NTC Thermistor Beta Formula: Resistance–Temperature Model
The NTC beta equation is a two-parameter approximation that relates resistance to absolute temperature over a stated range. It is useful for understanding or estimating an NTC resistance–temperature (R/T) curve, but it is not the Steinhart–Hart equation and should not be treated as a universal accuracy guarantee. This guide explains the model, shows how to estimate temperature from resistance, and identifies when supplier R/T data is needed.
Table of Contents
- NTC resistance behavior
- The beta equation and its assumptions
- Estimate temperature from resistance
- Model limits and engineering use
NTC Resistance Behavior
An NTC thermistor’s resistance decreases as temperature increases. Its curve is nonlinear, so a resistance change is not a fixed linear temperature coefficient across the full range. A beta value summarizes curve behavior between stated reference temperatures; always identify that interval, such as B25/50, when comparing data.
The Beta Equation and Its Assumptions
For a reference resistance R0 at absolute temperature T0, the beta model estimates resistance R at absolute temperature T as:
R(T) = R0 × exp[B × (1/T − 1/T0)]
Temperatures must be in kelvins (K), with T(K) = t(°C) + 273.15. B is also expressed in kelvins. This model assumes one beta value adequately represents the interval being used. It is different from Steinhart–Hart, which uses a separate polynomial relationship between 1/T and ln(R).
If you have resistance measurements at two temperatures, calculate an interval-specific beta using B = ln(R1/R2) ÷ (1/T1 − 1/T2). The sign convention assumes each resistance is paired with its own temperature; use the same pairings consistently. Our NTC beta calculation guide walks through the two-point calculation and an example.
Estimate Temperature from Resistance
Rearrange the beta model to estimate temperature from a measured resistance:
T = 1 ÷ [1/T0 + ln(R/R0)/B]
Illustrative example only: assume a thermistor has R0 = 10,000 Ω at T0 = 25°C (298.15 K), and use B = 3,950 K for the interval that contains the estimate. If the measured resistance is 5,000 Ω, the model gives T ≈ 314.6 K, or about 41.5°C. This simplified example demonstrates the equation and does not specify a Starlight product or replace a datasheet curve.
Model Limits and Engineering Use
The beta model is most useful within the reference interval for which the selected B value is specified. Using one B value far outside that interval can introduce error. Resistance tolerance, B tolerance, measurement electronics, lead resistance where relevant, self-heating, thermal contact, and calibration also affect system temperature estimates.
For design approval, use the exact supplier R/T table or curve across the required operating span and validate the conversion with the production measurement circuit. Compare the controller’s input network and software conversion with the sensor data. See our NTC circuit design guide for ADC and self-heating checks, browse the NTC sensor range, or request an OEM quotation with the target curve and application details.
Technical reference: TDK, NTC Thermistor General Technical Information.
