What is the formula for Capacitor Charge / Discharge Energy Calculator?

Core formula: ΔQ = C·(V1−V0) | ΔE = ½C(V1²−V0²) | charge E_source = Vs·ΔQ | E_loss = E_source − ΔE. The tool returns results instantly using this formula and the selected parameters.

Capacitor Charge / Discharge Energy Calculator

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Energy accounting for capacitor charge / discharge: source output, capacitor energy change, resistor / loop loss, charging efficiency, and average power at a repetition rate.

Key points

Capacitor Charge / Discharge Energy Calculator: Energy accounting for capacitor charge / discharge: source output, capacitor energy change, resistor / loop loss, charging efficiency, and average power at a repetition rate. Formula: ΔQ = C·(V1−V0) | ΔE = ½C(V1²−V0²) | charge E_source = Vs·ΔQ | E_loss = E_source − ΔE. Enter parameters on the DD-CAT IDE online tool page to get results instantly, with a calculation-model diagram that updates with the inputs. When a constant-voltage source charges a capacitor through a resistor, source energy is Vs·C·ΔV while capacitor energy rises by only ½C(V1²−V0²); the difference is dissipated in the resistor / loop. Classic 0→Vs charge: source supplies C·Vs², capacitor stores ½C·Vs², loss is ½C·Vs², so efficiency is at most 50%. Charging from a non-zero voltage can exceed 50%.

Inputs

ΔQ = C·(V1−V0) | ΔE = ½C(V1²−V0²) | charge E_source = Vs·ΔQ | E_loss = E_source − ΔE

Calculation model (updates with parameters)

Charge transferred ΔQ	12 mC	C·(V1−V0)
Initial stored energy E0	0 J	½·C·V0²
Final stored energy E1	72 mJ	½·C·V1²
Capacitor energy change ΔE	72 mJ	Energy added to the capacitor
Source output energy E_source	144 mJ	Vs·ΔQ (constant-voltage source)
Resistor / loop loss E_loss	72 mJ	E_source − ΔE
Charging efficiency η	50.0 %	At most 50% when charging from 0 V
Full 0→Vs charge (reference)	Source 144 mJ ｜储能 72 mJ ｜损耗 72 mJ	Classic 50% efficiency: half the source energy is stored, half is dissipated

⚠ 从 0 充满的经典结论：supply输出 C·Vs²，Capacitance只存 ½C·Vs²，另外 ½C·Vs² 全部损耗在Resistance / 回路中，效率 50%。

Engineering notes

When a constant-voltage source charges a capacitor through a resistor, source energy is Vs·C·ΔV while capacitor energy rises by only ½C(V1²−V0²); the difference is dissipated in the resistor / loop.
Classic 0→Vs charge: source supplies C·Vs², capacitor stores ½C·Vs², loss is ½C·Vs², so efficiency is at most 50%. Charging from a non-zero voltage can exceed 50%.
During discharge, stored energy is delivered to the load / resistor; if only a resistor is used, all of it becomes heat. Energy recovery requires a DC-DC or regeneration circuit.
Loss is independent of resistance with an ideal constant-voltage source, but charge / discharge time and peak current depend on R·C; check resistor power for pulse energy and repetition rate.

FAQ

What is Capacitor Charge / Discharge Energy Calculator for?: Energy accounting for capacitor charge / discharge: source output, capacitor energy change, resistor / loop loss, charging efficiency, and average power at a repetition rate.
What is the formula for Capacitor Charge / Discharge Energy Calculator?: Core formula: ΔQ = C·(V1−V0) | ΔE = ½C(V1²−V0²) | charge E_source = Vs·ΔQ | E_loss = E_source − ΔE. The tool returns results instantly using this formula and the selected parameters.
What engineering notes should I keep in mind when using Capacitor Charge / Discharge Energy Calculator?: When a constant-voltage source charges a capacitor through a resistor, source energy is Vs·C·ΔV while capacitor energy rises by only ½C(V1²−V0²); the difference is dissipated in the resistor / loop. Classic 0→Vs charge: source supplies C·Vs², capacitor stores ½C·Vs², loss is ½C·Vs², so efficiency is at most 50%. Charging from a non-zero voltage can exceed 50%. During discharge, stored energy is delivered to the load / resistor; if only a resistor is used, all of it becomes h…