NTC Thermistor Calculator (Beta)

Convert NTC thermistor resistance to temperature and vice versa using the Beta (β) equation. Supports the common 10k/B=3950 thermistor and any custom R25/β pair.

Calculator Electronics Updated Apr 18, 2026
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How to Use
  1. Enter R25 (resistance at 25°C), Beta (β) value from datasheet.
  2. Convert between temperature ↔ resistance.
  3. Typical 10k NTC with β=3950 for 3D printer hot-ends, battery monitoring, etc.
  4. For higher accuracy, use the 3-parameter Steinhart-Hart equation (not shown here).
Input
Ω (k, M OK)
K
°C
Presets
R vs. T Curve
Temperature
—°C
Resistance
—
dR/dT @ T
—
Sensitivity (α)
—%/°C

Show Work

Enter values.

Formulas (Beta equation)

Resistance at T
R(T) = R25 · eβ(1/T − 1/T25)
T in Kelvin; T25 = 298.15 K.
Temperature
T = 1 / (1/T25 + ln(R/R25)/β)
Solve for T given R.
Convert to °C
°C = K − 273.15
Thermistor equations use Kelvin.
Sensitivity α
α = −β / T²
Fractional change per °C.
dR/dT
dR/dT = −R · β / T²
Local slope of resistance curve.
Self-heating
ΔT = I² × R × θSA
Error from measurement current.

History of the Thermistor

Samuel Ruben patented the first NTC thermistor at Vega Electronics in 1930, exploiting the steep negative temperature coefficient of semiconductor metal oxides (manganese, nickel, cobalt). By the 1940s, Bell Labs was producing commercial thermistors for telephone-exchange inrush-current limiting — cold thermistors presented high resistance to limit startup surge, then heated up and dropped to low resistance during normal operation.

John Steinhart and Stanley Hart at Woods Hole Oceanographic Institution published the three-parameter Steinhart-Hart equation in 1968, providing a much more accurate fit to thermistor R-T curves than the simpler Beta equation. The Beta equation (used in this calculator) is accurate to ±1 °C within ±50 °C of the reference temperature; Steinhart-Hart achieves ±0.1 °C over wider ranges at the cost of three coefficients instead of one.

Modern thermistors are everywhere inexpensive temperature monitoring is needed: 3D printer hot-ends (100k NTC in a voltage divider), lithium battery packs (10k NTC glued to cells for overtemperature cutoff), automotive coolant sensors, HVAC duct monitoring, and laser-diode bias compensation. For laboratory-grade precision, platinum RTDs or thermocouples win, but thermistors dominate the "good enough and cheap" segment.

About This Calculator

Enter the thermistor\'s resistance at 25°C (from its datasheet), the Beta coefficient (typically 3380, 3950, or 4150 K), and then either a temperature (to compute resistance) or a measured resistance (to compute temperature). The tool returns the other value plus sensitivity in %/°C and dR/dT at that temperature.

Read resistance in circuit via a voltage divider: put the thermistor in series with a known pull-up, measure the midpoint with an ADC, back out R. Keep excitation current low (< 1 mA for a 10k NTC) to avoid self-heating error. For ±0.1 °C accuracy over wide ranges, use Steinhart-Hart with three calibration points instead of the Beta equation. Everything runs client-side.

Frequently Asked Questions

What is an NTC thermistor?

NTC (Negative Temperature Coefficient) thermistors are resistors made from semiconductor materials that decrease in resistance as temperature rises. Nonlinear but sensitive — a 10k NTC at 100°C reads about 680Ω. Used everywhere inexpensive temperature sensing is needed.

What is Beta?

Beta (β) is the material constant that describes how steeply resistance changes with temperature. Higher β = more sensitive. Common β values: 3380K, 3950K, 4150K. Given β and R at one temperature (usually 25°C), you can calculate R at any other temperature.

Beta vs. Steinhart-Hart?

The Beta equation is a 2-parameter simplification, accurate to ±1°C within a ±50°C window. Steinhart-Hart uses 3 parameters (or 4 with C=0) and achieves ±0.1°C over wider ranges. For precision use S-H; for general sensing β is fine.

How do I read the resistance?

Put the thermistor in a voltage divider with a known pull-up. Measure the midpoint voltage with an ADC. R_NTC = R_pull × V_adc / (V_rail − V_adc). Keep excitation current low (< 1 mA) to minimize self-heating errors.

Self-heating effect?

Current through the thermistor causes I²R dissipation — the sensor heats itself slightly. Typical NTCs have ~1 mW/°C dissipation in still air. Keep power dissipation below 1mW for minimal error (~1°C).

Common Use Cases

3D Printer Hot-End

100k NTC, β=3950 in a voltage divider. Read 200-300°C with reasonable accuracy for plastic extrusion.

Battery Pack Monitoring

10k NTC glued to a cell to detect overtemperature during charging. Shuts down charger above 55°C.

Liquid Cooling

10k NTC on the return line of a water block. Reads coolant temperature for fan speed control.

HVAC Sensing

10k NTC on supply/return air ducts for thermostat feedback and flow sensing.

Motor Overtemperature

NTC embedded in motor windings. Opens a relay at set temperature to protect insulation.

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