RC Circuit Solver Calculator

RC Solver Inputs

Choose a mode and a solve option. Provide the needed values with units. Results appear above this form after you submit.

Mode *

Charging uses source voltage Vs. Discharging ignores Vs.

Solve For *

Solver validates log-domain limits automatically.

Source Voltage Vs (V) *

Used for charging formulas. Leave blank for discharging.

Initial Voltage V0 (V) *

Enter a valid initial voltage.

Target Voltage Vt (V)

Used for “time to voltage” and component targeting.

Resistance R *

Required for voltage and time solutions.

Capacitance C *

1 µF = 1e−6 F. Use decimals freely.

Time t *

Needed for voltage, R, or C targeting.

Quick guidance

τ = R·C is the time constant.
After 5τ, the transient is nearly settled.
Charging needs Vs; discharging does not.

Common checks

Keep R > 0 and C > 0.
For charging time: Vt < Vs.
For discharging time: Vt > 0.

What you get

Voltage, current, charge, and energy.
Component targeting using logarithms.
CSV and PDF for quick sharing.

Example Data Table

Example uses charging with Vs = 5 V, V0 = 0 V, R = 10 kΩ, C = 100 µF.

t (s)	τ (s)	Vc(t) (V)	i(t) (mA)	q(t) (mC)
0 s	1 s	0 V	0.5 mA	0 mC
0.5 s	1 s	1.967347 V	0.303265 mA	0.196735 mC
1 s	1 s	3.160603 V	0.18394 mA	0.31606 mC
2 s	1 s	4.323324 V	0.067668 mA	0.432332 mC
5 s	1 s	4.96631 V	0.003369 mA	0.496631 mC

Formulas Used

Time constant

τ = R · C

τ controls how fast the capacitor voltage changes.

Charge and energy

q(t) = C · Vc(t)

E(t) = ½ · C · Vc(t)²

Charging (with source Vs)

Vc(t) = Vs − (Vs − V0) · e^(−t/τ)

i(t) = (Vs − V0)/R · e^(−t/τ)

Time to reach Vt: t = −τ · ln((Vs − Vt)/(Vs − V0))

Discharging (source removed)

Vc(t) = V0 · e^(−t/τ)

i(t) = −V0/R · e^(−t/τ)

Time to reach Vt: t = −τ · ln(Vt/V0)

How to Use This Calculator

Select Charging or Discharging.
Choose what you want to solve in Solve For.
Enter required values and unit choices.
Click Submit and Solve to view results above.
Use Download CSV or Download PDF after a run.

FAQs

1) What does the time constant mean?

The time constant τ equals R·C. After one τ, the voltage moves about 63% toward its final value. After about five τ, the transient is very close to steady behavior.

2) Why does charging require Vs but discharging does not?

Charging uses an applied source voltage Vs to push the capacitor toward a final value. Discharging assumes the source is removed and the capacitor releases stored energy through the resistor.

3) When can the logarithm formulas fail?

Log terms require positive ratios. For charging time, Vt must be less than Vs and Vs must differ from V0. For discharging, Vt and V0 must be positive and nonzero in the ratio.

4) Can I compute R or C for a required settling time?

Yes. Use the “Resistance required” or “Capacitance required” option with V0, Vt, and time t. The solver rearranges the exponential form and returns a positive component when inputs are physically consistent.

5) Why can current be negative during discharging?

The sign indicates direction. With a common sign convention, discharging current flows opposite to charging current, so the expression includes a negative sign while the magnitude still decays exponentially.

6) Does this include capacitor leakage or ESR?

No. This is an ideal single-resistor, single-capacitor model. Leakage, ESR, and source resistance can be approximated by adjusting R, but precise modeling needs a more detailed circuit.

7) What units should I use for best accuracy?

Use realistic values and avoid extreme scaling when possible. Select kΩ and µF for typical timing circuits. The solver converts units internally, so you can input decimals and mix common prefixes safely.