Steinhart-Hart Thermistor Calculator

High-accuracy temperature & resistance conversion for NTC thermistors. Choose between the full Steinhart‑Hart equation (A,B,C coefficients) or the Beta parameter model.

? 10kΩ NTC (β=3435) → A=1.12924e-3, B=2.34108e-4, C=8.767e-8 ? 10kΩ NTC (β=3950) → A=1.02459e-3, B=2.49102e-4, C=1.352e-7 ? 100kΩ NTC (β=3950) → A=1.07407e-3, B=2.42293e-4, C=1.238e-7 ? Generic NTC (typical)
Resistance → Temperature
Temperature (Celsius): -- °C
Kelvin: -- K  |  Fahrenheit: -- °F
Calculated using Steinhart‑Hart equation.
Temperature → Resistance
Recommended range: -30°C to +150°C for best accuracy (extended range possible but errors may increase).
Resistance: -- Ω
For NTC thermistors, resistance decreases as temperature rises. Numerical root-finding ensures high precision.
Resistance vs. Temperature Curve (NTC Characteristic)
Updated with current coefficients

Curve based on active model (Steinhart‑Hart or Beta) over -30°C to +150°C. Markers show current computed values.

Privacy first: All calculations happen locally in your browser – no data uploaded.

Understanding the Steinhart‑Hart Equation & NTC Thermistor Modelling

The Steinhart‑Hart equation is the most accurate empirical model for the resistance–temperature relationship of NTC (Negative Temperature Coefficient) thermistors. Proposed by John S. Steinhart and Stanley R. Hart in 1968, it overcomes limitations of the simple β (beta) approximation across wide temperature ranges. The standard form is:

1/T = A + B·ln(R) + C·[ln(R)]³

Where T is absolute temperature (Kelvin), R is thermistor resistance (Ω), and A, B, C are calibration coefficients specific to each thermistor. The cubic term in ln(R) corrects for non-linear deviations, delivering ±0.01°C accuracy within the calibrated range — essential for medical devices, meteorological stations, and precision industrial controls.

Beta Parameter Model

For applications with limited temperature range, the β (beta) model is widely used: 1/T = 1/T₀ + (1/β)·ln(R/R₀). Although less accurate outside 0–70°C, it’s simpler and requires only three parameters: β, reference resistance R₀ at reference temperature T₀. Many manufacturers provide β values. Our calculator supports both, allowing engineers to switch seamlessly and compare results.

Engineering Case Study: 3D Printer Hotend Thermistor

Popular 3D printers use 100kΩ NTC thermistors (β=3950) to monitor the hotend up to 300°C. Using Steinhart‑Hart coefficients ensures accurate PID temperature regulation and prevents thermal runaway. The calculator above reproduces the same characteristic curve, enabling firmware calibration (e.g., Marlin or Klipper) by extracting resistance values at critical temperatures.

Determining Coefficients: Calibration & Datasheets

High-quality thermistors (Vishay, Murata, TDK, EPCOS) provide Steinhart‑Hart coefficients in their datasheets. You can also derive them from three calibration points (e.g., ice bath, boiling water, and an intermediate stable temperature). Our preset buttons give instant access to common NTC families, saving hours of parameter research. For lab-grade measurements, the iterative fit of A,B,C yields inter-changeability error below 0.1°C.

Thermistor Type Reference R@25°C Beta (β) value Typical Steinhart‑Hart coefficients (approximated)
10k NTC (β=3435) 10 kΩ 3435 K A=1.12924e-3, B=2.34108e-4, C=8.767e-8
10k NTC (β=3950) 10 kΩ 3950 K A=1.02459e-3, B=2.49102e-4, C=1.352e-7
100k NTC (β=3950) 100 kΩ 3950 K A=1.07407e-3, B=2.42293e-4, C=1.238e-7
References: Steinhart, J. S., Hart, S. R. "Calibration curves for thermistors" (Deep-Sea Research, 1968); NIST Thermistor Calibration Guidelines; AN-685 Application Note (Microchip).

Frequently Asked Questions & Application Notes

The Beta model assumes a constant material constant β, but actual NTC materials exhibit slight β variation with temperature. Steinhart‑Hart adds a cubic term compensating for this, providing <0.05°C accuracy over -40 to 125°C vs. 1–2°C error for β model outside narrow range.

Method 1: Manufacturer datasheet. Method 2: Three-point calibration – measure resistance at 0°C (ice water), 25°C (ambient), 100°C (boiling water), then solve for A,B,C. Use our calculator’s values as a starting point.

Thermistors often work in voltage divider circuits. The temperature vs. output voltage is non-linear; using Steinhart‑Hart directly on measured resistance ensures best linearization via lookup tables or analog polynomial fitting.
The calculator implements double-precision Newton-Raphson iteration for reverse solving (temperature to resistance) with convergence < 1e-6 Ω. Regularly updated to reflect latest NTC datasheets from major manufacturers (TDK, Vishay, Murata). Last review: May 2026.