How to Calculate NTC Resistance and Temperature: Worked Examples

When to use an NTC equation

An NTC thermistor’s resistance falls as its temperature rises. A resistance-to-temperature model lets a controller convert a measured resistance into temperature, or lets an engineer estimate resistance at a design temperature. The calculation is only as reliable as the part-specific R/T data, model, measurement circuit, and calibration behind it. This guide gives a worked example; it is not an online calculator and the example values do not represent a specific Starlight product.

Inputs and units

For the simple Beta model, you need the nominal resistance at a reference temperature (commonly R₂₅), the corresponding reference temperature T₀, and a Beta value specified for a temperature pair such as B_25/50. Use the exact B interval and R/T data stated in the selected thermistor’s datasheet.

• Use absolute temperature in kelvin in the equation: K = °C + 273.15.
• Use the same resistance units for R and R₀ (for example, both in Ω or both in kΩ).
• Beta is expressed in kelvin (K); use natural logarithm ln.
• Do not treat an NTC’s B value as the A, B, C coefficients of a Steinhart–Hart model.

Beta equation

To estimate resistance at temperature T from a known resistance R₀ at T₀, use:

R(T) = R₀ × exp[B × (1/T − 1/T₀)]

To estimate temperature from measured resistance R, rearrange:

T = 1 ÷ [1/T₀ + ln(R/R₀)/B]

Both T and T₀ in these formulas are kelvin. A Beta value is a two-point approximation for the specified interval; the result can diverge from the actual part curve, especially outside that interval. For the definition and limits of B values, see TDK’s NTC thermistor technical information.

Worked 10 kΩ example

For illustration only, assume a thermistor with R₂₅ = 10.0 kΩ and B_25/50 = 3950 K. These are example inputs, not a specification for a particular product.

Estimate resistance at 30 °C

Convert temperatures: T₀ = 25 + 273.15 = 298.15 K; T = 30 + 273.15 = 303.15 K. Substitute into the Beta equation:

R(30 °C) = 10.0 kΩ × exp[3950 × (1/303.15 − 1/298.15)] ≈ 8.04 kΩ.

Estimate temperature from an 8.00 kΩ reading

T = 1 ÷ [1/298.15 + ln(8.00/10.0)/3950] ≈ 303.26 K = 30.11 °C.

These rounded calculations omit resistance and Beta tolerances, self-heating, lead and circuit effects, ADC error, and calibration uncertainty. Use the model’s R/T table or a validated conversion implementation when the error budget requires more precision.

Beta, Steinhart–Hart, or R/T table?

• Beta equation: a compact two-point approximation for a defined temperature interval when the datasheet provides R₀ and B.
• Steinhart–Hart: a three-coefficient empirical model, commonly written 1/T = a + b ln(R) + c[ln(R)]³. Use the coefficients supplied or calculated for the exact thermistor; the coefficients depend on the resistance units and curve fit.
• Manufacturer R/T table: use table values or interpolation when supplied, especially if the required interval is broad or the model error needs closer control.

The Beta and Steinhart–Hart equations are different model forms; the B value is not interchangeable with any one Steinhart–Hart coefficient. Analog Devices’ thermistor transfer-function note describes how the Beta and Steinhart–Hart approaches use different input data.

For a background on Beta and R/T curves, see our NTC thermistor alpha and beta guide and the B3950 selection guide.

OEM design checks

Before release, check that the selected part’s resistance tolerance, Beta interval and tolerance, operating range, dissipation/self-heating behavior, package, lead arrangement, and environmental qualification fit the application. Validate the complete sensing circuit over the required operating range; changing the thermistor model, excitation current, mounting, or thermal contact can change system error.

If you are sourcing a custom assembly, share your target R₂₅, R/T curve or Beta interval, tolerance, operating range, lead and package requirements, and test conditions. Explore NTC thermistor products or request an OEM quote.