NTC Thermistor Temperature Calculator (Beta Equation)

How it works

1/T = 1/T₀ + (1/β) × ln(R/R₀), T₀ = 298.15 K; R = R₀ × e^(β(1/T − 1/T₀)); divider: R = Rs × ADC ÷ (ADCmax − ADC)

Negative-temperature-coefficient thermistors are the cheap temperature sensors in 3D printers, battery packs, thermostats and appliances. Their resistance falls roughly exponentially with temperature, and the beta equation captures that with one constant — typically 3,435 to 3,950 K for common 10 kΩ parts — referenced to the resistance at 25 °C. Read through a voltage divider into an ADC, the resistance is recovered from the count ratio and the equation gives the temperature. Sensitivity is high (about 4% per degree near room temperature) but non-linear, and the single β value drifts from reality far from 25 °C; the three-coefficient Steinhart-Hart equation fixes that when accuracy matters. Self-heating from the divider current is another small error worth keeping in mind.

Worked example

A 10 kΩ, β 3950 thermistor reading 4.2 kΩ: 1/T = 1/298.15 + ln(0.42)/3950 → T = 319.0 K, about 45.9 °C.

Frequently asked questions