Resistor tolerance and temperature coefficient
Initial tolerance, TCR in ppm/°C, thermal drift, and calculating a resistor's minimum and maximum limits across its operating range.
Written and technically reviewed byElectroDesignForge Engineering Team
View the editorial process📖 Definition
Tolerance defines the allowed initial difference between a resistor's measured value and its nominal value. The temperature coefficient of resistance (TCR) describes how that value can change as the resistor temperature moves away from its reference temperature.
Nominal Value and Initial Tolerance
A marked 10 kΩ ±1% resistor is not guaranteed to measure exactly 10 kΩ. At the specified reference conditions, its permitted initial range is:
Rmin = RN × (1 − tolerance / 100)
Rmax = RN × (1 + tolerance / 100)
For 10 kΩ ±1%, this gives 9.9 kΩ to 10.1 kΩ. Tolerance is an initial production limit; it does not include every later change caused by temperature, load, ageing, humidity, soldering or mechanical stress.
What TCR Means
TCR is normally expressed in parts per million per degree Celsius (ppm/°C). One ppm is one millionth, or 0.0001%. The first-order resistance change is:
ΔR / RN = TCR × (T − Tref) × 10⁻⁶
A 100 ppm/°C limit corresponds to 0.01% per °C, 0.1% over 10°C, or 1% over 100°C. Datasheets commonly specify TCR as a limit such as ±100 ppm/°C across a stated temperature interval. The actual curve may have a positive slope, a negative slope, or some curvature within that limit.
The reference temperature is often 25°C, but the component datasheet and test conditions are authoritative.
Combining Tolerance and TCR at Worst Case
For a conservative limit calculation, add the absolute initial tolerance and the largest TCR contribution across the required temperature range:
ΔTmax = max(|Tmin − Tref|, |Tmax − Tref|)
eT = |TCR| × ΔTmax × 10⁻⁶
eworst = tolerance / 100 + eT
Rmin,max = RN × (1 ∓ eworst)
This linear worst-case sum assumes the initial tolerance and thermal drift can act in the same adverse direction. It is intentionally more conservative than a root-sum-square statistical estimate.
Worked Example
Consider a 10 kΩ, ±1%, ±100 ppm/°C resistor specified from −40°C to +85°C, referenced at 25°C:
- Largest temperature difference:
max(65°C, 60°C) = 65°C - TCR contribution:
100 × 65 × 10⁻⁶ = 0.0065 = 0.65% - Combined worst-case deviation:
1% + 0.65% = 1.65% - Minimum resistance:
10 kΩ × (1 − 0.0165) = 9.835 kΩ - Maximum resistance:
10 kΩ × (1 + 0.0165) = 10.165 kΩ
Open the resistor min/max calculator to evaluate another nominal value, tolerance, TCR or temperature interval.
Tolerance and TCR Are Different Specifications
| Specification | Describes | Typical expression | Applied from |
|---|---|---|---|
| Initial tolerance | Value spread after manufacture | ±0.1%, ±1%, ±5% | Nominal resistance |
| Absolute TCR | Change of one resistor with temperature | ±5 to ±300 ppm/°C | Reference temperature |
| Tracking TCR | Change in the ratio between matched resistors | ppm/°C | Matched-network ratio |
| Load-life stability | Long-term change under electrical and thermal stress | ΔR/R after stated hours | Initial measured value |
Low initial tolerance does not guarantee low TCR. Conversely, a resistor with excellent TCR can still have a wider initial tolerance and require calibration.
Absolute TCR Versus Tracking TCR
In dividers, gain-setting networks and bridge circuits, the ratio between resistors may matter more than either absolute value. A matched resistor network can have an ordinary absolute TCR but a much smaller tracking TCR, because its elements share materials, processing and temperature.
Do not substitute tracking TCR for absolute TCR when the circuit depends on the absolute resistance, such as a current shunt, timing resistor or bias resistor.
Use the Resistor's Actual Temperature
TCR follows the resistor element temperature, not simply the ambient-air temperature. The part may run hotter because of power dissipation:
P = I²R = V²/R
Board copper, airflow, nearby heat sources, enclosure temperature and mounting geometry all affect the component temperature. Power derating and the maximum element temperature must be checked separately in the datasheet.
Limits of the Linear Model
The simple TCR equation is useful for first-pass error budgets, but it does not replace the manufacturer's resistance-versus-temperature curve. Precision resistor TCR can be nonlinear, and a single average value may hide different slopes above and below the reference temperature.
Also review these independent effects when accuracy matters:
- voltage coefficient and power coefficient;
- self-heating and thermal resistance;
- load-life drift and ageing;
- humidity, board strain and soldering shift;
- thermoelectric voltage in low-level measurements;
- noise and parasitic inductance or capacitance.
Selection Checklist
- Start with the required nominal resistance and circuit function.
- Set the allowed error at the reference temperature.
- Determine the resistor's realistic minimum and maximum body temperature.
- Convert the datasheet TCR limit into a resistance error over that interval.
- Add ageing, load, voltage and assembly shifts when the application requires them.
- Verify power rating, working voltage, pulse capability and package temperature limits.
- Prefer matched networks when ratio stability is more important than absolute accuracy.
Related Calculators and References
- Resistor min/max calculator — combine tolerance and TCR over an operating-temperature range.
- Resistor color code decoder — read nominal value, tolerance and TCR bands.
- E-series resistor values — choose a standardized preferred value.
- Series and parallel resistor calculator — analyse equivalent resistance and tolerance.
- Electrical resistivity — compare material resistivity and temperature coefficients.