NTC thermistor calculator: beta and Steinhart–Hart

How the calculation works

1. 01Beta model: 1/T = 1/T₀ + (1/B) ln(R/R₀), with T in kelvin. Two datasheet values, R₀ at T₀ and B, define the curve; the inverse is R = R₀ exp[B(1/T − 1/T₀)].
2. 02Steinhart–Hart: 1/T = A + B ln R + C (ln R)³. A, B and C are solved exactly from three (R, T) points; the inverse uses Hart's closed-form solution of the cubic, so no iteration is needed.
3. 03Sensitivity of the beta model is dR/dT = −B R / T², in ohms per kelvin at the current resistance.

Limitations

• The beta equation assumes B is constant, which it is not. The error grows with distance from T₀, so it suits a narrow span around the reference point.
• A Steinhart–Hart fit is only as good as its three points and holds inside the range they bracket; extrapolating beyond them is unreliable.
• Self-heating from the measuring current is not modelled and, in a low-dissipation-constant sensor, can exceed the other errors.

Frequently asked questions

How do I convert thermistor resistance to temperature?

With the beta equation: T = 1 / (1/T₀ + ln(R/R₀)/B), in kelvin, subtracting 273.15 for °C. For a 10 kΩ, B = 3950 K thermistor measuring 10 kΩ, T = T₀ = 25 °C.

What is the Steinhart–Hart equation?

A three-coefficient fit of 1/T against ln R and (ln R)³ that describes a real NTC thermistor much more accurately than the beta equation, typically to a few millikelvin over a range of tens of degrees. The coefficients come from three calibration points.

What does the B value mean?

B (beta) is the material constant that sets how steeply resistance falls as temperature rises. A larger B means a more sensitive thermistor. It is quoted between two temperatures, usually 25 °C and 85 °C, and a different pair gives a slightly different B.

Why does an NTC thermistor read high when I hold the probe?

The measuring current heats the bead, and body heat adds to it. Both lower the resistance and so raise the reading. Keep the dissipation small and let the sensor equalise before reading.