RC Circuit Calculator

The RC time constant tau = R x C (resistance in ohms times capacitance in farads) is the time in seconds for the capacitor voltage to rise to about 63.2% of the supply during charging, or fall to about 36.8% of its starting voltage during discharging. Example: R = 10 kohm and C = 100 uF gives tau = 10,000 x 0.0001 = 1.0 second.

In theory a capacitor never reaches 100% because charging follows Vc(t) = V x (1 - e^(-t/tau)). In practice engineers use 5 time constants (5 x tau) as fully charged, reaching 99.33% of the supply. At 3 x tau you are at 95.0%, at 2 x tau 86.5%, and at 1 x tau 63.2%.

Vc(t) = V x (1 - e^(-t/tau)), where V is the supply voltage, t is elapsed time, and tau = R x C. With R = 10 kohm, C = 100 uF (tau = 1 s) and V = 5 V, after 1 second the capacitor sits at 5 x (1 - e^-1) = 3.16 V, which is 63.2% of 5 V. This calculator plots the full exponential curve up to 5 x tau.

Vc(t) = V0 x e^(-t/tau), where V0 is the starting voltage. The capacitor loses about 63.2% of its voltage every time constant: after 1 x tau it holds 36.8% of V0, after 2 x tau 13.5%, after 5 x tau only 0.67%. The discharge is the mirror image of the charging curve.

Rearrange the charging equation: t = -tau x ln(1 - p/100) to reach p percent of the supply. For 90% that is t = 2.303 x tau; for 99% it is t = 4.605 x tau. For discharging to p percent of the start voltage: t = -tau x ln(p/100), so reaching 50% takes t = 0.693 x tau (one half-life).

A 555 in monostable (one-shot) mode outputs a single pulse of width T = 1.1 x R x C per trigger, where R is the timing resistor and C the timing capacitor. Example: R = 10 kohm, C = 100 uF gives T = 1.1 x 1.0 = 1.1 seconds. This calculator also solves backwards: enter the target pulse width plus one component to find the other.

A 555 in astable mode free-runs as an oscillator at f = 1.44 / ((R1 + 2 x R2) x C), with tHIGH = 0.693 x (R1 + R2) x C and tLOW = 0.693 x R2 x C. This tool gives a quick astable reference; for full astable design with duty cycle, reverse R/C design and E-series snapping, use the dedicated NE555 astable calculator (ne555-astable), and note this tool does cover 555 monostable one-shot timing, which the astable tool does not.

This tool works in the time domain: how capacitor voltage evolves over time (tau, charging, discharging curves). An RC cutoff frequency calculator works in the frequency domain: fc = 1 / (2 x pi x R x C), the -3 dB point of an RC low-pass or high-pass filter. Same R and C, different question. For filter design use the cutoff-frequency tool; for transient timing use this one.

Yes: when R is in kohm and C in microfarads, tau comes out directly in milliseconds, because 10^3 x 10^-6 = 10^-3. So 10 kohm x 100 uF = 1000 ms = 1.0 s, and 4.7 kohm x 10 uF = 47 ms. The calculator handles all unit combinations (ohm to Mohm, pF to F) automatically.

No. Tau = R x C depends only on the resistor and capacitor, never on the voltage. A higher supply voltage makes the capacitor charge to a higher final value but the 63.2% point still arrives after exactly one time constant, and 5 x tau still means 99.33% charged regardless of voltage.