Lumped Capacitance Calculator
Calculate transient temperature response and time constant with Biot number validity check
Lumped Capacitance Calculator
Calculate transient temperature response using the lumped capacitance method (Bi < 0.1).
Formulas
Sphere: r/3 | Cylinder: r/2 | Plane wall: L/2
Bi = h·L_c/k = 0.0333 ✓ Lumped method valid (Bi < 0.1)
Results
Time Constant τ
780.00 s
= 13.00 min
Temperature at t = 60.0 s
279.64 °C
(T−T_∞)/(T_i−T_∞)
0.925961
Common Material Properties
How to Use This Calculator
Enter your input values
Fill in all required input fields for the Lumped Capacitance Calculator. Most fields include unit selectors so you can work in your preferred unit system.
Review your inputs
Double-check that all values are correct and that you have selected the right units for each field. Incorrect units are the most common source of calculation errors.
Read the results
The Lumped Capacitance Calculator instantly computes the output and displays results with units. All calculations happen in your browser — no loading time and no data sent to a server.
Formula Reference
Lumped Capacitance Calculator Formula
See calculator inputs for the governing equation
Variables: All variables and their units are labeled in the calculator interface above.
When to Use This Calculator
- •Use the Lumped Capacitance Calculator when solving homework or exam problems that require quick numerical verification of your hand calculations.
- •Use it during the design phase to rapidly iterate on parameters before running detailed finite element simulations.
- •Use it when reviewing a colleague's calculation or checking a vendor's data sheet for plausibility.
- •Use it to generate reference data for a technical report or presentation without manual computation.
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