Calculated Results
This panel appears above the form after submission.
Interpretation
Response Graph
RC Circuit Inputs
Use the responsive input grid below. Large screens show three columns, medium screens show two, and phones show one.
Formula Used
The calculator uses a first-order RC transient model. It handles both charging and discharging with one general exponential equation.
| Quantity | Formula |
|---|---|
| Time Constant | τ = R × C |
| Capacitor Voltage | Vc(t) = V∞ + (V0 − V∞)e−t/τ |
| Current | I(t) = ((V∞ − V0) / R)e−t/τ |
| Resistor Voltage | Vr(t) = V∞ − Vc(t) |
| Charge on Capacitor | Q(t) = C × Vc(t) |
| Stored Energy | E(t) = ½CVc(t)2 |
| Resistor Power | P(t) = I(t)2R |
| Cutoff Frequency | fc = 1 / (2πRC) |
How to Use This Calculator
- Select charging or discharging mode.
- Enter resistance and choose its unit.
- Enter capacitance and choose its unit.
- Provide the source voltage and initial capacitor voltage.
- Enter the time point where you want values evaluated.
- Optionally add a target capacitor voltage to solve for target time.
- Set graph span in time constants and the number of graph points.
- Press Calculate RC Response to see results above the form.
- Use the CSV and PDF buttons to export the current results.
Example Data Table
These sample cases use the same formulas implemented in the calculator.
| Case | Mode | R (Ω) | C (F) | Vs (V) | V0 (V) | t (s) | τ (s) | Vc(t) (V) | I(t) (A) | Energy (J) |
|---|---|---|---|---|---|---|---|---|---|---|
| Charging at 1τ | Charge | 1000 | 0.001 | 12 | 0 | 1 | 1 | 7.585447 | 0.004414553 | 0.028769501 |
| Charging at 3τ | Charge | 1000 | 0.001 | 12 | 0 | 3 | 1 | 11.402555 | 0.000597445 | 0.065009132 |
| Discharging snapshot | Discharge | 2200 | 0.00047 | 0 | 10 | 0.5 | 1.034 | 6.165851 | -0.002802659 | 0.008934163 |
| Bias decay case | Discharge | 4700 | 0.0001 | 0 | 5 | 0.25 | 0.47 | 2.937395 | -0.000624978 | 0.000431414 |
Frequently Asked Questions
What does this RC circuit calculator compute?
It calculates time constant, cutoff frequency, capacitor voltage, resistor voltage, current, charge, stored energy, resistor power, and optional target time for charging or discharging cases.
What is the time constant in an RC circuit?
The time constant equals resistance multiplied by capacitance. It sets how quickly the capacitor approaches its final value. After one time constant, the remaining error falls to about 36.8%.
Why is the charging curve exponential?
The current depends on the voltage difference between the source and the capacitor. As that difference shrinks, current falls, causing an exponential response instead of a straight line.
What does the cutoff frequency represent?
The cutoff frequency marks the point where output magnitude drops to about 70.7% of its low-frequency value in a simple first-order RC filter. It equals 1 divided by 2πRC.
Can I use this for discharging without a supply?
Yes. Select discharging mode and enter the initial capacitor voltage. The calculator then assumes the capacitor decays toward zero volts through the resistor.
Why can target time sometimes be unavailable?
A target voltage must lie on the actual exponential path. If the target is beyond the starting value, beyond the final value, or exactly at the final value, finite time may not exist.
What units should I enter?
Enter the numeric value and select a unit scale for resistance, capacitance, and time. The calculator converts everything internally to base SI units before solving.
Is this useful for filter work too?
Yes. The time constant and cutoff frequency help analyze low-pass and high-pass RC filters, while the transient outputs help verify startup, pulse, and timing behavior.