RC Time Constant Calculator

Find the time constant of a resistor-capacitor circuit, how long it takes to charge or discharge, and the voltage at any moment.

Use k or M, like 10k or 1M.
Use p, n, u or m, like 100u for 100 µF.
See the voltage at a moment in time.
Capacitor Is
Fractions and decimals both work.
–
Time Constant
Time constant (τ)
Full (5τ)
Voltage at time
Half voltage at
Filter cutoff
Voltage After 1τ

Saved Circuits

Items you add are saved in this browser.

NameRCτ5τRemove

RC Time Constant

When a capacitor charges or discharges through a resistor, the voltage changes quickly at first and then more slowly, following an exponential curve. The time constant, tau (τ), is the resistance times the capacitance. After one time constant, a charging capacitor reaches about 63.2% of the supply voltage; after five, it's over 99% and is usually treated as full.

τ = R × C (ohms × farads = seconds)
Charging: V = Vs × (1 − e^(−t ÷ τ))   Discharging: V = V₀ × e^(−t ÷ τ)

Worked Example

A 10 kΩ resistor and a 100 µF capacitor give τ = 10,000 × 0.0001 = 1 second. Charging from a 5 V supply, the capacitor reaches 5 × 0.632 = 3.16 V after 1 second and about 4.97 V after 5 seconds.

Time Constants Table

TimeCharged ToDischarged To

Tips

RC timing is used in delays, debouncing, filters and 555 timers. Real capacitors have wide tolerances, often ±10% to ±20% for electrolytics, so RC timing is approximate. The cutoff frequency of a simple RC filter is 1 ÷ (2π × R × C).