This is the capacitor charge time calculator — helping you to quickly and precisely calculate the charge time of your capacitor. Here we answer your questions on how to calculate the charge time of a capacitor and how many time constants for a capacitor to fully charge does it take. Type your values into the ready-to-use calculator or scroll down to get more comfortable with the topic through our comprehensive explanations and step-by-step example calculation.
What is the capacitor charge time?
A capacitor stores electric charge in the form of an electrostatic field and will be charged or discharged during its use in the electric circuit. The charge time is the time it takes the capacitor to charge up to around 99%, reaching its charger's voltage (e.g., a battery).
Practically the capacitor can never be 100% charged as the flowing current gets smaller and smaller while reaching full charge, resulting in an exponential curve. This is why after a number of five multiples of the time constant, we regard the capacitor as fully charged. We'll explain the notion of time constant in the next section.
The capability of the capacitor to store energy is indicated in its capacitance. It is measured in farads (F). The resistor will affect our capacitor charge time, as it regulates the electric flow through the circuit. It is measured in ohms (Ω).
How many time constants to charge a capacitor?
To calculate the charge time of a capacitor, we need to consider the time constant τ (tau) of the electric circuit, measured in seconds. It is the time it takes the capacitor to charge to 63.2% of its charger's voltage (e.g., a battery) through the resistor. It is also referred to as the delay time or transient response time, indicating the time response of the circuit when the input voltage is applied. It is calculated as follows:
τ = R × C
where:
- τ — Time constant (seconds);
- R — Resistance (ohm); and
- C — Capacitance (farads).
Using the time constant, we can write the relationship between the percentage of charge and the charge time t as:
Percentage = 1 − e(−t/τ)
It's common knowledge that after five time constants, the capacitor is regarded as fully charged, reaching a charge of around 99%. We can derive this information by applying the formulas above. The table below shows the charge level reached at each multiple of the time constant:
| Time constants | Charge level | Remaining (discharge) |
|---|---|---|
| 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% |
Formula for capacitor charge time
The voltage across a charging capacitor as a function of time is given by:
V(t) = V₀ × (1 − e(−t/τ))
To find the time required to reach a certain percentage of charge, we rearrange the percentage formula and solve for the time t:
t = −τ × ln(1 − Percentage)
where the percentage is expressed as a decimal (for example, 0.99 for 99%).
Using the capacitor charge time calculator
- Choose your preferred unit system — metric (SI) or American.
- Enter the resistance (R) of the resistor in the circuit, selecting the appropriate unit (mΩ, Ω, kΩ, MΩ, or GΩ).
- Enter the capacitance (C) of the capacitor, selecting the appropriate unit (F, mF, µF, nF, or pF).
- Optionally, enter the supply voltage (V₀) of the charger to see the voltage reached at each time constant.
- Enter the target percentage of charge you want to reach (the default of 99% is the conventional "fully charged" level).
- The calculator instantly returns the time constant τ, the time to reach your target charge, the full charge time (5τ), the discharge time, and a complete time-constant table.
How to find time to defined % capacitor charge
To find the time it takes to reach a specific percentage of charge, use the formula t = −τ × ln(1 − Percentage). First calculate the time constant τ = R × C, then substitute your desired percentage (as a decimal). For example, to find the time to reach 90% charge, you would use t = −τ × ln(1 − 0.90) = −τ × ln(0.10) ≈ 2.303 × τ.
Example calculation for capacitor charge time
Let's calculate the charge time for a circuit with a resistance of R = 10 kΩ and a capacitance of C = 100 µF, charged from a 5 V supply.
- First, find the time constant:
τ = R × C = 10,000 Ω × 0.0001 F = 1 second - The capacitor reaches 63.2% of 5 V (≈ 3.16 V) after one time constant — that is, after 1 second.
- The capacitor is regarded as fully charged after five time constants:
t = 5 × τ = 5 × 1 s = 5 seconds (≈ 99.3% charge, ≈ 4.97 V). - To find the time to reach exactly 99%:
t = −τ × ln(1 − 0.99) = −1 × ln(0.01) ≈ 4.61 seconds.
Discharge time of a capacitor
The discharge of a capacitor follows the same exponential behavior, but in reverse. The voltage during discharge is described by:
V(t) = V₀ × e(−t/τ)
After one time constant, the capacitor discharges to 36.8% of its initial voltage; after five time constants, it is regarded as fully discharged (around 0.7% remaining). The discharge time constant is the same τ = R × C, so a larger resistance or capacitance means a slower discharge.