J, T, N, E, S, R, or B), set the cold junction temperature (typically 20–30°C for room-temperature instruments, or 0°C to work with raw NIST tables), choose direction, enter the value. Uses NIST ITS-90 polynomials for both directions with proper cold junction compensation.

RTD — Callendar-Van Dusen equation

The IEC 60751 standard defines the resistance-temperature relationship for platinum RTDs. Above 0°C the equation is quadratic:

R(T) = R₀ × (1 + A·T + B·T²)

Below 0°C it adds a fourth-order term to model the low-temperature curvature:

R(T) = R₀ × (1 + A·T + B·T² + C·(T−100)·T³)

Where R₀ is the resistance at 0°C (100 Ω for PT100, 1000 Ω for PT1000), and the coefficients from IEC 60751 (α = 0,00385) are:

  • A = 3,9083 × 10⁻³
  • B = −5,775 × 10⁻⁷
  • C = −4,183 × 10⁻¹² (used only for T < 0°C)

Reversing the equation is easier above 0°C — you solve a quadratic. Below 0°C the fourth-order term means no closed-form solution exists, so the calculator uses Newton-Raphson iteration. Both directions give ±0,001°C accuracy relative to the IEC standard curve.

Reference RTD values (verify against your calibration certificate)

Standard reference points from IEC 60751 for PT100 (multiply by 10 for PT1000):

  • T = −200°C: R = 18,52 Ω
  • T = −100°C: R = 60,26 Ω
  • T = 0°C: R = 100,00 Ω
  • T = 100°C: R = 138,51 Ω
  • T = 200°C: R = 175,86 Ω
  • T = 500°C: R = 280,98 Ω
  • T = 850°C: R = 390,48 Ω (upper limit)

PT100 vs PT1000 — which to choose

  • PT100 — industry-standard, most common, most calibration equipment supports it directly. Downside: at 100 Ω, lead-wire resistance is significant (2 Ω of wire = 5°C error at 100°C), so you must use 3-wire or 4-wire connection for accurate results.
  • PT1000 — 10× resistance, 10× better signal-to-noise. Lead resistance becomes 10× less important, making 2-wire connection viable for short runs. Better for battery-powered wireless sensors due to lower excitation current needs. Preferred choice for newer installations.
  • PT200, PT500 — uncommon but occasionally seen in specialty applications. Same coefficients, different R₀.

Thermocouple — NIST ITS-90 polynomials

Thermocouples work by the Seebeck effect: a temperature difference between two junctions of dissimilar metals generates a small voltage (typically microvolts to tens of millivolts). The relationship between temperature and voltage is not linear, and each TC type has different coefficients. The National Institute of Standards and Technology (NIST) publishes reference polynomials in ITS-90 that model V(T) and T(V) for each type across defined temperature ranges.

This calculator uses the NIST polynomials directly — same equations that vendor instruments and calibration labs use. Accuracy is typically within ±0,05°C of the NIST reference curve.

The eight standard thermocouple types

Each has a specific composition and use case:

  • Type K (Chromel-Alumel) — the workhorse. −270 to +1372°C. Highest sensitivity below 500°C among general-purpose types (~41 µV/°C). By far the most common industrial TC.
  • Type J (Iron-Constantan) — −210 to +1200°C. Similar sensitivity to K, but iron leg is prone to oxidation above 500°C. Best for reducing atmospheres and older installations. Cheaper than K.
  • Type T (Copper-Constantan) — −270 to +400°C. Excellent for cryogenic and food industry. Very stable at low temperatures. Copper leg limits high-T use.
  • Type N (Nicrosil-Nisil) — −270 to +1300°C. Modern replacement for K in high-temperature applications, more stable over time and less prone to “green rot” degradation in the 800–1050°C range. Growing adoption.
  • Type E (Chromel-Constantan) — −270 to +1000°C. Highest sensitivity of any base-metal TC (~62 µV/°C at 25°C). Good for low-level measurements. Non-magnetic legs, good in cryogenic use.
  • Type S (Pt-10%Rh vs Pt) — −50 to +1768°C. Precision high-temperature. Very low sensitivity (~6 µV/°C) but excellent stability. Historically the reference for temperature calibration between the freezing points of antimony and gold.
  • Type R (Pt-13%Rh vs Pt) — −50 to +1768°C. Very similar to S with slightly different chemistry. Common in Europe for glass melting, ceramics.
  • Type B (Pt-30%Rh vs Pt-6%Rh) — 0 to +1820°C. Highest useful temperature. Both legs are Pt-Rh alloys, giving excellent high-T stability. Near-zero output below 250°C — useless in that range but ideal for kilns and induction furnaces.

Cold junction compensation — the critical detail

A thermocouple only generates a voltage when there is a temperature difference between the “hot junction” (measurement point) and the “cold junction” (reference point, usually the instrument terminal block). The NIST polynomials assume the cold junction is at exactly 0°C — but in practice, your terminal block is at room temperature.

The compensation is straightforward:

V_measured = V(T_hot) − V(T_cold_junction)

To recover T_hot from a measurement:

  1. Measure V at the terminals
  2. Measure the terminal block (cold junction) temperature — usually with an RTD or thermistor on the instrument
  3. Look up V(T_cj) from the NIST polynomial for that TC type
  4. Add V(T_cj) to V_measured to get “V referenced to 0°C cold junction”
  5. Look up T_hot from the inverse NIST polynomial

This calculator does all four steps automatically — enter the cold junction temperature and the measured voltage, and it computes the actual hot junction temperature. Or enter the temperatures and it computes what a real instrument would see.

RTD vs Thermocouple — which to use

  • Range — RTDs top out at 850°C (some special types to 1000°C). Thermocouples go higher: K to 1372°C, S/R to 1768°C, B to 1820°C. For anything above 850°C, a TC is your only option.
  • Accuracy — RTDs are far more accurate. Class A PT100 is ±0,15°C at 0°C, versus ±1,5°C typical for a Class 1 K-type. RTDs are the choice when you need precision.
  • Cost — TCs are cheaper for the sensor itself, but instrumentation may cost more because they need better ADC resolution and cold junction compensation. RTD sensors cost more but instrumentation is simpler.
  • Speed — TCs have very small mass and can respond in milliseconds. RTDs are slower due to the platinum wire mass, typically 1–5 seconds thermal response.
  • Ruggedness — TCs are simpler and more robust; RTDs are more delicate. In vibration or high-shock environments, TCs win.
  • Signal level — RTDs use an excitation current and produce mV-level output. TCs produce µV to mV output that’s more susceptible to noise pickup.

What this calculator doesn’t cover

  • Individual sensor calibration — the calculator uses standard IEC 60751 and NIST ITS-90 curves. Real sensors have small individual deviations documented in their calibration certificates. For calibration-grade work, use the sensor’s certificate constants, not standard curves.
  • Non-standard alpha coefficients — some older US-style RTDs used α = 0,00392 or 0,003916 (US industrial standard, not IEC). These use different A, B, C values. The calculator uses IEC 60751 α = 0,00385 which is the global standard for new installations.
  • Sensor self-heating — RTD excitation current causes I²R heating in the sensor. Below 100 µA it’s negligible, above 1 mA it can be significant (0,1–1°C error). The calculator does not model this.
  • Lead-wire compensation — 2-wire, 3-wire, and 4-wire RTD connections have different lead-resistance error characteristics. The calculator gives the theoretical R at the sensor; real measurements include lead resistance depending on wiring.
  • Thermocouple aging and drift — TCs drift with time, especially at high temperatures. Long-term accuracy in industrial installations can be significantly worse than the calibration-new specs.
  • Extension wire matching — a K-type TC connected through the wrong extension wire generates additional junctions and voltage errors. The calculator assumes proper matched extension wire back to the instrument terminal.

For serious commissioning and troubleshooting, use this calculator alongside a calibrated reference thermometer and the sensor’s individual calibration certificate. When troubleshooting, always verify the cold junction compensation is enabled on your instrument — it’s the most common source of “TC reading is wrong by ~20-30°C” complaints.

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