What is the RC Time Constant Calculator?
Use this resistor-capacitor calculator to find the time constant τ = RC and the ideal response of one capacitor through one resistor. Choose charging from 0 V toward a fixed DC source, or discharging from an entered initial voltage toward 0 V with the source disconnected.
Use time constant only when you have just R and C. You can also calculate capacitor voltage after a selected time or capacitor charge/discharge time to a target voltage. The result also reports current magnitude and stored energy. Battery charging uses different chemistry and control behavior; the existing Battery Charging Time Calculator is a separate estimate and is not replaced by this RC model.
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Optional capacitance meters (paid link) can help check capacitance on an isolated, discharged component using the instrument’s instructions. No purchase is required.
How to calculate capacitor charge time or voltage
- Choose time constant only, voltage after elapsed time, or time to target voltage.
- For a voltage-response mode, choose charging or discharging.
- Enter resistance and capacitance with their units.
- Time constant only needs R and C. Other modes also need source voltage for charging or initial voltage for discharge.
- For a response mode, enter elapsed time or target voltage. Calculate and review the input-based steps.
Changing an R, C or time unit converts its entered number to preserve the represented quantity and clears the prior result. Charging always begins at 0 V in this tool; an already partially charged capacitor needs a more general initial-condition model. Discharge assumes a resistor path with no connected source.
For time to target, a charging target may be 0 V but must remain below the source voltage. A discharge target must be above 0 V and no greater than the initial voltage. The starting voltage is reached at time zero; the exact final voltage is an asymptotic limit. Optional capacitor assortments (paid link) should be checked for their actual polarity, tolerance and ratings.
RC time constant, charging and discharging formulas
Charging from 0 V: Vc(t) = Vs × (1 − exp(−t/τ))
Discharging: Vc(t) = Vinitial × exp(−t/τ)
Charge time: t = −τ × ln(1 − Vtarget/Vs)
Discharge time: t = −τ × ln(Vtarget/Vinitial)
Current magnitude: |I(t)| = (V/R) × exp(−t/τ)
Use ohms, farads and seconds in these formulas. For example, 10 kΩ × 100 µF = 10,000 × 0.0001 = 1 s. Doubling resistance or capacitance doubles τ. A larger time constant produces a slower response under the same ideal model.
Stored charge is Q = CVc and stored capacitor energy is E = ½CVc². The displayed current is a nonnegative magnitude; discharge current runs in the opposite direction to charging current. The source voltage and capacitor voltage are different during charging, so stored energy uses Vc, not the source voltage until the limiting final state.
RC circuit examples for charging and discharging
Take R = 10 kΩ, C = 100 µF and a 12 V source. The time constant is 1 s. Starting uncharged, after 1 s the capacitor reaches 12 × (1 − exp(−1)) ≈ 7.585447 V. Current magnitude is about 0.0004414553 A. At 5 s, voltage is about 11.91914 V, not exactly 12 V.
For capacitor charge time to 9 V with the same 12 V source, t = −1 × ln(1 − 9/12) = ln(4) ≈ 1.386294 s. Selecting time to target adds a separate logarithm step to the answer.
For discharge from 12 V with the same R and C, voltage after 1 s is about 4.414553 V. Time to fall to 3 V is also ln(4) ≈ 1.386294 s. These equal times correspond to complementary voltage fractions, not identical capacitor voltages.
Use the Series & Parallel Capacitor Calculator for nominal capacitance combinations and the Series & Parallel Resistor Calculator for a reducible resistor group before applying a valid single-RC model.
What one time constant and five time constants mean
At 1τ, charging reaches about 63.21206% of the source voltage; discharge leaves about 36.78794% of the initial voltage. At 5τ, charging reaches about 99.32621% and discharge leaves about 0.6737947%. These percentages describe an exponential curve, not a universal definition of fully charged or safe to touch.
The ideal response reaches its exact final voltage only as time tends to infinity. Finite-precision display and very large time ratios may round to the final voltage; that is not proof of exact completion or zero physical energy. The calculator rejects a target at the asymptotic endpoint instead of inventing a finite completion time.
Optional resistor assortments (paid link) let you compare nominal R values, but the tool does not select wattage or pulse-energy ratings. The existing Resistor Color Code Calculator decodes marked resistor values; it does not measure actual resistance or determine a real component’s power rating.
Accuracy, supported inputs and practical limitations
The calculation uses an ideal fixed DC source, one exact resistor and one exact capacitor. Charging starts from 0 V; discharge starts at the entered initial voltage with the source removed. No arbitrary initial-charge model, switching network, constant-current charging, AC filter/cutoff design or multi-time-constant solution is included.
Resistance must represent 0.001–1 trillion Ω and capacitance 1e−15–1,000 F. Entered source/initial voltage is 0.000001–60 V. Elapsed time is zero or 1e−18–1e18 seconds. A positive target voltage must be at least 1e−9 V and satisfy the selected response’s interval. These numerical bounds do not approve physical operating conditions.
Real source resistance, leakage, ESR, tolerances, dielectric effects, measurement loading, resistor heating and device protection can change the response. Results show up to seven significant digits. Stable exponential/logarithm functions reduce cancellation near the starting point, while floating-point endpoint rounding remains possible.
Optional solderless breadboards (paid link) should suit the actual components and low-voltage prototype. Computed current, charge and stored energy are model outputs, not discharge instructions or component approvals. For a static resistive relationship, use the Ohm’s Law Calculator.
RC Time Constant Calculator FAQs
The time constant is τ = R × C, using resistance in ohms and capacitance in farads to obtain seconds.
For charging from 0 V toward a fixed source, t = −RC × ln(1 − Vtarget/Vsource). The target must be below the source voltage.
For discharge through a resistor with the source disconnected, t = −RC × ln(Vtarget/Vinitial). The target must be above zero and no greater than the initial voltage.
At 5τ it reaches about 99.32621% of the source voltage in this ideal model. It does not reach exactly 100% at a finite time.
No. It models one ideal resistor and capacitor. Battery chemistry, charger control and constant-current capacitor charging require different models.
The R, C and elapsed-time unit selectors convert the entered number so the represented quantity stays the same. The old result clears until recalculated.
Sources and methodology
Independent circuit equations and implementation, reviewed October 25, 2026. Manufacturer datasheets control real component ratings. The linked organizations do not endorse this tool.