What is the formula for RC Charge / Discharge Time?

Core formula: τ = R·C | charge t = −τ·ln(1 − Vt/Vs) | discharge t = −τ·ln(Vt/Vs). The tool returns results instantly using this formula and the selected parameters.

What engineering notes should I keep in mind when using RC Charge / Discharge Time?

τ = R·C is the characteristic time: 1τ reaches 63.2%, 3τ 95%, and 5τ 99.3%. Charge: t = −τ·ln(1 − Vt/Vs); discharge: t = −τ·ln(Vt/Vs). The closer the target is to the supply, the longer it takes. Real circuits also have capacitor tolerance (often ±20% for electrolytics), leakage, resistor tolerance, and source resistance; leave margin and measure for precision timing.

RC Charge / Discharge Time

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First-order RC charge / discharge: compute the time constant, time to the target voltage, and the 63.2% / 95% / 99% and half-life points.

Key points

RC Charge / Discharge Time: First-order RC charge / discharge: compute the time constant, time to the target voltage, and the 63.2% / 95% / 99% and half-life points. Formula: τ = R·C | charge t = −τ·ln(1 − Vt/Vs) | discharge t = −τ·ln(Vt/Vs). Enter parameters on the DD-CAT IDE online tool page to get results instantly, with a calculation-model diagram that updates with the inputs. τ = R·C is the characteristic time: 1τ reaches 63.2%, 3τ 95%, and 5τ 99.3%. Charge: t = −τ·ln(1 − Vt/Vs); discharge: t = −τ·ln(Vt/Vs). The closer the target is to the supply, the longer it takes.

Inputs

τ = R·C | charge t = −τ·ln(1 − Vt/Vs) | discharge t = −τ·ln(Vt/Vs)

Calculation model (updates with parameters)

Time constant τ = R·C	1000 ms	10 kΩ × 100 µF
Time to target voltage (charge)	916.3 ms	Vt / Vs = 60.0%
Time to 63.2%	1000 ms	1τ：Charge到 63.2% / Discharge剩 36.8%
Time to 95%	3 s	3τ
Time to 99%	5 s	5τ，工程上常视为充满 / 放完
Half-life t½	693.1 ms	ln2·τ，Discharge到一半的Time
Initial current I0	500 µA	t=0 时Capacitance视为短路 / VoltageSource
Capacitor energy E	1.25 mJ	½·C·Vs²（充满时）
Equivalent cutoff frequency fc	159.2 mHz	1/(2πRC)，and RC 滤波器同一Time常数

Engineering notes

τ = R·C is the characteristic time: 1τ reaches 63.2%, 3τ 95%, and 5τ 99.3%.
Charge: t = −τ·ln(1 − Vt/Vs); discharge: t = −τ·ln(Vt/Vs). The closer the target is to the supply, the longer it takes.
Real circuits also have capacitor tolerance (often ±20% for electrolytics), leakage, resistor tolerance, and source resistance; leave margin and measure for precision timing.

FAQ

What is RC Charge / Discharge Time for?: First-order RC charge / discharge: compute the time constant, time to the target voltage, and the 63.2% / 95% / 99% and half-life points.
What is the formula for RC Charge / Discharge Time?: Core formula: τ = R·C | charge t = −τ·ln(1 − Vt/Vs) | discharge t = −τ·ln(Vt/Vs). The tool returns results instantly using this formula and the selected parameters.
What engineering notes should I keep in mind when using RC Charge / Discharge Time?: τ = R·C is the characteristic time: 1τ reaches 63.2%, 3τ 95%, and 5τ 99.3%. Charge: t = −τ·ln(1 − Vt/Vs); discharge: t = −τ·ln(Vt/Vs). The closer the target is to the supply, the longer it takes. Real circuits also have capacitor tolerance (often ±20% for electrolytics), leakage, resistor tolerance, and source resistance; leave margin and measure for precision timing.