Thermal Time Constant
τ = Cth × Rth
Quick answer
This calculator solves τ = Cth × Rth for Thermal Time Constant. With Thermal Capacitance 0.5 J/°C, Thermal Resistance 20 °C/W, the result is 10 s. It solves in 3 directions, so you can enter the values you have and get the one you need.
Calculator
Formula
Description
The thermal time constant determines how quickly a component heats up or cools down, analogous to the RC electrical time constant. It equals the product of thermal capacitance (the ability to store heat) and thermal resistance (the opposition to heat flow). After one time constant, the temperature reaches 63.2% of its final steady-state value. Small components with low thermal mass (SMD resistors, small ICs) heat up in milliseconds, while large heatsinks may take minutes to reach thermal equilibrium. This is important for analyzing transient thermal behavior during power pulses.
Variables
- τ — Thermal time constant (s)
- Cth — Thermal capacitance (J/°C)
- Rth — Thermal resistance (°C/W)
Practical Notes
Thermal capacitance depends on mass and specific heat: Cth = m × cp. Copper has cp = 385 J/(kg·°C), aluminum 900 J/(kg·°C), silicon 700 J/(kg·°C). A TO-220 package has τ ≈ 1-5 seconds. An SOT-23 package has τ ≈ 10-50 ms. Transient thermal impedance curves in datasheets show how junction temperature evolves during power pulses.
Symbols and units
| Symbol | Meaning | Default unit | Accepted units |
|---|---|---|---|
| tau | Thermal Time Constant | s | ps, ns, µs, ms, s, min, h |
| Cth | Thermal Capacitance | — | J/°C |
| Rth | Thermal Resistance | °C/W | °C/W |
Step by step
- 1. What you know: Thermal Capacitance 0.5 J/°C, Thermal Resistance 20 °C/W
- 2. The relation: τ = Cth × Rth
- 3. Substitute: Cth = 0.5 J/°C, Rth = 20 °C/W
- 4. Result: Thermal Time Constant = 10 s
Worked examples
Minimum range
Given: Thermal Capacitance 0.025 J/°C, Thermal Resistance 0.1 °C/W
Result: Thermal Time Constant = 2.5 ms
Low range
Given: Thermal Capacitance 0.25 J/°C, Thermal Resistance 1 °C/W
Result: Thermal Time Constant = 0.25 s
Typical
Given: Thermal Capacitance 0.5 J/°C, Thermal Resistance 20 °C/W
Result: Thermal Time Constant = 10 s
High range
Given: Thermal Capacitance 0.8 J/°C, Thermal Resistance 100 °C/W
Result: Thermal Time Constant = 1.333 min
Maximum range
Given: Thermal Capacitance 8 J/°C, Thermal Resistance 1000 °C/W
Result: Thermal Time Constant = 2.222 h
Solving for each variable
Solve for Thermal Time Constant
Thermal Capacitance 0.025 J/°C, Thermal Resistance 0.1 °C/W → 2.5 ms
Solve for Thermal Capacitance
Thermal Time Constant 100 µs, Thermal Resistance 0.1 °C/W → 0.001 J/°C
Solve for Thermal Resistance
Thermal Time Constant 100 µs, Thermal Capacitance 0.025 J/°C → 0.004 °C/W
How Thermal Time Constant changes with Thermal Capacitance
| Thermal Capacitance (input) | Thermal Time Constant (result) |
|---|---|
| 0.05 J/°C | 1 s |
| 0.125 J/°C | 2.5 s |
| 0.25 J/°C | 5 s |
| 0.375 J/°C | 7.5 s |
| 0.5 J/°C | 10 s |
| 0.75 J/°C | 15 s |
| 1 J/°C | 20 s |
| 2 J/°C | 0.6667 min |
| 3.5 J/°C | 1.167 min |
| 5 J/°C | 1.667 min |
The same result in other units
| Unit | Value |
|---|---|
| ms | 10000 |
| s | 10 |
| min | 0.1667 |
| h | 0.002778 |
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<p><a href="https://vbatpower.com/formulas/thermal-time-constant/">Thermal Time Constant</a> Calculator by vbatpower.com</p>Frequently asked questions
How do you calculate Thermal Time Constant?
Use τ = Cth × Rth. With Thermal Capacitance 0.5 J/°C, Thermal Resistance 20 °C/W, Thermal Time Constant works out to 10 s.
What is the formula for Thermal Time Constant?
The formula is τ = Cth × Rth. The thermal time constant determines how quickly a component heats up or cools down, analogous to the RC electrical time constant.
How do you find Thermal Capacitance when you know the other values?
Rearrange for Thermal Capacitance: with Thermal Time Constant 100 µs, Thermal Resistance 0.1 °C/W, Thermal Capacitance is 0.001 J/°C.
How do you find Thermal Resistance when you know the other values?
Rearrange for Thermal Resistance: with Thermal Time Constant 100 µs, Thermal Capacitance 0.025 J/°C, Thermal Resistance is 0.004 °C/W.
What units does Thermal Time Constant use?
Thermal Time Constant is shown in ms, s, min, h. Values are held in SI base units internally, so you can mix prefixes without converting by hand.
Related Concepts
All Thermal formulas →Need more features?
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