Engineering Guide

Temperature Coefficients and Drift: ppm/°C, Linear Models, and Error Budgets

Temperature coefficients translate a component's temperature excursion into parameter drift. The arithmetic is simple, but reliable use requires a declared reference temperature, correct ppm conversion, sign handling, model limits, and an error budget that separates tolerance from drift.

ThermalIntermediate16 min readUpdated October 14, 2026

Drift Analysis Workflow

Step	Action	Boundary
Define the measurand	State exactly which value drifts: resistance, voltage, gain, offset, frequency, capacitance, or another parameter.
Choose the reference	Use the datasheet reference value Xref at its stated reference temperature Tref.
Normalize the coefficient	Convert ppm/°C or %/°C to a fractional coefficient before calculation.
Set temperature corners	Use the actual component temperature range, not automatically ambient temperature.
Apply the valid model	Use the linear equation only over the range where the coefficient is specified and curvature is acceptable.
Budget other errors	Keep initial tolerance, drift, aging, humidity, load, self-heating, and calibration residuals separate.
Combine deliberately	Use worst-case addition for guaranteed bounds; use RSS only for justified independent statistical terms.
Verify	Measure at stabilized temperature points with adequate instrument accuracy and controlled self-heating.

Linear Temperature-Coefficient Model

Formula reference

Signed first-order drift

ΔT = T - TrefΔX/Xref = αΔTX(T) = Xref(1 + αΔT)Drift percent = αΔT × 100

Variable definitions

α is a signed fractional coefficient per °C or K

Temperature differences have the same numeric value in °C and K

The model assumes α is constant over the evaluated range

Use the Temperature Coefficient Calculator to solve forward value, coefficient, or temperature change while retaining full-precision internal values.

ppm, Percent, and Fraction Conversion

Formula reference

Coefficient conversion

αfraction = αppm × 10^-6αpercent = αppm / 10,000αppm = αpercent × 10,000

Variable definitions

ppm/°C is relative to the reference value

Do not enter 100 ppm/°C as 100%/°C

Coefficient	Fraction per °C	Percent per °C
1 ppm/°C	0.000001 /°C	0.0001 %/°C
10 ppm/°C	0.000010 /°C	0.001 %/°C
100 ppm/°C	0.000100 /°C	0.01 %/°C
1000 ppm/°C	0.001000 /°C	0.1 %/°C
1 %/°C	0.010000 /°C	10,000 ppm/°C

Resistance, Derating, and Sensor Boundaries

The same linear form supports the Wire Resistance vs Temperature Calculator when the conductor coefficient is valid. It also helps interpret linear datasheet segments used by the Thermal Derating Calculator, although parameter drift and allowable-power derating are different quantities. NTC thermistors and platinum RTDs require their dedicated nonlinear or standardized models over broad temperature ranges.

Error Budgets and Correlation

Formula reference

Common combination rules

Eworst = Σ|Ei|ERSS = sqrt(ΣEi²)Etotal(T) = Einitial + Etemp + Eaging + Eother

Variable definitions

Worst-case addition preserves bounded guarantees

RSS requires justified independence and distributions

Signed nominal compensation differs from uncertainty

Keep a nominal predictable shift separate from its uncertainty. For ratio networks, use specified tracking or ratio TCR rather than subtracting two unrelated typical coefficients. Include temperature measurement uncertainty when the correction itself depends on a measured temperature.

Worked Checks

Resistor TCR

A 10 kΩ resistor with +50 ppm/°C over +60°C changes by +0.3%, or +30 Ω, giving about 10.03 kΩ.

Negative coefficient

A -200 ppm/°C coefficient over +40°C gives -0.8% drift. The sign must be retained.

Reverse solve

A 5.000 V reference measured at 5.0075 V after +50°C has +0.15% drift, equivalent to +30 ppm/°C in the linear model.

Temperature range

A ±25 ppm/°C part referenced at 25°C and used from -20°C to 85°C has unequal one-sided excursions because ΔT is -45°C and +60°C.

Ratio cancellation

Two resistors with the same tracking coefficient can preserve a ratio better than their absolute TCR values suggest; discrete uncorrelated parts may not.

Initial plus thermal

A ±0.1% initial tolerance plus a worst-case ±0.25% temperature term gives ±0.35% by arithmetic worst-case addition.

Self-heating

A component at 70°C in a 50°C ambient must use its 70°C body temperature when applying the coefficient.

Curvature boundary

A single linear coefficient cannot represent an NTC thermistor over a wide range; use its nonlinear resistance-temperature model.

Common Mistakes

Dropping the sign of a negative coefficient.

Entering ppm as percent without conversion.

Using ambient instead of component temperature.

Applying a typical coefficient as a guaranteed maximum.

Extrapolating a linear coefficient beyond its specified range.

Adding temperature in °C instead of using temperature difference.

Assuming every parameter has the same coefficient.

Ignoring initial tolerance and aging.

Using RSS for correlated or bounded errors without justification.

Assuming matched ratios from unrelated discrete parts.

Treating NTC behavior as linear across a wide range.

Measuring before thermal equilibrium or with excessive self-heating.

Verification

Test enough temperature points to reveal curvature and hysteresis, allow thermal equilibrium, control electrical loading, and record the component rather than chamber-air temperature when possible. Compare the fitted coefficient and residual error with datasheet limits across production samples. Critical designs need environmental validation, not only a room-temperature calculation.

Support reference

FAQ

What does ppm per degree Celsius mean?

It is a relative change of one part per million of the reference value for each Celsius degree of temperature change.

How do I convert ppm/°C to percent/°C?

Divide ppm/°C by 10,000. For example, 100 ppm/°C equals 0.01%/°C.

How do I calculate a value at a new temperature?

For a valid linear model, use X(T) = Xref[1 + α(T - Tref)] with α expressed as a fraction per degree.

Can a temperature coefficient be negative?

Yes. A negative coefficient means the parameter decreases as temperature rises over the stated range.

Is temperature drift the same as initial tolerance?

No. Initial tolerance is the value error at a reference condition; temperature drift is an additional change as temperature moves away from the reference.

Should I use worst-case addition or RSS?

Use arithmetic worst-case addition for guaranteed independent bounds unless a defensible statistical model supports RSS and correlation is handled.

Does the coefficient use ambient temperature?

It uses the temperature of the element whose parameter is changing. Self-heating and thermal gradients can make that different from ambient.

Can I use a linear coefficient for an NTC thermistor?

Only over a very narrow local range if justified. Wide-range NTC conversion requires a beta or Steinhart-Hart model.

Why can ratio drift be smaller than absolute drift?

Matched elements can share correlated temperature behavior, so their ratio changes less than either absolute value. Tracking must be specified; it cannot be assumed.

How should temperature drift be verified?

Stabilize the device at controlled temperature points, limit self-heating, use calibrated instruments, record hysteresis, and compare measured curvature with the assumed model.

Summary

Convert coefficients into a signed fraction, apply them to the correct reference value and component temperature, and remain inside the model's valid range. Keep initial tolerance, predictable drift, uncertainty, aging, and self-heating separate, then verify curvature and hysteresis with controlled measurements.