Steinhart-Hart Temperature
1/T = A + B×ln(R) + C×(ln(R))³
Quick answer
This calculator solves 1/T = A + B×ln(R) + C×(ln(R))³ for 1/T. With Coefficient A 0.5, Coefficient B 1.1, Coefficient C 2.35, Thermistor Resistance 10 kΩ, the result is -273.1.
Calculator
Formula
Description
The Steinhart-Hart equation provides a precise mathematical model for the resistance-temperature relationship of NTC thermistors. The three coefficients (A, B, C) are determined from calibration data at three known temperatures. The result T is in Kelvin and is converted to Celsius by subtracting 273.15. This equation is accurate to within ±0.02°C over a 100°C range, making it much more accurate than the simpler Beta equation, especially over wide temperature ranges. It is the standard method used in precision temperature measurement with thermistors.
Variables
- T — Temperature in Kelvin (converted to °C in output)
- A, B, C — Steinhart-Hart coefficients (from calibration or datasheet)
- R — Thermistor resistance at the temperature being measured (Ω)
Practical Notes
Common 10kΩ NTC thermistor coefficients (for a typical Vishay NTCLE100E3): A = 1.009249522e-3, B = 2.378405444e-4, C = 2.019202697e-7. The simplified Beta equation (1/T = 1/T0 + (1/B)×ln(R/R0)) uses only one parameter and is accurate to ±0.5°C over a narrow range. For microcontroller implementations, a lookup table with interpolation is often more computationally efficient.
Symbols and units
| Symbol | Meaning | Default unit | Accepted units |
|---|---|---|---|
| A | Coefficient A | — | — |
| B | Coefficient B | — | — |
| C | Coefficient C | — | — |
| R | Thermistor Resistance | kΩ | mΩ, Ω, kΩ, MΩ |
Step by step
- 1. What you know: Coefficient A 0.5, Coefficient B 1.1, Coefficient C 2.35, Thermistor Resistance 10 kΩ
- 2. The relation: 1/T = A + B×ln(R) + C×(ln(R))³
- 3. Substitute: A = 0.5, B = 1.1, C = 2.35, R = 10 kΩ
- 4. Result: 1/T = -273.1
Worked examples
Minimum range
Given: Coefficient A 0.025, Coefficient B 0.055, Coefficient C 0.118, Thermistor Resistance 100 Ω
Result: 1/T = -273.1
Low range
Given: Coefficient A 0.25, Coefficient B 0.55, Coefficient C 1.18, Thermistor Resistance 1 kΩ
Result: 1/T = -273.1
Typical
Given: Coefficient A 0.5, Coefficient B 1.1, Coefficient C 2.35, Thermistor Resistance 10 kΩ
Result: 1/T = -273.1
High range
Given: Coefficient A 0.8, Coefficient B 1.76, Coefficient C 3.76, Thermistor Resistance 100 kΩ
Result: 1/T = -273.1
Maximum range
Given: Coefficient A 8, Coefficient B 17.6, Coefficient C 37.6, Thermistor Resistance 1 MΩ
Result: 1/T = -273.1
How 1/T changes with Coefficient A
| Coefficient A (input) | 1/T (result) |
|---|---|
| 0.05 | -273.1 |
| 0.125 | -273.1 |
| 0.25 | -273.1 |
| 0.375 | -273.1 |
| 0.5 | -273.1 |
| 0.75 | -273.1 |
| 1 | -273.1 |
| 2 | -273.1 |
| 3.5 | -273.1 |
| 5 | -273.1 |
Embed this calculator
Paste this into any page. It keeps working when this page updates, and credits the source.
<iframe src="https://vbatpower.com/embed/thermistor-steinhart/" width="100%" height="460" style="border:1px solid #1f2a37;border-radius:12px" loading="lazy" title="Steinhart-Hart Temperature"></iframe>
<p><a href="https://vbatpower.com/formulas/thermistor-steinhart/">Steinhart-Hart Temperature</a> Calculator by vbatpower.com</p>Frequently asked questions
How do you calculate Steinhart-Hart Temperature?
Use 1/T = A + B×ln(R) + C×(ln(R))³. With Coefficient A 0.5, Coefficient B 1.1, Coefficient C 2.35, Thermistor Resistance 10 kΩ, 1/T works out to -273.1.
How do you calculate calcul coefficient formule de steinhart-hart?
Rearrange for 1/T: with Coefficient A 0.25, Coefficient B 0.55, Coefficient C 1.18, Thermistor Resistance 1 kΩ, 1/T is -273.1.
What are the a b and c in the steinhart-hart?
Rearrange for 1/T: with Coefficient A 0.5, Coefficient B 1.1, Coefficient C 2.35, Thermistor Resistance 10 kΩ, 1/T is -273.1.
What is the formula for Steinhart-Hart Temperature?
The formula is 1/T = A + B×ln(R) + C×(ln(R))³. The Steinhart-Hart equation provides a precise mathematical model for the resistance-temperature relationship of NTC thermistors.
Related Concepts
All Sensors & ADC formulas →Need more features?
Save calculations, import telemetry data, simulate battery discharge, and collaborate with your team.
Try the App