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Thermistor Steinhart-Hart

Convert a measured NTC thermistor resistance to temperature with the Steinhart-Hart equation.

Input1/T = A + B·ln(R) + C·ln(R)³ , T in K

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The engineering

The Steinhart-Hart equation maps a negative-temperature-coefficient (NTC) thermistor's resistance to absolute temperature far better than a single-slope Beta model. The three coefficients A, B, C are fit from resistance measured at three known temperatures, and this card runs the equation forward: feed it a resistance and get temperature back.

Note the missing squared term — the classic form intentionally drops the ln(R)² coefficient because its contribution is negligible, so only A, B, and C survive. Over a typical −40 to +150 °C span a good fit holds to better than ±0.02 °C, which is why it beats Beta for precision work. If your answer is wildly off, the usual culprit is a coefficient set that belongs to a different thermistor or a units mixup on R.

Where this math comes from

John S. Steinhart and Stanley R. Hart were oceanographers, not instrument makers, when they published the equation in 1968. Working at the Carnegie Institution, they needed accurate deep-sea temperature profiles from thermistor probes and found the existing exponential Beta approximation simply wasn't good enough across the wide temperature ranges they measured.

Their empirical cubic-in-ln(R) fit came out of a Deep-Sea Research paper on calibration, and it stuck because it worked: three coefficients, no iteration, sub-hundredth-degree accuracy. It remains the standard interchange formula printed on thermistor datasheets and baked into data-acquisition firmware to this day.

  1. 1833Michael FaradayObserves the temperature-dependent resistance of silver sulfide — the first recorded thermistor behavior.
  2. 1930Samuel RubenPatents practical metal-oxide NTC thermistor elements.
  3. 1968J. S. Steinhart & S. R. HartPublish the cubic-in-ln(R) calibration equation in Deep-Sea Research.
  4. 1990Instrument industrySteinhart-Hart coefficients become standard on precision thermistor datasheets.

See the full timeline of the math behind every calculator →

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