Resistor Temperature Coefficient Calculator

This calculator works out how much a resistor’s resistance changes when its temperature changes, using the temperature coefficient of resistance (TCR). You enter the resistance at a reference temperature (usually 20°C or 25°C), the TCR value in ppm/°C, the reference temperature, and the new temperature; the calculator returns the resistance change, the new resistance, and the percentage change. The result is an estimate that assumes a linear relationship, which is accurate for most common resistors over a modest temperature range.

Formula

The basic linear formula used by the calculator is:

R(T) = R₀ × [1 + α × (T − T₀)]

Where:

• R(T) = resistance at the new temperature (Ω)
• Râ‚€ = resistance at the reference temperature (Ω)
• α = temperature coefficient of resistance (1/°C), often given in ppm/°C (parts per million per degree Celsius). 1 ppm/°C = 1 × 10â�»â�¶ /°C
• T = new temperature (°C)
• Tâ‚€ = reference temperature (°C)

The resistance change ΔR is simply R₀ × α × (T − T₀). The percentage change is α × (T − T₀) × 100%.

Worked Example

Using the default values from the calculator: R₀ = 1000 Ω, TCR = 100 ppm/°C, T₀ = 25°C, T� = 85°C.

1. Temperature difference: T� − T₀ = 85 − 25 = 60°C
2. Convert TCR to a decimal: 100 ppm/°C = 100 × 10�� = 0.0001 /°C
3. Resistance change: ΔR = 1000 × 0.0001 × 60 = 6 Ω
4. New resistance: R� = 1000 + 6 = 1006 Ω
5. Percentage change: (6 / 1000) × 100 = 0.6%

The calculator shows the same results: ΔR = 6.000 Ω, R� = 1006.000 Ω, and 0.600%.

What is TCR and Why Does It Matter?

The temperature coefficient of resistance (TCR) tells you how much a resistor’s resistance changes per degree Celsius of temperature change. It is usually expressed in ppm/°C. A resistor with a TCR of 100 ppm/°C changes its resistance by 0.01% for every 1°C change. For precision circuits—like voltage dividers, current sensors, or reference circuits—a high TCR can cause drift that ruins accuracy. That is why precision resistors often have TCR values of 5 ppm/°C or lower, while standard thick-film resistors might be 100–200 ppm/°C.

TCR is not always constant over a wide temperature range; the linear approximation works well for small ranges (e.g., −55°C to +125°C for many resistors), but for extreme temperatures, a quadratic term (the “beta� or “B� constant) may be needed. For most practical engineering work, the linear model is sufficient.

How to Choose the Right TCR for Your Application

Selecting a resistor with the appropriate TCR depends on the allowable resistance drift in your circuit:

• General purpose (100–200 ppm/°C): fine for LED current limiting, pull-ups, and other non-precision uses.
• Precision analog (10–50 ppm/°C): suitable for audio circuits, filters, and moderate-accuracy references.
• High precision (1–10 ppm/°C): needed for voltage references, precision dividers, and instrumentation.
• Ultra precision (below 1 ppm/°C): used in metrology and critical aerospace/scientific equipment.

Remember that TCR is only one source of drift. Self-heating from power dissipation also raises the resistor’s temperature. If a resistor dissipates 0.5 W and has a thermal resistance of 100°C/W, its body temperature rises 50°C above ambient. Use the calculator with the actual body temperature, not just the ambient temperature, to get a realistic drift estimate.

Common Mistakes and Misconceptions

• Mixing up ppm and decimal: 100 ppm/°C is 0.0001 /°C, not 0.01 /°C. Always divide by 1,000,000.
• Using Celsius vs. Kelvin: The formula uses temperature differences, so Celsius and Kelvin are interchangeable for ΔT. But never mix an absolute Kelvin temperature with a Celsius reference without converting.
• Assuming TCR is constant: The linear model fails at very low or very high temperatures. For example, carbon film resistors have a negative TCR at low temperatures and a positive TCR at high temperatures.
• Ignoring the reference temperature: A resistor’s nominal value is only valid at the reference temperature (often 20°C or 25°C). If you measure at 50°C, you must account for the difference.
• Confusing TCR with thermal resistance: TCR is about electrical resistance change; thermal resistance (°C/W) is about how hot the part gets per watt dissipated. They are related but not the same.

Limitations of the Linear Model

The linear formula is a first-order approximation. Real resistors show a slightly curved response over wide temperature ranges. For metal film and thick film resistors, the deviation from linearity is usually small over the military temperature range (−55°C to +125°C), but for precision work, the datasheet may provide a “R/T curve� or a polynomial fit. The linear model also assumes the TCR is constant, which is not true for all materials. For example, carbon composition resistors have a high negative TCR and are highly nonlinear.

Another limitation: the calculator gives the resistance at a single temperature point. In a real circuit, the resistor’s temperature may vary due to ambient changes and self-heating. To get a complete picture, you would need to model the thermal time constant and power dissipation.

Practical Applications

Knowing how resistance changes with temperature is critical in many fields:

• Voltage dividers: If two resistors have different TCRs, the divider ratio changes with temperature, causing output drift.
• Current sensing: A shunt resistor with a high TCR will produce a measurement error as it heats up.
• RTD (Resistance Temperature Detector) circuits: These use the predictable TCR of platinum to measure temperature. The calculator can be used with a PT100 RTD (100 Ω at 0°C, TCR ≈ 3850 ppm/°C) to estimate resistance at other temperatures, though the standard is actually a polynomial.
• Precision amplifiers: Gain-setting resistors must have matching TCRs to keep gain stable over temperature.
• Oscillator circuits: RC time constants change with temperature, affecting frequency stability.

Frequently Asked Questions

What is a good TCR for a resistor?

It depends on the application. For general use, 100 ppm/°C is acceptable. For precision analog circuits, look for 10–25 ppm/°C. For high-end instrumentation, 5 ppm/°C or less is typical. The “best� TCR is the one that keeps your circuit error within spec over the operating temperature range.

How do I convert TCR from ppm/°C to %/°C?

Divide by 10,000. For example, 100 ppm/°C = 0.01%/°C. So a 10°C rise changes the resistance by 0.1%.

Does the calculator work for negative TCR resistors like thermistors?

Yes, if you enter a negative TCR value (e.g., −4000 ppm/°C for an NTC thermistor), the calculator will show the resistance decreasing with temperature. However, thermistors are highly nonlinear, so the linear formula is only accurate over a very narrow temperature range (a few degrees). For wider ranges, use the Steinhart-Hart equation instead.

What is the difference between TCR and thermal resistance?

TCR (temperature coefficient of resistance) measures how much the electrical resistance changes per degree Celsius. Thermal resistance (in °C/W) measures how much the component’s temperature rises above ambient per watt of power it dissipates. They are different physical properties; a resistor can have a low TCR but a high thermal resistance, meaning it heats up a lot but its resistance doesn’t change much.

Why does my resistor’s measured TCR not match the datasheet?

Measurement error is common. The TCR is measured over a specific temperature range and often at a specific current. Self-heating during measurement can raise the resistor’s temperature above the intended value, skewing the result. Also, the TCR can vary slightly from batch to batch. Use a four-wire measurement and a low test current to get accurate results.

Can I use this calculator for a wire wound resistor?

Yes, wire wound resistors have a well-defined TCR that is usually positive for copper, nickel, or manganin. The linear model works well for manganin (low TCR) over a wide range. For copper, the TCR is about 3900 ppm/°C, so the resistance changes significantly with temperature—this is why copper is not used for precision resistors.

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in r0 | Resistance at reference temp | Ω | 1000 | 0
in tcr | TCR | ppm/°C | 100 | 0
in t0 | Reference temperature | °C | 25 | 0
in t1 | New temperature | °C | 85 | 0
out delta_r | Resistance change | Ω | r0 * tcr / 1e6 * (t1 - t0) | 3
out r1 | New resistance | Ω | r0 * (1 + tcr / 1e6 * (t1 - t0)) | 3
out pct | Percentage change | % | tcr / 1e6 * (t1 - t0) * 100 | 3