Junction Temperature

Tj = Ta + P × Rθja

Quick answer

This calculator solves Tj = Ta + P × Rθja for Junction Temp. With Ambient Temp 110 °C, Power 10 W, Thermal Resistance 20 °C/W, the result is 310 °C. It solves in 4 directions, so you can enter the values you have and get the one you need.

Calculator

Junction Temp (°C)
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Formula

Tj = Ta + P × Rθja

Description

Junction temperature is the temperature at the semiconductor die inside a package, and it determines the device's reliability and lifespan. The thermal resistance Rθja (junction-to-ambient) describes how effectively heat flows from the die to the surrounding air. Lower thermal resistance means better heat dissipation. This single-resistance model is a simplification but is widely used for quick estimates. Most semiconductors have a maximum junction temperature of 125-175°C, and exceeding it causes degradation or failure. For every 10°C above rated temperature, device lifetime roughly halves.

Variables

  • Tj — Junction temperature (°C)
  • Ta — Ambient temperature (°C)
  • P — Power dissipation (W)
  • Rθja — Thermal resistance junction-to-ambient (°C/W)

Practical Notes

Rθja depends on the package type, PCB copper area, and airflow. A TO-220 package has Rθja of about 60°C/W without a heatsink and 1-5°C/W with a good heatsink. SOT-23 packages are typically 200-300°C/W. Always design for worst-case ambient temperature, not room temperature.

Symbols and units

Symbol Meaning Default unit Accepted units
Tj Junction Temp °C °C
Ta Ambient Temp °C °C
P Power W µW, mW, W, kW
Rth Thermal Resistance °C/W °C/W

Step by step

  1. 1. What you know: Ambient Temp 110 °C, Power 10 W, Thermal Resistance 20 °C/W
  2. 2. The relation: Tj = Ta + P × Rθja
  3. 3. Substitute: Ta = 110 °C, P = 10 W, Rth = 20 °C/W
  4. 4. Result: Junction Temp = 310 °C

Worked examples

Minimum range

Given: Ambient Temp 5.5 °C, Power 10 mW, Thermal Resistance 0.1 °C/W

Result: Junction Temp = 5.501 °C

Low range

Given: Ambient Temp 55 °C, Power 100 mW, Thermal Resistance 1 °C/W

Result: Junction Temp = 55.1 °C

Typical

Given: Ambient Temp 110 °C, Power 10 W, Thermal Resistance 20 °C/W

Result: Junction Temp = 310 °C

High range

Given: Ambient Temp 187 °C, Power 1 kW, Thermal Resistance 100 °C/W

Result: Junction Temp = 100200 °C

Maximum range

Given: Ambient Temp 1870 °C, Power 10 kW, Thermal Resistance 1000 °C/W

Result: Junction Temp = 1 × 10⁷ °C

Solving for each variable

Solve for Junction Temp

Ambient Temp 5.5 °C, Power 10 mW, Thermal Resistance 0.1 °C/W → 5.501 °C

Solve for Ambient Temp

Junction Temp 2.5 °C, Power 10 mW, Thermal Resistance 0.1 °C/W → 2.499 °C

Solve for Power

Junction Temp 25 °C, Ambient Temp 11.8 °C, Thermal Resistance 1 °C/W → 13.2 W

Solve for Thermal Resistance

Junction Temp 2.5 °C, Ambient Temp 5.5 °C, Power 10 mW → -300 °C/W

How Junction Temp changes with Ambient Temp

Ambient Temp (input) Junction Temp (result)
24.2 °C 992.2 °C
60.5 °C 1029 °C
121 °C 1089 °C
181.5 °C 1150 °C
242 °C 1210 °C
363 °C 1331 °C
484 °C 1452 °C
968 °C 1936 °C
1694 °C 2662 °C
2420 °C 3388 °C

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Frequently asked questions

How do you calculate Junction Temperature?

Use Tj = Ta + P × Rθja. With Ambient Temp 110 °C, Power 10 W, Thermal Resistance 20 °C/W, Junction Temp works out to 310 °C.

What is the formula for Junction Temperature?

The formula is Tj = Ta + P × Rθja. Junction temperature is the temperature at the semiconductor die inside a package, and it determines the device's reliability and lifespan.

How do you find Ambient Temp when you know the other values?

Rearrange for Ambient Temp: with Junction Temp 2.5 °C, Power 10 mW, Thermal Resistance 0.1 °C/W, Ambient Temp is 2.499 °C.

How do you find Power when you know the other values?

Rearrange for Power: with Junction Temp 25 °C, Ambient Temp 11.8 °C, Thermal Resistance 1 °C/W, Power is 13.2 W.

Related Concepts

All Thermal formulas →
Junction Temperature Full Thermal Chain Required Heatsink Maximum Power (Junction to Case) Thermal Time Constant Forced Convection Heat Transfer Power Derating (Temperature) Natural Convection Thermal Resistance

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