calculator
RC time constant calculator
A resistor and a capacitor set every delay in electronics — button debouncing, camera-flash charging, the 555 timer's blink rate. Enter yours and this works out how long the capacitor takes to fill up, with the charging curve drawn below.
The answer
τ = 100.0 ms
10 kΩ × 10 µF = 100.0 ms
- Time constant τ = R × C: 100.0 ms
- After 1τ the capacitor is 63.2 % full: 100.0 ms
- After 3τ it's 95 % full: 300.0 ms
- Call it fully charged at 5τ (99.3 %): 500.0 ms
- 555 half-swing (1/3 → 2/3 Vcc) is ln 2 · τ ≈ 0.693 · τ: 69.3 ms
Real electrolytic capacitors are ±20 % off their label, so the actual charge time can be a fifth off in either direction. Film and ceramic capacitors are much tighter.
The charge curve
Green line: charging up through the resistor. Copper dashed: discharging through the same resistor. Both curves are exponential — steepest at the start, then flatter and flatter.
| Time | Charged | Left to go |
|---|---|---|
| 1τ = 100.0 ms | 63.2 % | 36.8 % |
| 2τ = 200.0 ms | 86.5 % | 13.5 % |
| 3τ = 300.0 ms | 95.0 % | 5.0 % |
| 4τ = 400.0 ms | 98.2 % | 1.8 % |
| 5τ = 500.0 ms | 99.3 % | 0.7 % |
What a time constant is
A capacitor is a tiny reservoir for charge. When you connect it through a resistor to a battery, current rushes in — a lot at first, because the capacitor is empty and the full battery voltage sits across the resistor. As the capacitor fills, its own voltage rises, so the voltage across the resistor drops, so the current slows. The result is an exponential curve: fast near the start, gentler at the end, never quite touching the top.
τ (tau) = R × C is the natural unit of time for that curve. In one τ the capacitor makes it 63.2 % of the way to the battery. In five τ it's 99.3 % — close enough that engineers say "fully charged" and move on. The curve is the same shape whether τ is a microsecond (audio) or an hour (a big electrolytic through a big resistor). Only the timescale changes.
Where you'll see this on the site
The 555 timer calculator lives on this formula. Inside a 555 the capacitor charges from 1/3 to 2/3 of the supply through R1 + R2, then discharges from 2/3 back to 1/3 through R2 alone. Each half-swing is ln 2 · τ ≈ 0.693 · τ — that's where the 0.693 in every 555 formula comes from. The 555 chip guide shows the wiring that turns this timing into a blink.
Sizing the parts
Pick τ first, then split it between R and C. A slow blink around one second wants τ ≈ 1 s, which is 1 MΩ × 1 µF, or 100 kΩ × 10 µF, or 10 kΩ × 100 µF — same τ, different trade-offs. Bigger resistors draw less current (good for battery projects) but pick up more electrical noise. Big electrolytic capacitors are cheap but loose (±20 %) and leak; small film or ceramic ones are tight but expensive above a microfarad or so. For beginner circuits, 10 kΩ + 10 µF is a safe starting pair.
Common questions
Why 63.2 % specifically? It's 1 − 1/e. The math of continuously-varying rates puts Euler's number at the centre of every process that slows down as it approaches its target — bank interest, radioactive decay, a hot mug cooling. RC is the electrical version.
Discharging follows the same time constant? Yes — a full capacitor connected across a resistor loses 63.2 % of its voltage in 1τ and 99.3 % in 5τ. That's the copper dashed curve above.
Does more voltage change τ? No. τ = R × C only. A bigger battery makes the capacitor charge to a bigger final voltage, but the curve gets there in the same number of τ.
See RC timing at work in the 555 frequency calculator, decode the number on the cap with the capacitor code calculator, or pick up the parts on the 10 µF capacitor guide.