Capacitor Charge Time Calculator

Calculate the time required for a capacitor to charge to a specific voltage in an RC circuit. Enter the supply voltage, target voltage, resistance, and capacitance to get the charge time instantly.

Target input mode

Supply voltage (V_s) V

Target voltage (V_t) V

Common charge presets

Resistance (R) Ω

R unit

Capacitance (C) F

C unit

Charge time (t) —

Time constant (τ = RC) —

Time constants elapsed —

Target as % of supply —

How to Use This Capacitor Charge Time Calculator

Enter all four values to instantly calculate capacitor charge time. You can input the target as either a voltage or a percentage of the supply using the toggle above the inputs.

Supply voltage (V_s) — the DC voltage charging the capacitor (e.g. 5 V).
Target voltage (V_t) — the capacitor voltage you want to reach. Must be less than V_s.
Resistance (R) — the series resistance. Select the correct unit (Ω, kΩ, or MΩ).
Capacitance (C) — the capacitor value. Select the correct unit (F, mF, µF, nF, or pF).

Use the preset buttons to quickly set a target to a known time-constant milestone (1τ = 63.2%, 5τ = 99.3%, etc.). Results update instantly as you type.

Capacitor Charge Time Formula

The charge time for a capacitor in an RC circuit is derived from the exponential charging equation:

t = −RC · ln(1 − V_t / V_s)

The time constant τ (tau) is the product of resistance and capacitance:

τ = RC

Variable definitions:

t — charge time (seconds)
R — resistance (ohms)
C — capacitance (farads)
V_s — supply voltage (volts)
V_t — target capacitor voltage (volts)
τ — time constant (seconds); one τ charges the capacitor to ≈63.2% of V_s
ln — natural logarithm

Example Calculation

Given: V_s = 5 V, V_t = 4 V, R = 10 kΩ, C = 100 µF

Step 1 — Convert units: R = 10,000 Ω, C = 0.0001 F

Step 2 — Time constant: τ = RC = 10,000 × 0.0001 = 1 s

Step 3 — Charge time:

t = −1 · ln(1 − 4/5)

t = −ln(0.2)

t ≈ 1.609 seconds (≈1.61τ)

The target of 4 V is 80% of the 5 V supply, which takes about 1.61 time constants to reach.

Frequently Asked Questions

Why can a capacitor never reach the supply voltage?
The charging equation is exponential — the capacitor approaches V_s asymptotically. As the voltage difference between the capacitor and supply shrinks, current flow decreases, slowing the charge rate. In theory it never reaches 100%, but at 5τ (99.3%) it is considered fully charged for practical purposes.

What is a time constant (τ)?
One time constant is the time it takes for the capacitor to charge to approximately 63.2% of the supply voltage. It equals R × C in seconds (when R is in ohms and C is in farads). Each additional τ adds less and less charge: 2τ ≈ 86.5%, 3τ ≈ 95%, 5τ ≈ 99.3%.

Does this formula assume the capacitor starts fully discharged?
Yes. The standard RC charge formula assumes the capacitor begins at 0 V. If your capacitor has an initial charge, the calculation is more complex and requires the full exponential form: V(t) = V_s(1 − e^−t/τ) + V₀·e^−t/τ.

What affects charge time the most?
Both R and C have equal weight — doubling either one doubles the charge time. If you need faster charging, reduce R (use a lower series resistance) or use a smaller capacitor. Increasing supply voltage V_s while keeping V_t constant also reduces charge time because the target becomes a smaller fraction of supply.

Why is V_t restricted to less than V_s?
The formula contains ln(1 − V_t/V_s). When V_t equals V_s, this becomes ln(0) which is negative infinity — meaning infinite time. When V_t exceeds V_s, the argument becomes negative, which has no real logarithm. Physically, a capacitor cannot charge beyond the supply voltage in a simple RC circuit.