Resistance to Temperature Calculator (incl. PT100 & PT1000)
Evaluate temperature variations in windings and RTD sensors. Convert measured electrical resistance (Ω) directly into Celsius or Fahrenheit.
Resistance to Temperature Calculator
How to Use the Resistance to Temperature Converter
Calculating the final operating temperature of a wire winding or RTD sensor from its resistance is direct. Follow these steps:
- 1Select Material Coefficient: Choose your metal type (e.g. Copper) or input a custom TCR coefficient (α).
- 2Enter Reference Parameters: Input the reference resistance (R₀) and reference temp (T₀), usually measured at room temp.
- 3Enter Measured Resistance: Input the heated/cooled resistance (R) measured during operation.
- 4Click Calculate: Click 'Calculate Temperature' to view the final temperature output.
How to Calculate Resistance to Temperature (Step-by-Step Guide)
In conductive metals, electrical resistance varies predictably with temperature. As thermal energy increases, lattice vibrations increase, which scatters current carriers and raises measured resistance. We compute this variation using the formulas below.
Conductor Resistance Temperature Formula
Where:
- T: Final calculated operating temperature in Celsius (°C)
- T₀: Baseline reference temperature in Celsius (°C)
- R: Measured resistance at final temperature in Ohms (Ω)
- R₀: Baseline resistance at reference temperature in Ohms (Ω)
- α (alpha): Temperature coefficient of resistance per degree Celsius (/°C)
Real-Life Scenario: Testing a Copper Motor Winding (10 Ohms to 12 Ohms)
A motor winding is made of copper (α = 0.00393). Its cold resistance R₀ is measured as 10 Ohms at standard room temperature T₀ of 20°C. After running the motor under full load, the hot resistance R measures 12 Ohms. Sizing the winding temperature rise is calculated as:
- 1Identify Parameters:
R₀ = 10 Ω,T₀ = 20°C,R = 12 Ω,α = 0.00393. - 2Solve the temperature deviation:
T = 20 + ((12 − 10) ÷ (0.00393 × 10))
T = 20 + (2 ÷ 0.0393) ≈ 20 + 50.89 = 70.89°C - 3Convert to Fahrenheit:
T(°F) = (70.89 × 1.8) + 32 = 159.60°F
Final Output: The copper motor winding operating temperature is exactly 70.89°C (159.60°F).
Resistance to Temperature Reference Conversion Chart
The table below displays pre-calculated resistance values (Ω) across typical temperatures for a standard copper conductor presenting a baseline resistance of 10.00 Ω at 20°C:
| Conductor Temperature (°C) | Conductor Temperature (°F) | Copper Winding Resistance (Ω) |
|---|---|---|
| 20°C | 68°F | 10.00 Ω |
| 30°C | 86°F | 10.39 Ω |
| 40°C | 104°F | 10.79 Ω |
| 50°C | 122°F | 11.18 Ω |
| 60°C | 140°F | 11.57 Ω |
| 80°C | 176°F | 12.36 Ω |
| 100°C | 212°F | 13.14 Ω |
Resistance to Temperature Conversion Table
Having a resistance to temperature conversion table is highly useful during industrial sensor inspections to verify RTD resistance outputs without manual calculations.
Resistance to Temperature Conversion Formula
The standard resistance to temperature conversion formula utilizes the material-specific temperature coefficient (TCR) to establish temperature shift vectors:
T = T₀ + ((R - R₀)/(α × R₀)).
Resistance to Temperature Calculation
Completing a resistance to temperature calculation is crucial in sizing motor windings, transformer cores, and electrical grid transmission line sag limits.
Resistance to Temperature Chart
A calibrated resistance to temperature chart displays pre-calculated ohm values for RTD models, standardizing calibration steps in industrial process controls.
Resistance to Temperature Graph
Plotting a resistance to temperature graph displays the linear coefficient limits of pure metals compared to the non-linear curves of negative coefficient thermistors.
Resistance to Temperature Sensor
An industrial resistance to temperature sensor (such as a Pt100 RTD) uses a small platinum film to change resistances predictably with heat variations.
PT100 and PT1000 Resistance to Temperature
PT100 and PT1000 sensors are platinum RTDs with 100 Ω and 1000 Ω at 0 °C. Their resistance follows the Callendar–Van Dusen equation from IEC 60751, which is more accurate than a single coefficient. The PT100 / PT1000 mode solves this equation for temperature.
Example: a PT100 reading 138.51 Ω is at 100.0 °C.
| Temperature (°C) | PT100 (Ω) | PT1000 (Ω) |
|---|---|---|
| 0 | 100.0 | 1,000 |
| 25 | 109.7 | 1,097 |
| 50 | 119.4 | 1,194 |
| 100 | 138.5 | 1,385 |
| 150 | 157.3 | 1,573 |
| 200 | 175.9 | 1,759 |
| 300 | 212.1 | 2,121 |
Frequently Asked Questions (FAQs)
Subtract reference resistance from measured resistance, divide by reference resistance times TCR (α), then add reference temperature: T = T₀ + (R - R₀)/(αR₀).
A standard Pt100 platinum sensor has a baseline resistance of exactly 100 Ohms at 0°C, and increases by approximately 0.385 Ohms per degree Celsius rise.
It represents standard room temperature reference resistance (R₀) used as the baseline comparison point for conductor heating calculations.
Use the linear expansion equation: R = R₀ × (1 + α(T - T₀)), where α is the material coefficient and T is final temperature.
For standard copper, resistance increases by 0.393% per degree Celsius rise. Aluminum increases by 0.403% per degree Celsius.
A temperature of 20°C corresponds to exactly 68°F (Fahrenheit) or 293.15 K (Kelvin), which serves as standard laboratory reference temperature.
