NTC Thermistor Calculator
Convert NTC thermistor resistance to temperature, temperature to resistance, derive Beta from two calibration points, evaluate Steinhart-Hart coefficients, and estimate measurement self-heating.
THM-005 uses Kelvin internally for all thermistor equations and natural logarithm for Beta and Steinhart-Hart calculations. It does not model RTDs, thermocouples, PTC thermistors, ADC divider optimization, or closed-loop electrothermal behavior.
Engineering tool
NTC Thermistor Calculator
Convert NTC thermistor resistance and temperature with the Beta equation, Steinhart-Hart coefficients, two-point Beta extraction, and self-heating estimates.
Measured or operating resistance. Internally converted to ohms.
Reference resistance, commonly 10 kΩ at 25°C but fully configurable.
Reference temperature for R0, often 25°C.
Beta is in kelvin. B25/85 is a temperature interval name, not Beta = 2585.
Display unit for temperatures and self-heating rise.
Result console
- Thermistor Temperature
- 25°C
- Temperature in Kelvin
- 298.15K
- Temperature in Celsius
- 25°C
- Resistance
- 10kΩ
- R / R0
- 1
Beta model uses Kelvin and natural logarithm. Accuracy depends on the thermistor and Beta temperature range.
Formula
Formula reference
NTC thermistor equations
Do not place Celsius or Fahrenheit directly into reciprocal-temperature terms.
Beta R -> T: 1/T = 1/T0 + ln(R/R0)/BT = 1 / [1/T0 + ln(R/R0)/B]Beta T -> R: R = R0 × exp[B(1/T - 1/T0)]Two-point Beta: B = ln(R1/R2) / (1/T1 - 1/T2)Steinhart-Hart: 1/T = A + B ln(R) + C[ln(R)]^3Inverse Steinhart-Hart: Cx^3 + Bx + A - 1/T = 0, where x = ln(R)Self-heating current mode: P = I²RSelf-heating voltage mode: P = V²/RSelf-heating rise: ΔTself ≈ P / DδVariable definitions
- T, T0
- absolute temperatures in K
- R, R0
- resistance in Ω after unit conversion
- B
- thermistor Beta value in K
- A, B, C
- Steinhart-Hart coefficients
- Dδ
- dissipation constant in W/°C or W/K
NTC Formula Audit
| Adopted Model | Single NTC resistance-temperature calculator covering Beta, Steinhart-Hart, two-point Beta, and self-heating. |
|---|---|
| Beta R to T | T = 1 / [1/T0 + ln(R/R0)/B]. |
| Beta T to R | R = R0 × exp[B(1/T - 1/T0)]. |
| Logarithm | Natural logarithm is used; log10 is not used. |
| Temperature Convention | All thermistor equations use Kelvin internally. |
| Reference Point | R0 and T0 are user-defined, not fixed to 10 kΩ at 25°C. |
| Beta Interval | B25/50 and B25/85 are interval labels, not numeric Beta values. |
| Two-Point Beta | B = ln(R1/R2) / (1/T1 - 1/T2). |
| Steinhart-Hart Forward | 1/T = A + B ln(R) + C[ln(R)]^3. |
| Steinhart-Hart Resistance Convention | R is converted to ohms before ln(R). |
| Steinhart-Hart Inverse | C x^3 + Bx + A - 1/T = 0, with x = ln(R). |
| C = 0 Solver | Direct linear ln(R) solution is used when C is zero. |
| B = 0 and C = 0 Boundary | No unique inverse resistance solution is reported. |
| Inverse Solver | Bounded log-resistance scan plus bisection with finite checks and round-trip verification. |
| Self-Heating Current | P = I²R. |
| Self-Heating Voltage | P = V²/R. |
| Self-Heating Rise | ΔTself ≈ P / Dδ. |
| Dissipation Constant | mW/°C and mW/K are treated as equivalent temperature intervals. |
| Negative Result Policy | Negative, zero, NaN, and Infinity physical results are rejected. |
| Scope Boundary | No RTD, thermocouple, PTC, ADC divider optimization, or closed-loop electrothermal simulation. |
Worked Examples
| Case | Calculation | Expected Result |
|---|---|---|
| 10 kΩ NTC at 25°C | R = R0, B = 3950 K | T = 25°C |
| 10 kΩ, B3950, 100°C | R = R0 exp[B(1/T - 1/T0)] | ≈697.5 Ω |
| 10 kΩ, B3950, 0°C | Cold resistance rises | ≈33.6 kΩ |
| 697.5 Ω with same Beta | R to T round trip | ≈100°C |
| 33.6 kΩ with same Beta | R to T round trip | ≈0°C |
| Reference point changed to 50°C | T0 is configurable | No hardcoded 25°C assumption |
| B25/85 = 3950 K | Use 3950 K as B | Do not enter 2585 K |
| 100 kΩ NTC | R0 = 100 kΩ | Same equations |
| 1 MΩ NTC | R0 = 1 MΩ | Same equations |
| Two-point Beta 25°C/85°C | R1 = 10 kΩ, R2 from B3950 | B ≈3950 K |
| Two equal temperatures | T1 = T2 | Rejected |
| Two equal resistances | R1 = R2 | Rejected |
| Higher temperature and higher resistance | Contradicts NTC behavior | Rejected |
| Steinhart-Hart 10 kΩ example | A=0.001129148, B=0.000234125, C=8.76741e-8 | Temperature near room range |
| Steinhart-Hart R -> T -> R | Inverse solver round trip | Resistance recovered |
| Steinhart-Hart T -> R -> T | Forward solver round trip | Temperature recovered |
| C = 0 simplified coefficients | Linear ln(R) inverse | Direct solution |
| B = 0 and C = 0 | No unique inverse | Rejected |
| Coefficient finite check | NaN coefficient | Rejected |
| R = 0 | ln(R) invalid | Rejected |
| Negative R | physical resistance invalid | Rejected |
| T = 0 K | absolute temperature invalid | Rejected |
| Current self-heating | R=10 kΩ, I=100 µA | P=0.1 mW |
| Current self-heating with D=1 mW/°C | 0.1 mW / 1 | ΔT≈0.1°C |
| Voltage self-heating | R=10 kΩ, V=1 V | P=0.1 mW |
| Voltage self-heating with D=1 mW/K | 0.1 mW / 1 | ΔT≈0.1 K |
| 1°C rise | temperature difference | 1 K rise |
| 1°C rise | temperature difference | 1.8°F rise |
| 10 kΩ input | entered as 10 kΩ or 0.01 MΩ | same internal resistance |
| 25°C input | entered as 25°C, 298.15 K, or 77°F | same internal Kelvin |
Engineering Notes
NTC Thermistor
An NTC thermistor is a temperature-dependent resistor with resistance decreasing as temperature increases.
Beta Model
The Beta equation is useful for compact calculations over a specified temperature interval.
Steinhart-Hart Model
Steinhart-Hart can improve fit over a wider range when coefficients are supplied for the correct resistance unit convention.
Kelvin Requirement
Reciprocal temperature terms must use absolute temperature.
Natural Log
Use ln(R/R0) and ln(R), not base-10 logarithm.
Coefficient Range
A, B and C coefficients are valid only over their source calibration range.
Self-Heating
Measurement current creates power dissipation and can bias the measured temperature upward.
Dissipation Constant
Dissipation constant depends on thermistor body, medium, airflow, mounting, and PCB copper.
ADC Dividers
Voltage divider selection affects sensitivity, self-heating, ADC range, and source impedance.
Scope Boundary
This calculator is for NTC thermistors only; RTD, thermocouple, and PTC devices need different models.
Common Mistakes
- Using Celsius directly in 1/T terms.
- Using log10 instead of natural logarithm.
- Treating B25/85 as Beta = 2585 K.
- Hardcoding every thermistor as 10 kΩ at 25°C.
- Mixing Steinhart-Hart coefficients that expect different resistance units.
- Assuming Beta is accurate over every temperature range.
- Ignoring thermistor tolerance and Beta tolerance.
- Ignoring self-heating from ADC measurement current.
- Treating self-heating as a full electrothermal closed-loop simulation.
- Using NTC equations for RTD, thermocouple, or PTC sensors.
- Assuming Steinhart-Hart coefficients can be derived from two points.
- Forgetting that active circuitry and ADC divider choices affect measurement accuracy.
Support reference
FAQ
What is an NTC thermistor?
An NTC thermistor is a negative-temperature-coefficient resistor whose resistance decreases as temperature increases.
How does an NTC thermistor calculator work?
It converts between resistance and temperature using either the Beta equation or the Steinhart-Hart equation, with all temperature math performed in Kelvin.
What is the Beta equation for an NTC thermistor?
The Beta equation is 1/T = 1/T0 + ln(R/R0)/B, where T and T0 are absolute temperatures in Kelvin.
Why must Kelvin be used in NTC equations?
Reciprocal-temperature equations require absolute temperature. Celsius or Fahrenheit values cannot be placed directly inside 1/T terms.
Does the Beta equation use log10?
No. The standard thermistor Beta equation uses natural logarithm, ln(), which is Math.log() in JavaScript.
What does B25/85 mean?
B25/85 identifies the temperature interval used to specify Beta between 25°C and 85°C. It does not mean the Beta value is 2585 K.
Can I change R0 and T0?
Yes. R0 and T0 are configurable because not every thermistor is a 10 kΩ 25°C device.
What is the Steinhart-Hart equation?
Steinhart-Hart uses 1/T = A + B ln(R) + C[ln(R)]^3 to model thermistor resistance-temperature behavior over a specified range.
Which resistance unit is used for Steinhart-Hart coefficients?
This calculator uses resistance in ohms internally for Steinhart-Hart coefficients. Use coefficient data that follows the same convention.
Can the calculator solve resistance from Steinhart-Hart temperature?
Yes. It solves the inverse equation in log-resistance with a bounded numerical method and round-trip verification.
What happens when C is zero in Steinhart-Hart?
When C is zero, the inverse equation becomes linear in ln(R), so the calculator solves it directly.
Can the calculator derive Steinhart-Hart A, B and C from three points?
No. THM-005 V1 does not derive A, B and C from three calibration points.
How do I calculate Beta from two points?
Use B = ln(R1/R2) / (1/T1 - 1/T2), with T1 and T2 converted to Kelvin first.
Why does resistance decrease when temperature increases?
In an NTC thermistor, charge carrier behavior causes resistance to fall with increasing temperature over its specified operating range.
What is thermistor self-heating?
Self-heating is temperature rise caused by measurement power dissipated in the thermistor body.
How is NTC self-heating estimated?
The calculator uses P = I²R or P = V²/R, then estimates ΔTself ≈ P / dissipation constant.
Is self-heating a closed-loop thermal simulation?
No. It is a first-order operating-point estimate and does not solve the changing resistance-temperature-power loop.
Does THM-005 support RTD or PT100 sensors?
No. RTD and PT100/PT1000 calculations belong to THM-006.
Does this replace a thermistor datasheet?
No. Use datasheet Beta ranges, Steinhart-Hart coefficients, tolerance, dissipation constant, and operating limits.
Can an NTC thermistor be used in an ADC divider?
Yes, but divider optimization and ADC code conversion are outside THM-005 V1 scope.
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Documentation
Related Engineering Resources
Guides and lookup references linked to this tool.
Engineering Guide
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Design NTC and platinum RTD measurement chains with correct models, excitation, self-heating, wiring compensation, ADC interfaces, and error budgets.
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Calculate actual component dissipation and choose safe power ratings using thermal resistance, derating, junction temperature, SOA, pulse conditions, PCB heat spreading, and real operating conditions.
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Engineering Disclaimer
NTC thermistor calculations depend on thermistor tolerance, Beta range, Steinhart-Hart coefficient convention, self-heating, mounting, medium, ADC circuit, and calibration. Critical designs should be verified against datasheets and measured over the required range.