PT100 & PT1000 Resistance to Temperature Calculator
Convert PT100 and PT1000 RTD sensor resistance measurements (Ω) directly into Celsius (°C) and Fahrenheit (°F) values using precision IEC 60751 equations.
PT100 Resistance to Temperature Calculator
How to Use the PT100 Resistance to Temperature Calculator
Follow these technical steps to convert measured electrical resistance into Celsius and Fahrenheit values for PT100 sensors:
- 1Enter the measured resistance value in ohms (Ω) across the PT100 sensor terminals.
- 2Select the desired decimal precision output format.
- 3Click the Calculate to Temperature button.
- 4Review the calculated temperature in °C and °F, and check the sensor range status.
How to Calculate PT100 Resistance to Temperature Manually
Under the international IEC 60751 standard, the electrical resistance of platinum RTD sensors scales non-linearly with temperature. Converting the measured resistance back into temperature requires solving a quadratic equation derived from the Callendar-Van Dusen equation.
Callendar-Van Dusen Standard Formula
Where:
- R: Measured electrical resistance of the sensor (Ω)
- R0: Nominal resistance at 0°C (exactly 100 Ω for PT100)
- T: Calculated temperature in Celsius (°C)
- A: 3.9083 × 10−3 °C−1
- B: −5.775 × 10−7 °C−2
To determine the temperature, we rearrange the formula into standard quadratic form: B × T2 + A × T + (1 − R / 100) = 0. Solving for temperature (T) yields the following equation:
Real-Life Worked Example (Boiler Temperature Verification)
An instrumentation engineer measures a resistance of 138.51 Ω across a PT100 sensor inside a steam boiler loop. Let's calculate the temperature step-by-step manually to verify the boiler temperature:
-
1Calculate (1 − R / R0):
1 − (138.51 ÷ 100) = 1 − 1.3851 = −0.3851 -
2Calculate 4 × B × (1 − R / R0):
4 × (−5.775 × 10−7) × (−0.3851) = 8.89581 × 10−7 -
3Compute A2:
A2 = (3.9083 × 10−3)2 = 1.52748 × 10−5 -
4Subtract the Terms Under the Square Root:
1.52748 × 10−5 − 8.89581 × 10−7 = 1.43852 × 10−5 -
5Take the Square Root:
√(1.43852 × 10−5) ≈ 0.00379278 -
6Solve for Temperature (T):
T = (−0.0039083 + 0.00379278) ÷ (2 × −5.775 × 10−7)
T = −0.00011552 ÷ −0.000001155 ≈ 100.00°C
PT100 Resistance to Temperature Table
The chart below highlights PT100 resistance values at standard temperatures from 0°C to 850°C:
| Temperature (°C) | Current Excitation (mA) | Resistance (Ω) |
|---|---|---|
| 0 °C | 1.0 mA | 100.00 Ω |
| 20 °C | 1.0 mA | 107.79 Ω |
| 50 °C | 1.0 mA | 119.40 Ω |
| 100 °C | 1.0 mA | 138.51 Ω |
| 150 °C | 1.0 mA | 157.33 Ω |
| 200 °C | 1.0 mA | 175.86 Ω |
| 300 °C | 1.0 mA | 212.05 Ω |
| 400 °C | 1.0 mA | 247.09 Ω |
| 500 °C | 1.0 mA | 280.98 Ω |
| 850 °C | 1.0 mA | 390.48 Ω |
PT100 Resistance to Temperature Chart
A standard PT100 resistance to temperature chart lists resistance values in ohms corresponding to temperature points. These charts help verify sensor operation on-site using a standard multimeter. For instance, at 0°C a PT100 reads exactly 100 Ω, and at 100°C it reads 138.51 Ω. Technicians cross-reference measured ohms with standard curves to verify accuracy class specs.
PT100 Ohm to Celsius Calculator
A PT100 ohm to celsius calculator solves the non-linear relationship between platinum wire resistance and temperature. Because the curve bends slightly at higher temperatures, using a simple linear scale introduces unacceptable errors. Solvers use quadratic equations (the Callendar-Van Dusen equations) to determine temperature with high precision down to decimal places.
RTD PT100 Resistance Table
The RTD PT100 resistance table provides standard parameters defined under standard IEC 60751 / DIN 43760. Sizing table charts help classify sensor tolerances:
- Class AA (1/3 DIN): Tolerance of ±(0.1 + 0.0017 × |t|) °C
- Class A: Tolerance of ±(0.15 + 0.002 × |t|) °C
- Class B: Tolerance of ±(0.3 + 0.005 × |t|) °C
RTD Resistance to Temperature Chart
A general RTD resistance to temperature chart covers copper (Cu), nickel (Ni), and platinum (Pt) elements. Platinum is widely chosen because it resists corrosion, is stable at high temperatures, and offers a highly linear resistance change over a wide temperature range. Charts assist in selecting the correct RTD type for dynamic industrial process controls.
Ohm to Degree Celsius Formula
The ohm to degree celsius formula is derived from the Callendar-Van Dusen equation:
R(t) = R0(1 + At + Bt²) (for positive temperatures). Solving the quadratic equation yields the standard conversion equation:
t = [-A + √(A² - 4B(1 - R/R0))] ÷ 2B. Standard coefficients are: A = 3.9083 × 10⁻³, B = -5.775 × 10⁻⁷, and R0 = 100.
FAQs About Converting PT100 Resistance to Temperature
To calculate PT100 temperature, apply the Callendar-Van Dusen quadratic equation: R = R0(1 + At + Bt²). For positive temperatures, solving for temperature (t) yields t = [-A + √(A² - 4B(1 - R/100))] ÷ 2B, where A and B are standard coefficients and R is the measured resistance in ohms.
To convert ohms to temperature, you must know the type of resistance temperature detector (RTD) sensor or thermistor used. Each sensor type (like platinum PT100, PT1000, or copper Cu10) follows a specific resistance-to-temperature characteristic table or formula defined under standards like IEC 60751.
You calculate temperature from resistance by using standard polynomial equations. For a standard platinum RTD sensor, solving the Callendar-Van Dusen quadratic equation based on coefficients A, B, and the nominal resistance at 0°C provides the precise temperature value.
The standard formula for calculating electrical resistance is Ohm's Law: Resistance (R) = Voltage (V) ÷ Current (I). In RTD temperature sensors, resistance is calculated based on temperature using: R = R0 × (1 + A × T + B × T²).
The two main formulas for resistance in electrical circuits are:
1. Ohm's Law: R = V ÷ I (derived from voltage and current).
2. Power Formula: R = V² ÷ P or R = P ÷ I² (derived from active power parameters).
The simplest way to find total resistance depends on the circuit configuration:
- For series circuits: Add all individual resistance values directly: R_total = R1 + R2 + ...
- For parallel circuits: Settle the reciprocal sum: 1/R_total = 1/R1 + 1/R2 + ...
1 Ohm (1 Ω) is the resistance of a circuit element that permits a current flow of exactly 1 Ampere when a constant electrical pressure of 1 Volt is applied across its terminals.