Capacitor Charging Voltage Calculator
Solve the RC charging equation for capacitor voltage, time, source voltage, resistance or capacitance — with unit conversion and an interactive charging-curve graph.
Hover or touch the curve to read values at any time. The amber marker is your calculated operating point; dotted lines mark each time constant (τ, 2τ … 5τ).
Time constant τ = RC
Larger R or C stretches the curve horizontally — the capacitor charges more slowly, but the final value V₀ is unchanged.
Source voltage V₀
V₀ scales the curve vertically. The shape (percent charged versus t/τ) is identical for every source voltage.
Charging current
Current starts at V₀/R when the capacitor is empty and decays exponentially as V(t) rises. It falls to 36.8% after one τ.
Never fully charged
In theory V(t) only approaches V₀ asymptotically. In practice, 5τ (≈99.3%) is the usual rule of thumb for "fully charged".
How to Use This Calculator
The RC charging equation links five quantities: source voltage V₀, capacitor voltage V(t), time t, resistance R and capacitance C. Pick the one you want solved and fill in the other four.
1. Choose what to solve for
Select V(t), t, V₀, R or C under "Solve for". The greyed-out field is the one being calculated.
2. Enter the known values
Type a number or drag the slider. Sliders use a logarithmic scale, so a single drag covers everything from picofarads to farads or nanoseconds to hours.
3. Pick your units
Every field has its own unit selector (mV/V/kV, mΩ to MΩ, pF to F, ns to hours). Changing a unit converts the number so the physical value stays the same.
4. Try a quick preset
The RC presets set R and C for common timing values (τ = 1 ms, 1 s, 10 s) so you can explore the curve straight away.
5. Read the result and the graph
The result card shows the answer, τ and percent charged, plus the result in every unit. The graph plots the full charging curve with your operating point marked. Hover or touch it to read any point.
6. Switch to Advanced for more depth
Advanced mode adds sensitivity to a +1% change in each input, charging current, stored energy, and the time needed to reach 50%, 90% and 99%.
What This Tool Offers
Built around the standard series RC charging equation for a capacitor that starts uncharged and is driven by a DC step voltage.
Solve any of five variables
Find V(t), time, source voltage, resistance or capacitance — the equation is rearranged for you, using logarithms where needed.
Interactive charging graph
A live curve of voltage or current, with your operating point, time-constant markers, and hover/touch readout.
Full unit conversion
Independent unit selectors on every field, automatic conversion when units change, and the result shown in every unit at once.
Transparent step-by-step math
Every calculation shows τ, the exponential term and the substitution, so each answer can be checked by hand.
Energy and current
Advanced mode adds instantaneous charging current, energy stored in the capacitor, and the time needed to reach common charge levels.
Reference tables
Percent charged per time constant, typical RC combinations, and unit-conversion tables are included below.
What Is Capacitor Charging?
When a DC source is connected to a resistor and an initially uncharged capacitor in series, the capacitor does not charge instantly. Current flows through the resistor and piles charge onto the capacitor plates, and the voltage across the capacitor rises quickly at first and then more and more slowly as it approaches the source voltage. The speed of the process is set by the time constant τ = RC.
Capacitor Charging Formula
Rearranged for the other variables:
V₀ = V(t) / (1 − e−t/RC)
R = −t / (C · ln(1 − V(t)/V₀))
C = −t / (R · ln(1 − V(t)/V₀))
Formula Variables
| Symbol | Meaning | SI unit |
|---|---|---|
| V(t) | Voltage across the capacitor at time t | volt (V) |
| V₀ | DC source (final) voltage | volt (V) |
| t | Time since the source was connected | second (s) |
| R | Series resistance | ohm (Ω) |
| C | Capacitance | farad (F) |
| τ | Time constant, RC | second (s) |
Reference Table — Percent Charged by Time Constant
| Time | Voltage (% of V₀) | Remaining (% of V₀) | Charging current (% of V₀/R) |
|---|---|---|---|
| 0.693 τ | 50.0% | 50.0% | 50.0% |
| 1 τ | 63.2% | 36.8% | 36.8% |
| 2 τ | 86.5% | 13.5% | 13.5% |
| 2.303 τ | 90.0% | 10.0% | 10.0% |
| 3 τ | 95.0% | 5.0% | 5.0% |
| 4 τ | 98.2% | 1.8% | 1.8% |
| 4.605 τ | 99.0% | 1.0% | 1.0% |
| 5 τ | 99.3% | 0.67% | 0.67% |
Conversion Table — Units
| Quantity | Conversions |
|---|---|
| Capacitance | 1 F = 1,000 mF = 1,000,000 µF = 10⁹ nF = 10¹² pF |
| Resistance | 1 MΩ = 1,000 kΩ = 1,000,000 Ω = 10⁹ mΩ |
| Time | 1 h = 60 min = 3,600 s; 1 s = 1,000 ms = 10⁶ µs = 10⁹ ns |
| Voltage | 1 kV = 1,000 V; 1 V = 1,000 mV |
Typical RC Time Constants
| Resistor | Capacitor | τ = RC | ≈ 99% charged (4.6 τ) |
|---|---|---|---|
| 1 kΩ | 1 µF | 1 ms | 4.6 ms |
| 10 kΩ | 100 nF | 1 ms | 4.6 ms |
| 47 kΩ | 10 µF | 0.47 s | 2.16 s |
| 10 kΩ | 100 µF | 1 s | 4.6 s |
| 1 MΩ | 1 µF | 1 s | 4.6 s |
| 1 MΩ | 100 µF | 100 s | 460 s |
Worked Example
τ = R · C = 10,000 Ω × 0.0001 F = 1 s
t/τ = 2, so e−2 = 0.13534
V(t) = 12 × (1 − 0.13534) = 12 × 0.86466
V(t) = 10.376 V (86.5% of V₀)
Reference & Method Note
Frequently Asked Questions
It is the time for the capacitor to charge to about 63.2% of the source voltage. It is also the time the charging current takes to fall to 36.8% of its starting value. Multiplying resistance in ohms by capacitance in farads gives τ in seconds.
Mathematically it never reaches V₀ exactly. As a rule of thumb, 5τ gets you to about 99.3%, which is treated as fully charged in most designs.
A charging capacitor's voltage only approaches V₀. When solving for time, resistance or capacitance, the equation contains ln(1 − V(t)/V₀), which is undefined once V(t) reaches or exceeds V₀.
No. The time to reach a given percentage of V₀ depends only on R and C. A higher V₀ simply raises the final voltage, and also the starting current V₀/R.
Discharging through a resistor follows V(t) = Vi·e−t/RC, which is a pure decay from the initial voltage toward zero. This calculator covers charging only, but the same time constant τ = RC applies.
What it means
The voltage across a charging capacitor in an RC circuit as a function of time is V(t) = V₀ * (1 − e^(−t/τ)), where V₀ is the final voltage (supply voltage) and τ = RC is the time constant. The voltage rises exponentially from 0 towards V₀, never quite reaching it in finite time. This equation is derived from solving the differential equation for the circuit. It is fundamental for understanding timing circuits, such as those in 555 timers, integration circuits, and pulse delay generators. The exponential rise is also used in ramp generators and in analog computing. The time to reach a certain percentage of V₀ can be calculated: for 50%, t = τ * ln2; for 90%, t = τ * ln10. Example: V₀=10V, R=1kΩ, C=100µF → τ=0.1s. At t=0.1s (one τ), V = 10*(1 − e^(−1)) = 10*(1−0.368) = 6.32V. At t=0.2s (2τ), V = 10*(1−e^(−2)) = 10*(1−0.135) = 8.65V.
Worked example
Capacitor Charging – Practical Example
Real‑World| Parameter | Value |
|---|---|
| V₀ | 10 V |
| τ = RC | 0.1 s (from previous example) |
| t | 0.1 s |
| Formula | V(t) = V₀(1 − e−t/τ) |
Common mistakes
- V₀: The final voltage (source voltage) – not the initial voltage.
- Exponent: The term is −t/(RC) – ensure the time constant is correct.
- Initial condition: At t=0, V(0) = 0 (assuming capacitor initially uncharged).
- Asymptotic: The voltage never exactly reaches V₀; it asymptotically approaches.
- AC signals: This is for DC step input; for AC, use phasor analysis.
Applications
The capacitor charging voltage follows an exponential curve V(t) = V₀(1 − e^(−t/RC)), asymptotically approaching the source voltage. This formula is used to design timing circuits, to ensure proper operation of switched‑capacitor circuits, and to control the startup of power supplies. Engineers use it to calculate the charge time for a capacitor, to determine the time to reach a threshold voltage, and to design analog‑to‑digital converters. It also applies in oscillators and pulse generators. By understanding the charging curve, professionals can predict the voltage at any time and ensure that circuits operate reliably. This exponential response is a classic example of first‑order system behaviour.
- Timing and delay circuit design
- Switched‑capacitor filter and converter design
- Soft‑start circuits for power supplies
- ADC sample‑and‑hold circuit analysis
- Educational demonstration of exponential charging
Related calculators · Circuit Analysis
Recently updated formulas
Suggest an improvement
Found a mistake? Have a better example? Let us know.
You may send up to 3 suggestions per 24 hours.