Temperature Coefficient Calculator & Formula

This temperature coefficient calculator finds how much a material’s resistance changes when its temperature changes. You enter the material’s reference resistance, the reference temperature, and the new temperature, and it returns the new resistance value using the linear approximation formula. The result is given in ohms, and you can also see the temperature coefficient of resistance (TCR) in parts per million per degree Celsius (ppm/°C) if you provide two known resistance-temperature points.

Formula

The linear temperature coefficient formula is:

R(t) = R₀ × [1 + α × (t − t₀)]

Where:

• R(t) is the resistance at the new temperature (Ω).
• Râ‚€ is the known resistance at the reference temperature (Ω).
• α (alpha) is the temperature coefficient of resistance (1/°C). For most metals, α is positive (resistance increases with temperature); for semiconductors, it is often negative.
• t is the new temperature (°C).
• tâ‚€ is the reference temperature (°C).

This is a first-order (linear) approximation. It works well over a limited temperature range, typically a few tens of degrees around the reference. For wider ranges, the relationship becomes nonlinear, and a second-order term (β) is often added: R(t) = R₀ × [1 + α(t − t₀) + β(t − t₀)²].

Worked Example

Using the default values from the calculator:

• Râ‚€ = 100 Ω
• tâ‚€ = 20 °C
• t = 30 °C
• α = 0.0039 /°C (copper’s approximate value)

Step 1: Calculate the temperature difference: Δt = t − t₀ = 30 − 20 = 10 °C.

Step 2: Multiply by α: 0.0039 × 10 = 0.039.

Step 3: Add 1: 1 + 0.039 = 1.039.

Step 4: Multiply by R₀: 100 × 1.039 = 103.9 Ω.

The calculator shows 103.9000 Ω, which rounds to 103.9 Ω. The resistance change is 3.90%, and the TCR is 3900 ppm/°C.

When to Use This Calculator

Use this calculator whenever you need to predict how a resistor, wire, or other conductive component will behave at a different temperature. Common applications include:

• Designing circuits that operate in hot or cold environments.
• Selecting wire gauges for power transmission where heating raises resistance.
• Calculating the resistance of RTD (resistance temperature detector) sensors.
• Estimating the change in current in a circuit due to temperature-induced resistance changes.
• Checking if a component’s resistance drift will affect circuit performance.

It is also useful in education to illustrate how temperature affects conductors and insulators.

Common Mistakes and Limitations

The linear formula is only an approximation. For large temperature differences (more than ~100 °C), the error grows. For example, copper’s resistance at 200 °C is about 1.7 times its 20 °C value, but the linear formula predicts 1.7× only if α is constant—which it isn’t. Always check the material’s datasheet for the valid temperature range.

Another common mistake is mixing up Celsius and Kelvin. The formula uses temperature differences, so the units cancel—whether you use °C or K for Δt, the result is the same. However, if you input absolute temperatures, you must use the same scale for both t and t₀. The calculator uses °C by default.

Also, α is not truly constant—it changes with temperature. For precision work, use the polynomial model or look up the exact α at your operating temperature.

How to Choose the Right Temperature Coefficient

The temperature coefficient α depends on the material. Here are typical values at 20 °C:

• Copper: 0.00393 /°C
• Aluminum: 0.00429 /°C
• Gold: 0.0034 /°C
• Silver: 0.0038 /°C
• Platinum: 0.00385 /°C (standard for RTDs)
• Carbon: −0.0005 /°C (negative)
• Silicon: −0.07 /°C (strongly negative)

For resistors, the coefficient is often given in ppm/°C. To convert to 1/°C, divide by 1,000,000. For example, a 100 ppm/°C resistor has α = 0.0001 /°C. A 100 Ω resistor with that α will change by 0.01 Ω per degree Celsius.

Alternatives to the Linear Model

When the linear approximation is not accurate enough, use the Callendar-Van Dusen equation for platinum RTDs, or the Steinhart-Hart equation for thermistors. The Steinhart-Hart equation is:

1/T = A + B·ln(R) + C·(ln(R))³

where T is temperature in Kelvin, R is resistance in ohms, and A, B, C are calibration constants. This is more accurate over a wide range but requires three data points to solve for the constants. For most engineering work, the linear formula is sufficient.

Frequently Asked Questions

What does a negative temperature coefficient mean?

A negative α means resistance decreases as temperature increases. This is typical of semiconductors like silicon and germanium, and of carbon. In circuits, this can cause thermal runaway if not managed, because as current flows, heating lowers resistance, which increases current further.

How do I convert α from 1/°C to ppm/°C?

Multiply by 1,000,000. For example, 0.0039 /°C × 1,000,000 = 3900 ppm/°C. Conversely, divide ppm/°C by 1,000,000 to get 1/°C.

Does the formula work for Kelvin?

Yes, because the formula uses the temperature difference (t − t₀). A difference of 1 K equals a difference of 1 °C, so the result is identical. Just be consistent: if you enter both temperatures in Kelvin, the difference is the same as in Celsius.

Why is my calculated resistance different from the measured value?

Several reasons: the actual α may differ from the nominal value, the temperature may not be uniform, or the linear approximation may not be valid for the temperature range. Also, the resistance of the leads or connections can add to the measurement. For precision, use a four-wire (Kelvin) measurement.

What is the temperature coefficient of a standard resistor?

Standard resistors are designed to have a very low TCR, often 50 ppm/°C or less. Precision resistors can have 5 ppm/°C or better. In contrast, a copper wire has a TCR of about 3900 ppm/°C, which is why wire resistance changes noticeably with temperature.

Can I use this calculator for thermistors?

Thermistors have a highly nonlinear response, so the linear formula is only accurate over a very narrow range (a few degrees). For thermistors, use the Steinhart-Hart equation or a lookup table. This calculator is best suited for metals and alloy resistors.

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in r0 | Reference resistance | Ω | 100 | 0
in t0 | Reference temperature | °C | 20 | -273.15
in t1 | New temperature | °C | 30 | -273.15
in a | Temp. coefficient α | 1/°C | 0.0039 | 0
out r1 | New resistance | Ω | r0 * (1 + a * (t1 - t0)) | 4
out change | Resistance change | % | (r1 - r0) / r0 * 100 | 2
out tcr | TCR | ppm/°C | a * 1e6 | 0