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Home›Electronics & Physics›Capacitor Charge Discharge Calculator

Capacitor Charge / Discharge Calculator

Calculate Capacitor Voltage at Any Time During Charge or Discharge

Select Mode

Charging Discharging

Resistance R (Ω)

Capacitance C (F)

Supply/Initial V₀ (V)

Time t (s)

Charge/Discharge Formulas

Time Constant: τ = R × C

Charging: V(t) = V₀ × (1 - e^(-t/τ))

Discharging: V(t) = V₀ × e^(-t/τ)

% of steady state: 1τ=63.2%, 3τ=95%, 5τ=99.3%

The exponential charge and discharge curves are fundamental to RC circuit behavior. During charging, the capacitor voltage rises quickly at first then slows as it approaches the supply voltage. During discharge, the voltage drops quickly then tapers off.

⚠ After 1τ: 63.2% charge / 36.8% discharge. After 5τ: 99.3% charge / 0.67% discharge. For practical purposes, a capacitor is fully charged/discharged after 5τ.

How Capacitor Charge/Discharge Works

When voltage is applied to an RC circuit, current flows into the capacitor, storing energy in its electric field. The voltage rises exponentially toward the supply voltage. During discharge, the stored energy is released through the resistor. The time constant τ=RC determines how fast this process occurs.

Charging Curve

V(t) = V₀(1-e^(-t/τ)). Fast initial rise, slows near V₀. Current decreases exponentially. Energy stored in electric field.

Discharge Curve

V(t) = V₀×e^(-t/τ). Fast initial drop, slows near zero. Current reverses direction. Energy released as heat in R.

Time Constant Effect

Large τ = slow (big R or C). Small τ = fast (small R or C). τ sets the timescale for all exponential changes.

Key Percentage Points

50% = 0.693τ, 63.2% = 1τ, 86.5% = 2τ, 95% = 3τ, 98.2% = 4τ, 99.3% = 5τ. Memorize 1τ, 3τ, 5τ.

Teaching Example: R=10kΩ, C=100μF, V₀=5V, t=1s in charging mode.
τ = 10kΩ × 100μF = 1s. t/τ = 1/1 = 1.
V(1s) = 5 × (1 - e^(-1)) = 5 × (1 - 0.3679) = 5 × 0.6321 = 3.16V (63.2% of 5V).

Applications

Timing Circuits Power Supplies Oscillators PWM Smoothing Reset Circuits

Frequently Asked Questions

What is the charging formula?▼

V(t) = V₀ × (1 - e^(-t/τ)). At t=τ, V=63.2%. At 3τ, 95%. At 5τ, 99.3%. The capacitor is fully charged after ~5τ.

What is the discharge formula?▼

V(t) = V₀ × e^(-t/τ). At 1τ: 36.8% remains. At 3τ: 5%. At 5τ: 0.67%. Considered fully discharged at 5τ.

How to calculate time constant?▼

τ = R × C. Example: 10kΩ × 100μF = 1 second. Use consistent units: Ω × F = seconds.

What happens if R or C changes?▼

Doubling R or C doubles τ (slower). Halving R or C halves τ (faster). The steady-state voltage stays the same, only the speed changes.

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