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Resistance Temperature Coefficient Calculator

Calculate R = R₀(1 + αΔT) - Resistance vs Temperature

Material Presets
R₀ at T₀ (Ω)
TCR α (/°C)
Reference Temp T₀ (°C)
Target Temp T₁ (°C)

TCR Formula

R = R₀ × (1 + α × ΔT)
ΔT = T₁ - T₀ (temperature change)
ΔR = R - R₀ = R₀ × α × ΔT
% change = α × ΔT × 100%

The temperature coefficient of resistance (TCR or α) describes how a material's resistance changes with temperature. Metals have positive TCR (resistance increases with temperature). Semiconductors (NTC thermistors) have negative TCR. Understanding TCR is critical for temperature sensing, circuit design, and compensating for temperature drift in precision circuits.

⚠ TCR is approximately linear over limited temperature ranges. For wide ranges, use the Callendar-Van Dusen equation for platinum RTDs. NTC thermistors are highly non-linear; use the Steinhart-Hart equation for precision.

TCR and Temperature Measurement

Temperature coefficient is used in RTD sensors (resistance temperature detectors), where precise TCR of platinum provides accurate temperature measurement. Pt100 sensors have R₀=100Ω at 0°C with α=0.00385/°C. Thermistors (NTC) have much higher sensitivity but non-linear response. TCR also affects resistor tolerance over temperature in circuit design.

PTC (Metals)

Resistance increases with temperature. Copper: 0.393%/°C. Platinum: 0.385%/°C. Used in RTD sensors and overcurrent protection.

NTC (Thermistors)

Resistance decreases with temperature. Typical α: -3% to -8%/°C. High sensitivity, non-linear. Used for temperature sensing and inrush limiting.

Resistor TCR

Standard resistors: ±100 to ±500 ppm/°C. Precision: ±5 to ±25 ppm/°C. Ultra-precision: ±0.2 to ±2 ppm/°C. Lower TCR = better stability.

Unit Conversion

TCR in /°C or ppm/°C. 0.00385/°C = 3850 ppm/°C. 1 ppm = 0.0001%. Example: 100ppm/°C = 0.01% change per °C.

Teaching Example: Pt100 RTD: R₀=100Ω at 0°C, α=0.00385/°C, T₁=100°C.
ΔT = 100 - 0 = 100°C. R = 100 × (1 + 0.00385 × 100) = 100 × 1.385 = 138.5Ω.
ΔR = 38.5Ω. % change = 38.5%. At T₁=200°C: R = 100 × (1 + 0.00385 × 200) = 177Ω.

Applications

Temperature Sensing Circuit Compensation RTD Design Inrush Limiting Precision Resistors

Frequently Asked Questions

What is TCR?▼
Temperature Coefficient of Resistance. R = R₀(1 + αΔT). Metals: PTC (+α). Thermistors: NTC (-α).
How to measure temperature with resistance?▼
Measure R, compute T = (R/R₀ - 1)/α + T₀. Pt100: T(°C) = (R/100 - 1)/0.00385. Measure with 4-wire Kelvin connection for accuracy.
PTC vs NTC?▼
PTC: R increases with T (metals, positive α). NTC: R decreases with T (semiconductors, negative α). NTC is more sensitive.
What ppm/°C means?▼
Parts per million per °C. 100 ppm/°C = 0.01%/°C. A 1000Ω resistor with 100ppm/°C changes 0.1Ω per °C. Precision: 5ppm/°C = 0.0005%/°C.

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