Thermal Formulas

Thermal formulas relate power dissipation, thermal resistance, and temperature rise across semiconductors and heatsinks. These calculators predict junction temperature and help you choose adequate cooling before a part overheats. They are critical for reliable power and high-density designs.

Thermal Formula Calculators

Worked result for every Thermal formula

Formula Expression Worked result
Junction Temperature Tj = Ta + P × Rθja Ambient Temp 5.5 °C, Power 10 mW, Thermal Resistance 0.1 °C/W → Junction Temp = 5.501 °C
Full Thermal Chain Tj = Ta + P × (Rθjc + Rθcs + Rθsa) Ambient Temp 2.5 °C, Power 10 mW, Rθjc 0.1 °C/W, Rθcs 0.22 °C/W, Rθsa 0.47 °C/W → Tj = 2.508 °C
Required Heatsink Rθsa = (Tj,max − Ta) / P − Rθjc − Rθcs Max Junction Temp 2.5 °C, Ambient Temp 5.5 °C, Power 10 mW, Rθjc 0.1 °C/W, Rθcs 0.22 °C/W → Rθsa = -300.3 °C/W
Maximum Power (Junction to Case) Pmax = (Tj − Tc) / θjc Max Junction Temp 25 °C, Case Temperature 11.8 °C, θjc (Junction-to-Case) 1 °C/W → Maximum Power = 13.2 W
Thermal Time Constant τ = Cth × Rth Thermal Capacitance 0.025 J/°C, Thermal Resistance 0.1 °C/W → Thermal Time Constant = 2.5 ms
Forced Convection Heat Transfer Q = h × A × ΔT Convection Coefficient 0.025 W/(m²·°C), Surface Area 10 mm², Temperature Difference 2.5 °C → Heat Transfer Rate = 0.625 µW
Power Derating (Temperature) Pmax = Prated × (Tmax−T) / (Tmax−Tknee) Rated Power 22 mW, Max Temperature 2.5 °C, Operating Temperature 5.5 °C, Derating Start Temp 11.8 °C → Derated Power = 22 mW
Natural Convection Thermal Resistance Rsa = 1 / (h × A) Convection Coefficient 0.025, Surface Area 10 mm² → Surface-to-Ambient Rth = 4 × 10⁶ °C/W
Thermal Runaway Stability Check Stable if dP/dT < 1/Rth_ja Power Temp Coefficient 0.025, Junction-to-Ambient Rth 0.1 °C/W → Stable if dP/dT < 1/Rth_ja = 9.975
PCB Copper Thermal Resistance Rth = d / (k × A) Conduction Path Length 0.1 mm, Cross-Section Area 0.1 mm² → Thermal Resistance = 2.597 °C/W
Cooling Fan Airflow Requirement CFM = P / (1.08 × ΔT) Heat Dissipation 10 mW, Temperature Rise 2.5 °C → Airflow = 0.003704

Variables used across Thermal formulas

  • Tj — Junction temperature (°C)
  • Ta — Ambient temperature (°C)
  • P — Power dissipation (W)
  • Rθja — Thermal resistance junction-to-ambient (°C/W)
  • Rθjc — Junction-to-case thermal resistance (°C/W)
  • Rθcs — Case-to-sink thermal resistance (°C/W)
  • Rθsa — Sink-to-ambient thermal resistance (°C/W)
  • Tj_max — Maximum allowable junction temperature from datasheet (°C)
  • Pmax — Maximum allowable power dissipation (W)
  • Tc — Case temperature (°C)
  • θjc — Junction-to-case thermal resistance (°C/W)
  • τ — Thermal time constant (s)
  • Cth — Thermal capacitance (J/°C)
  • Rth — Thermal resistance (°C/W)
  • Q — Heat transfer rate (W)
  • h — Convection heat transfer coefficient (W/(m²·°C))
  • A — Surface area exposed to airflow (m²)
  • ΔT — Temperature difference between surface and ambient air (°C)
  • Prated — Full rated power at or below Tknee (W)
  • Tmax — Maximum rated temperature at zero power (°C)
  • T — Actual operating temperature (°C)
  • Tknee — Temperature where derating begins (°C)
  • R_sa — Surface-to-ambient thermal resistance (°C/W)
  • dP/dT — Rate of power increase with temperature (W/°C)
  • Rth_ja — Junction-to-ambient thermal resistance (°C/W)
  • d — Length of the conduction path (m)
  • CFM — Required airflow in cubic feet per minute

Questions people ask about Thermal

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