Capacitor Charge Time Calculator: RC Time Constant and Voltage
Enter your resistance, capacitance, and supply voltage to find how long it takes your capacitor to charge. You get the RC time constant, the voltage and charge percentage at every time constant milestone, the time to reach any target percentage, and the energy stored when fully charged. The chart shows the full exponential charging curve, and the steps panel works through the maths with your exact values.
Formula
Worked example
A 3 kΩ resistor in series with a 1000 μF capacitor charged from a 9 V supply: τ = 3000 Ω × 0.001 F = 3 s. After 1τ (3 s) the voltage is 9 × (1 - e⁻¹) ≈ 5.69 V (63.2%). After 5τ (15 s) it is 9 × (1 - e⁻⁵) ≈ 8.94 V (99.3%), which is the practical full-charge point.
What is the RC time constant?
The time constant, written as the Greek letter tau (τ), is the fundamental measure of how quickly an RC circuit charges or discharges. It equals the product of the resistance in ohms and the capacitance in farads: τ = R × C. After one time constant the capacitor has reached 63.2% of the supply voltage, after two it is at 86.5%, and after five time constants it is at 99.3%. Engineers treat five time constants as the practical point of full charge, because a true 100% would require infinite time. The time constant has units of seconds when R is in ohms and C is in farads.
How to use this calculator
Enter the series resistance, capacitance (with the correct unit prefix), and supply voltage. The calculator returns the time constant, the time to reach your chosen percentage, the practical full-charge time (99%), and the energy stored. The chart shows the full exponential charging curve over five time constants, and the steps panel shows every formula substituted with your actual numbers. To find time to a specific voltage rather than a percentage, set the target percentage to (V_target / V_supply) × 100.
The charging formula and how to read it
The voltage across the capacitor at any time t is V(t) = V_s × (1 - e^(-t/τ)), where V_s is the supply voltage and e is Euler's number (~2.718). The curve rises steeply at first and flattens as it approaches V_s, which is the classic shape of exponential growth toward a ceiling. To invert this and find the time at which the capacitor reaches a given voltage V: t = -τ × ln(1 - V/V_s). For example, to find the time to reach 90% of supply voltage, substitute 0.9: t = -τ × ln(1 - 0.9) = -τ × ln(0.1) = τ × 2.303, or about 2.3 time constants.
Energy stored in a capacitor
When the capacitor is fully charged to voltage V_s, the energy stored is E = ½ × C × V_s², measured in joules. Because energy scales with the square of voltage, doubling the supply voltage stores four times the energy. Doubling the capacitance doubles the stored energy. This stored energy is what allows capacitors to act as short-burst power sources in camera flashes, defibrillators, and power-supply smoothing circuits. Note that only half the energy drawn from the supply ends up stored in the capacitor; the other half is dissipated as heat in the resistor.
Practical notes for real circuits
- Real resistors and capacitors have tolerances (often 5-10%), so the actual charge time may differ from the calculated value.
- Electrolytic capacitors have significant equivalent series resistance (ESR) that adds to the external resistance; use total R when precision matters.
- For timing circuits (555 timers, RC filters), choose standard resistor and capacitor values and verify the resulting τ is within tolerance for your application.
- The formula assumes a step-function supply. If the input voltage ramps or oscillates, the response is different.
RC charging milestones
| Time constants (nτ) | Charge percentage | Remaining to full charge |
|---|---|---|
| 1τ | 63.2% | 36.8% |
| 2τ | 86.5% | 13.5% |
| 3τ | 95.0% | 5.0% |
| 4τ | 98.2% | 1.8% |
| 5τ | 99.3% | 0.7% |
Voltage and charge percentage reached at each time constant for a standard RC circuit.
Frequently asked questions
How long does it take a capacitor to fully charge?
A capacitor never technically reaches exactly 100% charge, because the charging follows an exponential curve that approaches but never reaches the supply voltage. In practice, engineers consider a capacitor fully charged after five time constants (5τ), when it is at 99.3% of supply voltage. For a 1 kΩ resistor and 100 μF capacitor, τ = 0.1 s and full charge takes about 0.5 s.
What is the RC time constant formula?
The time constant τ (tau) equals resistance multiplied by capacitance: τ = R × C. When R is in ohms and C is in farads, τ is in seconds. For example, 10 kΩ and 47 μF gives τ = 10,000 × 0.000047 = 0.47 s.
What percentage does a capacitor charge to after one time constant?
After one time constant the capacitor charges to exactly 1 - 1/e ≈ 63.2% of the supply voltage. This value comes directly from the exponential charging formula V(t) = V_s(1 - e^(-t/τ)): at t = τ, the exponent is -1, so V = V_s(1 - e^(-1)) = V_s × 0.632.
How do I calculate the time to charge to a specific voltage?
Use the inverted formula: t = -τ × ln(1 - V/V_s), where V is your target voltage, V_s is the supply, and τ = R × C. For a 9 V supply and a target of 8 V: t = -τ × ln(1 - 8/9) = -τ × ln(0.111) = τ × 2.197, just over 2.2 time constants. You can also enter 88.9% (8/9 × 100) in the target percentage field above.
Why does energy scale with voltage squared?
The energy stored E = ½CV² comes from integrating the instantaneous power over the charging process. Because power is proportional to V and the voltage is itself proportional to charge, the total work done scales as V². This means doubling the voltage stores four times the energy, which is why high-voltage capacitors are used in flash photography and pulsed-power applications.
What is the difference between charging and discharging an RC circuit?
During charging, the voltage across the capacitor rises as V(t) = V_s(1 - e^(-t/τ)). During discharging through the same resistor, the voltage falls as V(t) = V_0 × e^(-t/τ), where V_0 is the initial voltage. Both processes use the same time constant τ = RC, so a capacitor that takes 5τ to charge also takes 5τ to discharge to under 1% of its initial voltage.