Temperature Coefficient of Resistance

R(T) = Rref × (1 + α × ΔT)

Quick answer

This calculator solves R(T) = Rref × (1 + α × ΔT) for Resistance at T. With Reference Resistance 1.03 kΩ, Temp Coefficient (ppm/°C) 0.5, Temperature Change 50 °C, the result is 1.03 kΩ. It solves in 2 directions, so you can enter the values you have and get the one you need.

Calculator

Resistance at T (Ω)
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Formula

R(T) = Rref × (1 + α × ΔT)

Description

Resistance of most materials changes with temperature. The temperature coefficient α defines the fractional change in resistance per degree Celsius. Metals have positive temperature coefficients (resistance increases with temperature), while semiconductors and carbon have negative coefficients. This first-order linear approximation is valid over moderate temperature ranges. For precision applications over wide temperature ranges, second-order terms become significant. This relationship is exploited in RTD temperature sensors and must be compensated for in precision resistor networks.

Variables

  • R — Resistance at operating temperature (Ω)
  • Rref — Resistance at reference temperature, usually 25°C (Ω)
  • α — Temperature coefficient in ppm/°C
  • ΔT — Temperature change from reference (°C)

Practical Notes

Copper TCR is about +3930 ppm/°C, meaning resistance increases 0.39% per degree. Precision resistors have TCR as low as 1-5 ppm/°C. NP0/C0G ceramic capacitors have near-zero TCR. PT100 RTDs use platinum with α = 3850 ppm/°C as a temperature standard. The α value entered here is in ppm/°C and is automatically scaled by 1e-6 internally.

Symbols and units

Symbol Meaning Default unit Accepted units
R Resistance at T Ω mΩ, Ω, kΩ, MΩ
Rref Reference Resistance Ω mΩ, Ω, kΩ, MΩ
alpha Temp Coefficient (ppm/°C) — —
dT Temperature Change °C °C

Step by step

  1. 1. What you know: Reference Resistance 1.03 kΩ, Temp Coefficient (ppm/°C) 0.5, Temperature Change 50 °C
  2. 2. The relation: R(T) = Rref × (1 + α × ΔT)
  3. 3. Substitute: Rref = 1.03 kΩ, alpha = 0.5, dT = 50 °C
  4. 4. Result: Resistance at T = 1.03 kΩ

Nearest standard component values

Series Nearest value Error
E12 1 kΩ 2.9%
E24 1 kΩ 2.9%

Worked examples

Minimum range

Given: Reference Resistance 2.2 Ω, Temp Coefficient (ppm/°C) 0.025, Temperature Change 2.5 °C

Result: Resistance at T = 2.2 Ω

Low range

Given: Reference Resistance 22 Ω, Temp Coefficient (ppm/°C) 0.25, Temperature Change 25 °C

Result: Resistance at T = 22 Ω

Typical

Given: Reference Resistance 1.03 kΩ, Temp Coefficient (ppm/°C) 0.5, Temperature Change 50 °C

Result: Resistance at T = 1.03 kΩ

High range

Given: Reference Resistance 10.3 kΩ, Temp Coefficient (ppm/°C) 0.8, Temperature Change 85 °C

Result: Resistance at T = 10.3 kΩ

Maximum range

Given: Reference Resistance 103 kΩ, Temp Coefficient (ppm/°C) 8, Temperature Change 850 °C

Result: Resistance at T = 103.7 kΩ

Solving for each variable

Solve for Resistance at T

Reference Resistance 2.2 Ω, Temp Coefficient (ppm/°C) 0.025, Temperature Change 2.5 °C → 2.2 Ω

Solve for Reference Resistance

Resistance at T 1 Ω, Temp Coefficient (ppm/°C) 0.025, Temperature Change 2.5 °C → 1 Ω

How Resistance at T changes with Reference Resistance

Reference Resistance (input) Resistance at T (result)
103 Ω 103 Ω
0.2575 kΩ 0.2575 kΩ
0.515 kΩ 0.515 kΩ
0.7725 kΩ 0.7725 kΩ
1.03 kΩ 1.03 kΩ
1.545 kΩ 1.545 kΩ
2.06 kΩ 2.06 kΩ
4.12 kΩ 4.12 kΩ
7.21 kΩ 7.21 kΩ
10.3 kΩ 10.3 kΩ

The same result in other units

Unit Value
mΩ 1030000
Ω 1030
kΩ 1.03
MΩ 0.00103

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Frequently asked questions

How do you calculate Temperature Coefficient of Resistance?

Use R(T) = Rref × (1 + α × ΔT). With Reference Resistance 1.03 kΩ, Temp Coefficient (ppm/°C) 0.5, Temperature Change 50 °C, Resistance at T works out to 1.03 kΩ.

What is the formula for Temperature Coefficient of Resistance?

The formula is R(T) = Rref × (1 + α × ΔT). Resistance of most materials changes with temperature.

How do you find Reference Resistance when you know the other values?

Rearrange for Reference Resistance: with Resistance at T 1 Ω, Temp Coefficient (ppm/°C) 0.025, Temperature Change 2.5 °C, Reference Resistance is 1 Ω.

What units does Temperature Coefficient of Resistance use?

Resistance at T is shown in mΩ, Ω, kΩ, MΩ. Values are held in SI base units internally, so you can mix prefixes without converting by hand.

Related Concepts

All Basic Electronics formulas →
Ohm's Law Electrical Power Voltage Divider Current Divider Thévenin Equivalent Norton Equivalent Temperature Coefficient of Resistance Kirchhoff's Voltage Law (KVL)

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