The capacitor charge time calculator above answers the question a datasheet rarely does directly: how many seconds pass before the capacitor in your circuit actually reaches the voltage you need. Not the generic time constant, and not a vague "about five RC" — the real elapsed time from a starting voltage to a target voltage, for the exact resistance and capacitance in front of you.
Arb Digital publishes free tools that each do one job properly and point at the neighbour when the job changes. This page is about time. If you need the capacitance itself from plate geometry, that is the capacitance calculator. If you already have the value and want the stored energy, the capacitor energy calculator is quicker. For networks of several capacitors, the capacitor combination calculator reduces them to one equivalent value you can paste in here.
What This Capacitor Charge Time Calculator Does
A capacitor charged through a resistor does not fill up at a steady rate. At the instant power is applied the capacitor is empty and the full supply voltage sits across the resistor, so the current is at its maximum. As charge accumulates, the capacitor's own voltage opposes the supply, the voltage across the resistor shrinks, and the current falls with it. The result is an exponential curve that rises quickly at first and then flattens out, approaching the supply voltage without ever quite touching it.
That shape is why "how long does it take to charge" needs a target voltage before it has an answer. A 100 microfarad capacitor charging through 10 kilohms from a 12 volt supply reaches 9 volts in under a second and a half, reaches 11.9 volts in nearly five seconds, and reaches 12 volts never. The calculator asks for the target explicitly for that reason, and refuses to return an answer when the target is set at or above the supply.
The discharge mode is the mirror image. A charged capacitor bleeding through a resistor loses voltage exponentially toward zero, dropping to 36.8 per cent of its starting value after one time constant. This is the calculation behind bleeder resistors, power-down delays and the safety wait before touching a high-voltage rail.
The constant-current mode covers the case where a regulator, a current-limited bench supply or a dedicated charge pump pushes a fixed current into the capacitor regardless of its voltage. There is no exponential at all here: the voltage climbs in a perfectly straight line, and the time is simply the charge required divided by the current supplied. The difference matters, because engineers who assume an exponential in a constant-current circuit consistently overestimate the time.
How to Use It
- Pick the charging method. Resistor charging and constant-current charging follow completely different curves, and the answer differs by a large factor for the same components.
- Enter capacitance and resistance with the right units. Microfarads and kilohms are the common pairing, and the two default units multiply out to a convenient time constant in the tens of milliseconds to seconds.
- Set the supply and starting voltages. A capacitor that is already partly charged reaches the target faster, and the calculation accounts for that rather than assuming it starts at zero.
- Choose a realistic target. For logic thresholds use the actual switching level from the datasheet, not the supply rail. For a full charge, 99 per cent of the supply is the practical stopping point.
- Read the peak current. The first instant is the hardest one on the supply, the switch and the capacitor itself, and it is the figure that decides whether a component survives.
The Formula: How Charge Time Is Calculated
The charging curve is derived in section 21.6 of OpenStax College Physics 2e, on DC circuits containing resistors and capacitors, which gives the capacitor voltage as V = Vs(1 − e−t/RC) when charging from empty, and defines the time constant τ = RC as the time in which the voltage rises to 0.632 of its final value.
Rearranged for time, and generalised to a capacitor that starts at some voltage V₀ rather than zero, that becomes t = RC × ln((Vs − V₀) ÷ (Vs − Vt)). Discharging toward zero from V₀ down to Vt uses t = RC × ln(V₀ ÷ Vt). Constant-current charging uses the definition of capacitance directly: charge equals capacitance times voltage change, and time equals charge divided by current, so t = C(Vt − V₀) ÷ I.
Work the defaults through by hand. The capacitance is 100 microfarads and the resistance is 10 kilohms, so τ = 10,000 × 0.0001 = 1 second. The supply is 12 volts, the capacitor starts at zero and the target is 9 volts, so the ratio is (12 − 0) ÷ (12 − 9) = 4, and the time is 1 × ln(4) = 1.386 seconds. The peak current at the instant of switch-on is 12 ÷ 10,000 = 1.2 milliamps, and the energy on the capacitor at 9 volts is half of 0.0001 times 81, which is 4.05 millijoules.
The farad itself is the coulomb per volt, one of the SI derived units set out in the BIPM SI Brochure. That definition is the whole of the constant-current case: a farad charged by an amp gains a volt every second, so a 100 microfarad capacitor fed 5 milliamps climbs at 50 volts per second and covers 9 volts in 180 milliseconds. The same components, one hundred and eighty milliseconds instead of one and a third seconds, purely because the current no longer tapers off.
Why Five Time Constants Became the Rule, and Where It Misleads
The convention that a capacitor is fully charged after five time constants comes from the arithmetic of the exponential. After one τ the capacitor holds 63.2 per cent of the supply, after two 86.5 per cent, after three 95.0 per cent, after four 98.2 per cent and after five 99.3 per cent. Beyond that the remaining gap is smaller than the tolerance on the components themselves, so treating it as complete is reasonable.
It misleads in two directions. In precision work, five time constants is not nearly enough. A sample-and-hold circuit that needs to settle to twelve-bit accuracy has to reach within one part in four thousand of the final value, which takes about 8.3 time constants; sixteen-bit accuracy needs roughly 11.1. Designing a settling delay around five τ and then wondering why the last few counts drift is a common and expensive mistake.
In the other direction, five time constants is often far too conservative. A power-on reset circuit only has to cross a logic threshold, typically somewhere between 0.5 and 0.7 of the supply. That happens in under 1.2 time constants, so a designer sizing an RC for five τ ends up with a reset delay four times longer than the circuit actually needs. Set the target voltage to the real threshold and the calculator gives the real delay.
The percentages are also independent of the component values, which is the useful part. Any RC network anywhere reaches 63.2 per cent in one time constant, whether that constant is a nanosecond or an hour. The bar display in the result panel shows those three landmark points so you can see where your chosen target falls relative to them.
Inrush Current Is the Number That Breaks Things
The charging time is usually the reason people arrive at this calculation, but the peak current is more often the number that matters. At the moment a supply is connected to an empty capacitor, the capacitor behaves as a short circuit. The only thing limiting the current is the series resistance, and that includes every resistance in the path, not just the resistor you drew on the schematic.
In a deliberate RC timing network the series resistor is large and the inrush is trivial. In a power supply it is the opposite: the bulk capacitor sits across the rail with almost nothing in series but the wiring resistance and the capacitor's own equivalent series resistance. A 1,000 microfarad capacitor on a 24 volt rail with 50 milliohms of total path resistance sees a theoretical peak of 480 amps. Real inductance limits it well below that, but the surge is still enough to weld relay contacts, blow fuses that are correctly rated for the running current, and trip the over-current protection on a switching supply that would otherwise be fine.
This is what soft-start circuits and inrush limiters exist to control, and it is why the peak-current figure appears in the results grid rather than being buried. If that number is uncomfortable, the fix is series resistance during the first few milliseconds — a negative temperature coefficient thermistor, or a resistor bypassed by a relay once the capacitor is up. The Ohm's law calculator sizes that resistor and the electrical power calculator checks it can dissipate the pulse.
Where the Real Circuit Departs From the Curve
The exponential assumes an ideal capacitor, a constant resistance and a stiff supply. Real circuits break all three assumptions in ways worth knowing about.
Equivalent series resistance adds to whatever resistor you specified, which lengthens the time constant slightly and, more importantly, turns the charging current into heat inside the capacitor. In electrolytics this is the dominant self-heating mechanism and the reason ripple-current ratings exist. Leakage works the other way: every capacitor has a parallel leakage path, so a capacitor charged through a very large resistor may never reach the target at all, settling instead at the point where the charging current equals the leakage current. With megohm-scale resistors and electrolytic capacitors this is a real limit rather than a theoretical one.
Dielectric absorption is the strangest effect. Discharge a capacitor fully, disconnect it, and come back a few minutes later to find several per cent of the original voltage has reappeared on its own. The dielectric relaxes and releases charge that the fast discharge did not reach. It is a nuisance in sample-and-hold and integrator circuits, and a genuine hazard in high-voltage equipment, which is why safety procedures call for a shorting bar left in place rather than a quick discharge.
Finally, Class 2 ceramic capacitors lose a large fraction of their capacitance under DC bias. A part marked 10 microfarads may measure 4 at its rated voltage, which shortens the real charging time well below the calculated one. For timing that matters, use a film or Class 1 ceramic part, or measure the capacitance under the bias it will actually see.
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Browse All Free Tools Talk to Arb DigitalCommon Mistakes to Avoid
- Setting the target equal to the supply voltage — the exponential approaches the supply asymptotically, so that target takes infinite time. Use 99 per cent of the supply as the practical equivalent.
- Forgetting the capacitor's starting voltage — a partly charged capacitor is already part of the way there, and assuming it starts at zero overstates the time, sometimes badly.
- Applying the exponential to a constant-current charger — a current source charges linearly, and the RC formula gives an answer that is simply wrong rather than approximate.
- Counting only the resistor you drew — wiring resistance, switch contact resistance and the capacitor's own ESR all belong in the series total, and in low-impedance circuits they dominate it.
- Ignoring the inrush current — a design with a comfortable charging time can still destroy a switch, a fuse or a supply in the first millisecond.
Related Free Tools From Arb Digital
Find the capacitance from geometry with the capacitance calculator, reduce a network to one value with the capacitor combination calculator, and read off the stored energy with the capacitor energy calculator. Size the series resistor using the Ohm's law calculator, check the dissipation with the electrical power calculator, and decode the resistor you actually have with the resistor colour code calculator. For cells rather than capacitors, the battery charge time calculator is the right page. Everything Arb Digital publishes is listed on the free online tools hub.
Frequently Asked Questions
Strictly, it never does, because the voltage approaches the supply exponentially without reaching it. In practice five time constants gets you to 99.3 per cent of the supply, which is inside the tolerance of ordinary components, so that is the figure used as fully charged.
It is resistance multiplied by capacitance, in ohms and farads, giving a result in seconds. In one time constant a charging capacitor reaches 63.2 per cent of the supply voltage, and a discharging one falls to 36.8 per cent of where it started.
Take the natural logarithm of the supply minus the starting voltage, divided by the supply minus the target voltage, then multiply by RC. That handles a capacitor that starts partly charged as well as one that starts empty.
Because the current does not taper off. In an RC circuit the current falls as the capacitor voltage rises, so the last part of the curve is very slow. A current source pushes the same current at every voltage, so the capacitor voltage rises in a straight line.
The supply voltage divided by the total series resistance, because an empty capacitor initially behaves like a short circuit. In a low-impedance power circuit this inrush can reach hundreds of amps for a few milliseconds and is what welds contacts and blows fuses.
Through the same resistor, yes, in direct proportion, since the time constant is resistance times capacitance. Doubling the capacitance doubles every point on the curve. From a fixed current source the relationship is also linear, for the same reason.
That is a discharge calculation using the bleeder resistance actually fitted, and it should never be answered from a formula alone. High-voltage capacitors can recover voltage on their own through dielectric absorption, so equipment procedures call for measuring the terminals and leaving a shorting link in place.
This tool is provided for educational and design-estimating use. It models ideal components and does not account for leakage, dielectric absorption or bias-dependent capacitance, and it is not a substitute for manufacturer data or a qualified safety procedure when working on energised or high-voltage equipment.
