Tools

Thermistor Steinhart-Hart coefficients

Solve the four inverse Steinhart-Hart coefficients (resistance as a function of temperature) for an NTC thermistor from four temperature and resistance calibration points.

Calculator

Calibration points

Enter the standard temperature (°C) and measured resistance (Ω) of the thermistor at four points spread across its working range. The coefficients update automatically.

Temp (°C) Resistance (Ω)
Point 1
Point 2
Point 3
Point 4
B₀ (constant) —
B₁ (1/T) —
B₂ (1/T²) —
B₃ (1/T³) —

The coefficients fit ln(R) = B₀ + B₁/T + B₂/T² + B₃/T³, with T in kelvin (T = °C + 273.15) and R in ohms — the inverse Steinhart-Hart form used to program resistance-vs-temperature tables into meters and dataloggers.

Check the fit

Convert with these coefficients

Enter a temperature to get the modelled resistance, or a resistance to get the temperature. Useful for confirming the fit reproduces your calibration points.

Temperature —
Temperature —
Resistance —

How it works

  • ln(R) = B₀ + B₁/T + B₂/T² + B₃/T³ — inverse Steinhart-Hart, T in kelvin
  • Each calibration point gives one equation; four points solve the 4×4 linear system for B₀…B₃.
  • R = e^(B₀ + B₁/T + B₂/T² + B₃/T³) — resistance from temperature
  • T ← e^(…) = R — temperature from resistance is found numerically (NTC resistance is monotonic in temperature)
  • °F = °C × 9/5 + 32,   T(K) = °C + 273.15

The fit is only as accurate as the calibration points and is most reliable within the temperature range they span. Spread the four points across the range you care about for best results.

Frequently asked questions

What is the Steinhart-Hart equation?

It models an NTC thermistor as 1/T = A + B·ln(R) + C·(ln R)³, where T is temperature in kelvin and R is resistance. This calculator solves the inverse coefficients from calibration points.

How many calibration points do I need?

Four temperature/resistance points are required to solve the four inverse coefficients used here.

Why use Steinhart-Hart instead of a Beta value?

The Steinhart-Hart equation is far more accurate over a wide temperature range than a single Beta constant, which is only accurate near its two defining points.