Calculator Inputs
The page stays single-column, while the calculator fields adapt to screen size.
Example Data Table
These sample rows help verify units and compare methods before using live values.
| Case | Method | Known Inputs | Formula | Estimated τ |
|---|---|---|---|---|
| Thermistor Bead | Direct | Rth = 2.4 K/W, Cth = 18 J/K | τ = Rth × Cth | 43.2 s |
| Metal Block | Mass + Resistance | m = 0.50 kg, cp = 900 J/kg·K, Rth = 0.60 K/W | τ = mcpRth | 270 s |
| Small Heat Sink | Convection | m = 0.15 kg, cp = 900 J/kg·K, h = 22, A = 0.06 | τ = mc / hA | 102.27 s |
| Power Module | Direct | Rth = 1.1 K/W, Cth = 320 J/K | τ = Rth × Cth | 352 s |
| Sensor Housing | Mass + Resistance | m = 0.08 kg, cp = 500 J/kg·K, Rth = 1.9 K/W | τ = mcpRth | 76 s |
Formula Used
τ = Rth × CthThermal time constant equals thermal resistance multiplied by thermal capacitance.
Cth = m × cpThis converts material properties into heat storage capacity.
Rth = 1 / (h × A)τ = (m × cp) / (h × A)This is useful when convective cooling dominates.
T(t) = Teq + (Ti − Teq) × e^(−t/τ)It predicts heating or cooling toward equilibrium.
t(p) = −τ × ln(1 − p)For 63.2% response,
t = τ.
How to Use This Calculator
- Select the method that matches your known data.
- Enter initial temperature, equilibrium temperature, and elapsed time.
- Fill the method-specific inputs using consistent SI units.
- Click the calculate button to generate the result block.
- Review the time constant, response percentages, and milestone times.
- Use the chart to visualize how temperature approaches equilibrium.
- Export CSV for spreadsheets or PDF for reports and documentation.
Frequently Asked Questions
1. What does the thermal time constant represent?
It shows how quickly a body approaches a new thermal equilibrium. After one time constant, the system completes about 63.2% of the total temperature change toward its final value.
2. Why does the calculator offer multiple methods?
Different projects provide different known values. Some designs already have thermal resistance and capacitance, while others only provide mass, specific heat, surface area, or convection data.
3. When should I use the direct method?
Use it when thermal resistance and thermal capacitance are known from measurement, simulation, or a prior model. It is the fastest and most direct first-order estimate.
4. Is the convection method always accurate?
No. It is an approximation that works best when convection dominates and the body behaves like a lumped thermal mass. Strong radiation, conduction paths, or internal gradients reduce accuracy.
5. Why is one time constant linked to 63.2% response?
The first-order exponential model gives 1 - e^-1 after one time constant. That value is about 0.632, so the response reaches 63.2% of the total change.
6. Can this calculator model both heating and cooling?
Yes. The same equation works for both. The direction of change depends on the difference between initial temperature and equilibrium temperature.
7. What units should I use for reliable results?
Use seconds, kilograms, joules, kelvin, watts, square meters, and degrees Celsius for temperatures. Keeping units consistent is essential for correct time-constant values.
8. Can I use the output for control or electronics work?
Yes. The result helps estimate sensor lag, enclosure response, cooling delay, and thermal filtering behavior. It is also useful for rough control tuning and thermal protection timing.