# RTD Temperature Coefficient Calculation

**What is the coefficient factor of RTD?**

- Resistance Temperature Detectors (RTDs), also known as platinum resistance thermometers (PRTs), are widely used temperature sensors that rely on the principle that the resistance of a metal, in this case, platinum, increases with temperature.
- RTDs functions according to the theory that the resistance of a metal will increase as temperatures increase.
- The Temperature Coefficient of Resistance (TCR), denoted by αo, is a crucial parameter for RTDs.
- It represents the average resistance change per degree Celsius over a specified temperature range, usually 0°C to 100°C, divided by the resistance of the RTD, Ro, at 0°C.

**How is RTD coefficient calculated?**

Here’s a step-by-step explanation of how to calculate the TCR for a PT100 RTD, along with an example calculation:

**α**_{o}** = (R**_{100}**−R**_{0}**) / (R**_{0}** X 100**^{o}**C) ** – Equation no. 1

R0 is the resistance of the RTD at zero degrees Celsius (ohm).

R100 is the resistance (ohm) of the RTD at 100 °C.

Note: For the purpose of this conversation, we will only be referring to RTD PT100.

The relationship between resistance (Rt) and temperature (t) for a PT100 RTD is described by the following formula:

**R**_{t}**= R**_{0}**(1+α**_{o}**.t)**** **** ** – Equation no. 2

Where:

R_{t } is the RTD‘s output resistance in Ohms at temperature t.

R_{0} is the resistance of the RTD at 0°C (ohms).

*α*_{o} is the temperature coefficient of resistance (TCR) at 0°C (per °C).

t is the temperature in degrees Celsius.

**Example Calculation**

Platinum RTD PT100 has a resistance of 100 ohms at 0 degrees Celsius and 139.1 ohms at 100 degrees Celsius.

- Find out how much resistance the RTD has at a temperature of 60 degrees Celsius.
- Perform the TCR (Temperature Coefficient of Resistance) calculation for platinum.
- Determine the temperature at which the resistance is 120 degrees Celsius.

**What is temperature coefficient of Pt100?**

**Perform the Temperature Coefficient Calculation on the RTD PT100**.

From Equation no.1:

α_{o} = (R_{100}−R_{0}) / (R_{0} X 100^{o}C)

α_{o} = (139.1 -100) / (100 X 100)

α_{o} = 0.00391 per degrees Celsius

**Determine the RTD’s resistance at 60°C**

From Equation no.2:

R_{t}= R_{0}(1+α_{o}.t)

R_{60} = R_{o}(1 + αt)

R_{60} = 100(1 + 0.00391×60)

R_{60} = 123.46Ω

**Determine the temperature at which the resistance is 120**

From Equation no.2 :

R_{120} = R_{o}(1 + αt)

120 = 100(1 + 0.00391t)

1 + 0.00391t =120/100

0.00391t = 1.2-1

t = 0.2/0.00392

t = 51.02 degrees Celsius

Refer the link for **RTD Calculator: Converting Process Temperature to measured Output Resistance****.**

Refer the link for** ****RTD Calculator: Converting Measured Resistance to Process Temperature****.**

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