Capacitor Discharging Calculator
RC Circuit · solve V(t) = V₀ · e−t/RC for the voltage, initial voltage, time, or time constant — with a circuit diagram, a universal discharge curve, and an R·C builder.
At t = 0 the switch closes, connecting the charged capacitor to the resistor. Current flows until the capacitor's voltage decays to zero.
V₀ — scales the curve
Every voltage on the curve is a fixed fraction of V₀; doubling V₀ doubles V(t) at every instant.
τ = RC — sets the timescale
A larger resistance or capacitance means a slower discharge. τ is the single number that fully sets how fast the curve decays.
t — exponential decay
Voltage falls by the same fraction (≈63.2%) every τ seconds, regardless of how much time has already passed.
Never quite zero
Mathematically V(t) only approaches zero as t→∞. In practice, the capacitor is considered fully discharged after about 5τ (under 1% of V₀ remains).
R·C Builder & Unit Conversions
τ depends only on the product R×C — split it into resistance and capacitance, or convert between common electronics units.
Build τ from R and C
Resistance converter
Capacitance converter
Time converter
Discharge by Number of Time Constants
| t (× τ) | V(t)/V₀ | % discharged | Time (this τ) |
|---|
Typical RC Time Constants
| Example | R | C | τ = RC |
|---|---|---|---|
| Debounce / timing circuit | 10 kΩ | 100 nF | 1 ms |
| Audio coupling filter | 10 kΩ | 1 µF | 10 ms |
| Power-supply smoothing | 100 Ω | 1000 µF | 100 ms |
| Slow timer / flasher | 1 MΩ | 10 µF | 10 s |
How to Use This Calculator
The discharge equation links four quantities: initial voltage V₀, elapsed time t, the time constant τ = RC, and the resulting voltage V(t).
Choose what to solve for
Pick V(t), V₀, t, or τ — the formula rearranges automatically.
Enter values or use presets
V₀ has common voltage presets; t has handy "n × τ" presets.
Need τ from real components?
Use the R·C builder to compute τ = R × C from resistance and capacitance, in any common unit.
Read the universal curve
The chart shows V/V₀ against t/τ — the same shape for every RC circuit — with your point marked.
Check the diagram
See how the capacitor, resistor, and switch connect, and which way current flows during discharge.
Go Advanced
Adds sensitivity and companion metrics like charge remaining and the half-voltage time.
What This Tool Offers
Solve any variable
Compute V(t), V₀, t, or τ from the other three.
Circuit diagram
A labeled RC discharge schematic with current direction.
Universal discharge curve
The normalized V/V₀ vs. t/τ curve that applies to every RC discharge.
R·C builder
Split τ into resistance and capacitance, in Ω/kΩ/MΩ and F/µF/nF/pF.
Conversion tables
Resistance, capacitance, and time unit converters plus reference tables.
Sensitivity check
See how a 1% change in an input moves the result.
What Does V(t) = V₀·e−t/RC Measure?
When a charged capacitor is connected across a resistor, current flows and the capacitor's voltage decays exponentially. The time constant τ = RC sets the pace: after each τ seconds, the remaining voltage falls by the same 63.2% fraction, regardless of the starting voltage.
V₀ = V(t) · e^(t/τ)
t = −τ · ln( V(t)/V₀ )
τ = −t / ln( V(t)/V₀ )
i(t) = (V₀/R) · e^(−t/τ)
Frequently Asked Questions
τ = R×C is the time for the voltage to fall to about 36.8% (1/e) of its starting value. It fully determines the shape of the discharge curve regardless of R and C individually.
Mathematically never — the curve only approaches zero. In practice, 5τ is commonly treated as "fully discharged," since under 1% of V₀ remains.
Because they only ever appear as the product RC in the exponent. A 10 kΩ resistor with a 100 nF capacitor gives the same τ, and the same discharge curve, as a 100 Ω resistor with a 10 µF capacitor.
Current follows the same exponential shape as voltage: i(t) = (V₀/R)·e^(−t/τ), starting at its maximum the instant the switch closes and decaying toward zero alongside the voltage.
Charging follows a related but different curve, V(t) = V_final·(1 − e^(−t/τ)), rising toward the supply voltage rather than decaying from it. This calculator covers discharging specifically.
Variables
| Symbol | Quantity | Unit |
|---|---|---|
| V(t) | Voltage at time t | V |
| V₀ | Initial capacitor voltage | V |
| t | Time elapsed | s |
| R | Resistance | Ω |
| C | Capacitance | F |
| τ | Time constant (R×C) | s |
What it means
The voltage across a discharging capacitor in an RC circuit as a function of time is V(t) = V₀ * e^(−t/τ), where V₀ is the initial voltage and τ = RC is the time constant. The voltage decays exponentially from V₀ towards 0. This equation is derived from the same differential equation as the charging case, with the opposite sign. Discharge circuits are used in timing, pulse generation, and in flash cameras. The discharge time to reach a certain fraction of V₀ is analogous to charging: after one τ, the voltage drops to 36.8% of its initial value. Example: V₀=10V, τ=1s. At t=1s, V = 10 * e^(−1) = 3.68V. At t=3s, V = 10 * e^(−3) = 0.50V. The discharge curve is essential for designing blinking LEDs, relaxation oscillators, and for timing applications.
Worked example
Capacitor Discharging – Practical Example
Real‑World| Parameter | Value |
|---|---|
| V₀ | 10 V |
| τ | 0.1 s |
| t | 0.1 s |
| Formula | V(t) = V₀ · e−t/τ |
Common mistakes
- V₀: The initial voltage across the capacitor (at t=0).
- Decay: The voltage decays exponentially to zero.
- Time constant: Same as charging: τ = RC.
- Energy: The energy is dissipated in the resistor.
- Discharge path: Ensure there is a closed path for the current to flow.
Applications
The capacitor discharging voltage decays exponentially as V(t) = V₀·e^(−t/RC), falling to 36.8% of the initial value after one time constant. This formula is used to design discharge circuits, to ensure safe residual voltage removal, and to analyse the decay of stored energy. Engineers apply it in timing circuits, in reset circuits, and in the design of capacitance touch sensors. It is also used to calculate the time for a capacitor to discharge to a safe level for servicing. By understanding the discharge process, professionals can predict when the voltage will drop below a threshold, enabling reliable logic transitions and safe operation.
- Discharge path design for safety (bleeder resistors)
- Reset and power‑on‑reset circuits
- Capacitive sensing and touch detection
- Timer and monostable multivibrator circuits
- Educational understanding of exponential decay
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