Temperature Coefficient Calculator
Calculate generic first-order temperature drift for electronics parameters such as resistance, voltage, gain, capacitance, sensor output, frequency or another consistent quantity.
THM-012 is intentionally generic. It does not replace NTC thermistor curves, PT100/PT1000 RTD equations, crystal oscillator compensation models or device-specific resistor TCR data.
Engineering tool
Temperature Coefficient Calculator
Calculate first-order linear temperature drift using relative ppm/% coefficients or absolute quantity-per-degree coefficients.
Use one consistent unit for Xref, measured value and target value. Examples: ohm, V, Hz, pF, lux.
Reference value at Tref. May be zero in forward modes, but inverse relative coefficient modes require nonzero Xref.
Relative coefficient alpha. Positive, zero and negative coefficients are allowed.
Reference absolute temperature.
Target or second absolute temperature.
Result console
- Final Value
- 100.5unit
- Absolute Change
- 0.5unit
- Fractional Change
- 0.005
- Percentage Change
- 0.5%
- PPM Change
- 5000ppm
- Temperature Difference
- 50K
- Absolute Coefficient
- 0.01unit/K
Formula
Formula reference
Linear temperature coefficient formulas
Fahrenheit temperature differences are converted by 5/9 before using the kelvin-sized temperature interval.
X(T) = Xref [1 + alpha(T - Tref)]Delta T = T - Trefdelta = alpha Delta T% change = 100 alpha Delta Tppm change = 1,000,000 alpha Delta TDelta X = Xref alpha Delta Talpha = (X2/Xref - 1) / (T2 - Tref)Xref = X / (1 + alpha Delta T)Delta T = (X/Xref - 1) / alphaAbsolute model: X(T) = Xref + beta Delta TVariable definitions
- Xref
- reference value at the reference temperature
- X(T)
- value at the target temperature
- alpha
- relative temperature coefficient in 1/K
- beta
- absolute temperature coefficient in quantity units per K
- Delta T
- temperature interval in K or °C-equivalent units
Temperature Coefficient Formula Audit
| Relative Linear Model | X(T)=Xref[1+alpha(T-Tref)]. |
|---|---|
| Temperature Difference Formula | Delta T = T - Tref, using kelvin-sized intervals. |
| Fractional Change Formula | delta = alpha Delta T. |
| Percentage Change Formula | % change = 100 alpha Delta T. |
| Absolute Change Formula | Delta X = Xref alpha Delta T. |
| Coefficient From Two Points Formula | alpha = (X2/Xref - 1)/(T2-Tref). |
| Reference Value Inverse Formula | Xref = X/(1+alpha Delta T). |
| Target Temperature Inverse Formula | Delta T = (X/Xref - 1)/alpha. |
| PPM Conversion | ppm = fraction x 1,000,000. |
| Percent Conversion | percent = fraction x 100. |
| Celsius/Kelvin Coefficient Convention | Per °C and per K coefficients are numerically equivalent for intervals. |
| Fahrenheit Difference Convention | Fahrenheit intervals use 5/9 to convert to kelvin-sized intervals. |
| Fahrenheit Coefficient Convention | alpha per °F = alpha per K / 1.8. |
| Positive Coefficient Policy | Positive alpha increases X as temperature rises. |
| Negative Coefficient Policy | Negative alpha is allowed and decreases X as temperature rises. |
| Zero Coefficient Policy | Forward X remains Xref; inverse target temperature is unreachable or indeterminate. |
| Zero Reference Inverse Policy | Relative coefficient-from-points and target-temperature modes reject Xref=0. |
| Zero Temperature Difference Inverse Policy | Coefficient-from-points rejects T2=Tref. |
| Inverse Denominator Policy | 1+alpha Delta T close to zero is rejected before division. |
| Relative vs Absolute Coefficient Boundary | Alpha uses relative units; beta uses quantity units per degree. |
| Linear Approximation Boundary | Constant alpha is a first-order approximation, not a nonlinear device model. |
| Large Drift Warning Policy | A warning appears when |alpha Delta T| exceeds 0.1. |
| NTC Boundary | NTC Beta and Steinhart-Hart calculations remain in THM-005. |
| RTD Boundary | PT100/PT1000 IEC behavior remains in THM-006. |
| Resistor TCR Boundary | Device-specific resistor TCR tables remain with resistor references and datasheets. |
| Capacitor Boundary | Class II ceramic capacitance can be nonlinear with temperature, DC bias and aging. |
| Oscillator Boundary | Crystal and oscillator temperature behavior can be parabolic or compensated. |
| Sensor Boundary | Sensor calibration and nonlinear transfer functions remain in Sensors. |
| Initial Tolerance Boundary | Initial tolerance is not the same as temperature coefficient. |
| Internal Precision Policy | Calculations use full precision; formatting occurs only in the display layer. |
Worked Examples
| Input | Calculation | Result |
|---|---|---|
| 100 ppm/K | 100 x 1e-6 | 0.0001 /K |
| 100 ppm/K | 0.0001 x 100 | 0.01 %/K |
| 0.5 %/K | 0.5 / 100 | 0.005 /K |
| 0.5 %/K | 0.005 x 1e6 | 5000 ppm/K |
| Xref=100, alpha=100 ppm/K, Delta T=50K | delta = 0.0001 x 50 | 0.005 |
| Same | percent = 100 x 0.005 | 0.5% |
| Same | Delta X = 100 x 0.005 | 0.5 |
| Same | X = 100 + 0.5 | 100.5 |
| Delta T=-50K | X = 100(1 - 0.005) | 99.5 |
| alpha=-100 ppm/K, Delta T=50K | X = 100(1 - 0.005) | 99.5 |
| alpha=0 | X = Xref(1+0) | X = Xref |
| T=Tref | Delta T=0 | X = Xref |
| Xref=100, X2=100.5, Delta T=50K | (100.5/100 - 1)/50 | 100 ppm/K |
| Same | alpha in 1/K | 0.0001 /K |
| Same | alpha x 100 | 0.01 %/K |
| Xref=0 coefficient inverse | relative denominator unavailable | rejected |
| Delta T=0 coefficient inverse | division by zero avoided | rejected |
| X=100.5, alpha=100 ppm/K, Delta T=50K | 100.5 / 1.005 | Xref=100 |
| Xref=100, target=100.5, alpha=100 ppm/K | (1.005 - 1)/0.0001 | Delta T=50K |
| Tref=25°C plus 50K | 25 + 50 | 75°C |
| alpha=0, target != Xref | no first-order change | unreachable |
| alpha=0, target = Xref | all temperatures satisfy | indeterminate |
| 250 ppm/K | 250 x 1e-6 | 0.00025 /K |
| 250 ppm/K | 0.00025 x 100 | 0.025 %/K |
| 1 %/K | 0.01 x 1e6 | 10000 ppm/K |
| 1 ppm/K | 1e-6 x 100 | 0.0001 %/K |
| 25°C to 75°C | 75 - 25 | 50K |
| 298.15K to 348.15K | same Celsius endpoints | 50K |
| 77°F to 167°F | (167 - 77) x 5/9 | 50K |
| 100 ppm/K over 90°F difference | 100 ppm/K over 50K | 0.5% change |
| 100 ppm/K coefficient | 100 / 1.8 | 55.5556 ppm/°F |
| Xref=100 ohm, alpha=100 ppm/K | beta = alpha Xref | 0.01 ohm/K |
| Xref=5V, beta=-2mV/K, Delta T=50K | Delta X=-0.1V | 4.9V |
| positive alpha + positive Delta T | positive delta | positive drift |
| negative alpha + positive Delta T | negative delta | negative drift |
| positive alpha + negative Delta T | negative delta | negative drift |
| alpha Delta T near -1 | inverse denominator close to zero | safe rejection |
| 0.001 ppm/K over 0.001K | 1e-9 x 0.001 | 1e-12 fraction retained |
| NaN input | finite validation | rejected |
| Infinity input | finite validation | rejected |
Engineering Notes
| Temperature Coefficient | The calculator uses a first-order coefficient that relates value change to temperature change. |
|---|---|
| Relative Temperature Coefficient | Relative alpha is normalized by Xref and expressed in 1/K, %/K or ppm/K. |
| Absolute Temperature Coefficient | Absolute beta is expressed in quantity units per degree, such as mV/K, ohm/K or Hz/K. |
| Reference Value | Xref is the value at the reference temperature and must use the same unit as all X values. |
| Reference Temperature | Tref anchors the linear model; calculations use T - Tref, not absolute temperature alone. |
| Temperature Drift | Drift is the signed change from Xref caused by the modeled temperature interval. |
| Fractional Change | Fractional change is alpha Delta T before percent or ppm scaling. |
| PPM per Degree | One ppm is 10^-6, so 100 ppm/K equals 0.0001/K. |
| Positive Temperature Coefficient | A positive coefficient produces higher value at higher temperature. |
| Negative Temperature Coefficient | A negative coefficient produces lower value at higher temperature. |
| Linear Approximation | Alpha is assumed constant over the interval. Real components can be nonlinear. |
| TCR | Resistor TCR can be estimated with this model only when the datasheet supports a linear range. |
| Temperature Range | Use coefficients only over the temperature span for which they are specified. |
| Initial Tolerance | Initial tolerance and temperature coefficient are separate error terms. |
| Nonlinearity | NTCs, RTDs, ceramic capacitors and crystals can require specialized models. |
Common Mistakes
- • Treating ppm as percent.
- • Entering 100 ppm as 100%.
- • Forgetting the 1e-6 ppm factor.
- • Treating 0.01% as 0.01 instead of 0.0001.
- • Multiplying the coefficient by absolute temperature instead of T - Tref.
- • Using a Fahrenheit interval as if it were a kelvin interval.
- • Confusing temperature coefficient with initial tolerance.
- • Forcing a negative coefficient to be positive.
- • Trying to derive a relative coefficient from Xref=0.
- • Trying to derive a coefficient from two equal temperatures.
- • Using constant alpha for an NTC thermistor over a wide range.
- • Replacing an RTD Callendar-Van Dusen model with a generic alpha.
- • Treating one generic temperature coefficient as an exact model for all devices.
- • Rounding tiny ppm values before the final display.
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Related Engineering Resources
Guides and lookup references linked to this tool.
Engineering Guide
Temperature Coefficients and Drift: ppm/°C, Linear Models, and Error Budgets
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Support reference
FAQ
What is a temperature coefficient?
A temperature coefficient describes how a quantity changes with temperature. This calculator uses a first-order linear coefficient around a reference temperature.
How do I calculate temperature coefficient?
For two measured points, use alpha = (X2 / Xref - 1) / (T2 - Tref), where Xref is nonzero and the temperature difference is nonzero.
What is the formula for temperature coefficient?
The relative linear model is X(T) = Xref[1 + alpha(T - Tref)]. The coefficient alpha is normally in 1/K, percent per K, or ppm per K.
What does ppm/°C mean?
ppm/°C means parts per million change per degree Celsius temperature interval. One ppm is 0.000001 of the reference value.
What does ppm/K mean?
ppm/K means parts per million change per kelvin temperature interval. For temperature intervals, ppm/K and ppm/°C are numerically equivalent.
Are ppm/°C and ppm/K the same?
They are the same for temperature differences because a 1 °C interval equals a 1 K interval. Absolute Celsius and kelvin temperatures are not numerically the same.
How do I convert ppm/°C to percent per degree?
Divide ppm by 10000. For example, 100 ppm/°C equals 0.01%/°C.
How do I convert percent per degree to ppm?
Multiply percent per degree by 10000. For example, 0.5%/K equals 5000 ppm/K.
What does 100 ppm/°C mean?
It means the quantity changes by 100 parts per million per °C. Over 50 °C, the first-order change is 5000 ppm, or 0.5%.
How do I calculate a value at a different temperature?
Convert the coefficient to 1/K, calculate delta T = T - Tref, then use X = Xref(1 + alpha delta T).
How do I calculate temperature drift?
Use delta X = Xref alpha delta T for a relative coefficient, or delta X = beta delta T for an absolute coefficient.
How do I calculate temperature coefficient from two measurements?
Use alpha = (X2 - Xref) / (Xref delta T). Xref must be nonzero because the coefficient is relative to the reference value.
What is a positive temperature coefficient?
A positive coefficient means the modeled quantity increases as temperature increases.
What is a negative temperature coefficient?
A negative coefficient means the modeled quantity decreases as temperature increases.
Can a temperature coefficient be zero?
Yes. A zero coefficient means the first-order model predicts no temperature dependence.
What is the difference between temperature coefficient and tolerance?
Tolerance describes initial value spread. Temperature coefficient describes change with temperature after the reference value is defined.
What is the difference between relative and absolute temperature coefficient?
A relative coefficient uses 1/K, percent per K, or ppm/K. An absolute coefficient uses quantity units per K, such as mV/K, ohm/K, or Hz/K.
How do I convert an absolute coefficient to ppm?
Divide the absolute coefficient by the nonzero reference value to get 1/K, then multiply by one million.
Why is a reference value required for ppm conversion?
PPM is relative. Without a nonzero reference value, an absolute change per degree cannot be normalized.
How do Fahrenheit temperature differences affect temperature coefficients?
A Fahrenheit interval must be converted by 5/9 when used as a kelvin interval. A coefficient per °F is smaller than the equivalent per K by a factor of 1.8.
Is the temperature coefficient always linear?
No. This calculator assumes a constant coefficient over the interval. Real parts can be nonlinear, piecewise, or table based.
Can I use this calculator for resistors?
Yes for a first-order resistor TCR estimate over a valid range, but resistor-specific color code and material data belong to resistor tools and datasheets.
Can I use this calculator for NTC thermistors?
Not for wide temperature ranges. NTC thermistors are strongly nonlinear and should use the NTC Thermistor Calculator.
Can I use this calculator for PT100 or PT1000 RTDs?
Use the RTD PT100/PT1000 Calculator for IEC 60751 RTD behavior instead of replacing the full curve with a generic constant alpha.
Disclaimer
This calculator provides first-order engineering estimates. Critical designs should be verified against device datasheets, temperature ranges, nonlinear models, simulation and measurement.