RTD Resistance to Temperature Calculator
Temperature from the measured resistance of a platinum RTD such as Pt100 or Pt1000. With the formula, a worked example and typical values.
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Estimate only. Not engineering or safety advice. Check the result against the applicable standard and the equipment data, and have a competent engineer review it before it is relied on. Terms of use.
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About this calculator
This page calculates temperature and sensitivity at this point from measured resistance and resistance at 0 °C. Change any value or its unit and the result updates. The steps below show the working for the default values, so you can check each line against your own method.
Limits of this calculator
Two-wire connections add lead resistance, which reads as a temperature error of about 2.6 °C per ohm for a Pt100. Below 0 °C a third term is needed and this calculator does not cover it.
Cross-check: 6 reference cases, calculated from textbook formulas coded separately from the engine by the same author, agree with this calculator. This is not an independent review.
Verification status: Engineering reference
Engineering reference. Formula and method documented and tested against separately coded reference calculations. Not yet Verified: the evidence listed on this page is still needed. Basis: Callendar-Van Dusen coefficients from the RTD standard.
What this calculator checks
- The arithmetic of the published formula for the values you entered.
What remains unverified
- The constants and size lists against the licensed edition of the standard.
- Any check outside the formula shown (see the notes).
Verification register entry
| Calculation author | Rahul Sharma (author) |
|---|---|
| Technical review | No independent technical review has been carried out |
| Individual professional approval | Not recorded |
| Formula reference | not recorded |
| Standard and edition | IEC 60751, 2022 Ed 3 |
| Standard review state | Public-scope screened; licensed clause review still pending |
| Scope-screening note | Industrial platinum resistance thermometers and sensors, including the resistance-temperature relationship, are directly relevant. Confirm tolerance class, connection arrangement, self-heating and temperature range. |
| Cross-check test cases | 6 reference vectors (tests/reference_vectors.json) |
| Review date | not recorded |
| Next review date | not recorded |
| Status | Engineering reference |
Needed before this calculator can be marked Verified: reviewer name, qualification and review date; licensed clause-by-clause standard review; exact formula reference; formula source (textbook or standard); next review date.
Formula
Worked example
| Input | Value |
|---|---|
| Measured resistance | 138.51 Ω |
| Resistance at 0 °C | 100 Ω |
- R / R0 = 138.51 / 100 = 1.3851
- T = (−A + √(A² − 4B(1 − R/R0))) / 2B = 100.012 °C
- Sensitivity = R0 (A + 2BT) = 0.3793 Ω/°C
Assumptions
- Standard platinum RTD, 0 to 850 °C range
- Lead wire resistance already subtracted or a 3 or 4-wire connection
Two-wire connections add lead resistance, which reads as a temperature error of about 2.6 °C per ohm for a Pt100. Below 0 °C a third term is needed and this calculator does not cover it.
Inputs and results
| Input | Unit | Allowed or shown | Note |
|---|---|---|---|
| Measured resistance | Ω | greater than 0 Ω | |
| Resistance at 0 °C | Ω | greater than 0 Ω | 100 Ω for Pt100, 1000 Ω for Pt1000 |
| Result | Unit | Allowed or shown | Note |
|---|---|---|---|
| Temperature (°C) | (number) | Shown to 2 decimal places | |
| Sensitivity at this point (Ω/°C) | (number) | Shown to 4 decimal places |
How it is calculated
Each input is converted to the base unit of its quantity, the formula above is applied in the order shown in the worked example, and each result is shown in the unit you choose. Results are held at full precision and rounded only for display, except where a step selects a standard size, as the worked example shows. A value outside its allowed range is refused with a message instead of giving a result.
How the result changes with measured resistance
| Measured resistance (Ω) | Temperature | Sensitivity at this point |
|---|---|---|
| 139 | 101.3 | 0.3791 |
| 277 | 488.08 | 0.3345 |
| 554 | 1,489.42 | 0.2188 |
| 1,390 | — | — |
Other inputs are the same as in the worked example above.
Standards and further reading
These are textbook circuit relationships. The component data sheet sets the real limits, tolerances and ratings, and takes priority over the calculated value.
Frequently asked questions
What do I need to enter?
Enter measured resistance and resistance at 0 °C. Change the unit of a value with its selector and the result stays the same.
What does this calculator assume?
Standard platinum RTD, 0 to 850 °C range. Lead wire resistance already subtracted or a 3 or 4-wire connection.
Which calculators should I use next?
Common next steps are 4-20 mA Signal Scaling and Insulation Resistance Temperature Correction. The related links at the bottom of this page open them.
How accurate are the results?
Every figure comes from the same tested engine as the Elecmetric calculators and is meant for estimating. 6 reference cases, calculated from textbook formulas coded separately from the engine by the same author, agree with this calculator. This is not an independent review. Check design values against the standard and the equipment data you work to.
Formula guides and reference
Longer explanations with worked examples and tables, written for the same topic.
- Pt100 RTD Formulas: Resistance and Temperature: Pt100 RTD formulas: resistance from temperature (Callendar-Van Dusen), temperature from resistance
- NTC Thermistor Formulas: Beta Equation: NTC thermistor formulas: resistance from temperature with the beta equation, temperature from resistance
- Thermocouple Voltage Formulas: Thermocouple formulas: the voltage from the temperature difference
- Wheatstone Bridge Formulas: Balance and Output: Wheatstone bridge formulas: the balance condition, unknown resistance
More Electronics and Instrumentation calculatorsAll engineering calculatorsRTD Resistance to Temperature in Elecmetric