Compute τ, Rθ, or Cθ with unit conversions. Model temperature curves for step power events. Download neat tables for sharing and documentation anytime anywhere.
The lumped thermal model treats the system like a first‑order network: τ = Rθ × Cθ.
Cooling toward ambient: T(t)=Tamb+(T0-Tamb)e-t/τ.
Step‑power heating: ΔT(t)=P·Rθ(1-e-t/τ), and T(t)=Tamb+ΔT(t).
| Case | Rθ (K/W) | Cθ (J/K) | τ (s) | Mode note |
|---|---|---|---|---|
| Heatsink + device | 2.5 | 120 | 300 | τ = Rθ×Cθ |
| Small enclosure | 6.0 | 85 | 510 | Longer response time |
| Metal block | 1.2 | 450 | 540 | High heat capacity dominates |
| Fast sensor mount | 0.8 | 30 | 24 | Quick settling behavior |
Values are illustrative; real systems may deviate from a single time constant.
The thermal time constant τ is the characteristic response time of a lumped body exchanging heat with its environment. After a sudden change, the temperature moves exponentially toward its new value. At one τ, the system has completed about 63.2% of the total change, making τ a practical “speed” metric.
In the first‑order model, thermal resistance Rθ (K/W) plays the role of an electrical resistor and thermal capacitance Cθ (J/K) behaves like a capacitor. Their product gives τ = Rθ·Cθ. This approximation is strong when temperature within the body is nearly uniform and heat flow paths are stable.
Rθ is often dominated by interfaces and convection. For conduction through a layer, a simple estimate is R ≈ L/(kA). For convection, R ≈ 1/(hA). In electronics, published junction‑to‑ambient values provide a fast starting point, but mounting, airflow, and enclosure choices can shift Rθ significantly.
Cθ can be approximated using C ≈ m·cp, where m is mass and cp is specific heat capacity. Metals with high density can yield large Cθ even in small volumes. If only a portion of the structure heats quickly, use the “effective” mass participating during the time window of interest.
The same τ shapes both heating and cooling. In step‑power heating, ΔT(t)=P·Rθ(1−e−t/τ) approaches the final rise ΔT∞=P·Rθ. In cooling, the difference from ambient shrinks as e−t/τ. This calculator reports settling times for common remaining fractions to support quick design checks.
Many specifications use “within 10%” or “within 1%” of final value. For a first‑order response, 10% remaining occurs at about 2.303τ and 1% remaining occurs at about 4.605τ. These relationships help translate a measured curve into a single τ for documentation and comparison.
Multi‑layer structures may show multiple slopes because different masses and resistances dominate at different times. If the curve is clearly non‑exponential, consider fitting two exponentials or using a thermal network. Still, an effective τ is useful for early estimates, control tuning, and communicating trends.
To measure τ, apply a step (power or ambient) and log temperature at a consistent sample rate. Avoid sensor self‑heating, ensure good contact, and keep airflow steady. Fit the exponential region, then validate by checking the 63.2% point. This workflow produces repeatable, decision‑ready parameters.
After one time constant, the temperature completes about 63.2% of its total change toward the new steady state. It is a convenient benchmark for comparing how quickly systems respond.
Yes. Temperature differences in °C and K are numerically identical, so ΔT computations are unchanged. Just keep units consistent when entering ambient and initial temperatures.
Compute mass from density and volume, then multiply by specific heat: Cθ ≈ m·cp. If only part of the structure heats quickly, use an effective mass for that region.
Real assemblies may have multiple heat paths and distributed masses, creating more than one dominant time constant. Airflow changes and contact resistance can also distort the curve, especially early in the transient.
Common choices are 0.9 (90%) for fast checks and 0.99 (99%) for near‑settled conditions. The calculator converts your chosen fraction into an equivalent time based on the first‑order model.
For linear, temperature‑independent properties, τ depends on Rθ and Cθ, not power. At high temperatures, convection coefficients and material properties can change, causing τ to shift with operating conditions.
Reduce τ by lowering Rθ (better conduction paths, improved convection, larger area) or lowering Cθ (less mass, lower heat capacity). In many designs, reducing interface resistance yields the biggest gain.
Important Note: All the Calculators listed in this site are for educational purpose only and we do not guarentee the accuracy of results. Please do consult with other sources as well.