The series & parallel circuit calculator computes equivalent values for resistors, capacitors, and inductors in series or parallel configurations. Designed for physics students, this unified calculator handles all three component types — unlike specialized electronics tools that focus on a single component. Enter up to 8 component values and get the equivalent resistance, capacitance, or inductance with KaTeX-rendered formulas.
Optional: Source Values
Results
Voltage / Current Distribution
How to Use the Series & Parallel Circuit Calculator
This calculator finds the equivalent value for resistors, capacitors, or inductors connected in series or parallel. It covers all three component types in one interface, making it ideal for general physics coursework (AP Physics, university introductory circuits).
Step 1: Select Component Type
Click the "Resistors," "Capacitors," or "Inductors" tab. Note that capacitors combine in the opposite sense from resistors and inductors: series capacitors use the reciprocal formula (like parallel resistors), while parallel capacitors add directly (like series resistors).
Step 2: Enter Component Values
Enter at least two values. Click "Add component" for up to 8 components. Use the unit prefix selector to enter values in Ω/kΩ/MΩ for resistors, pF/nF/μF for capacitors, or μH/mH/H for inductors without manual unit conversion.
Example: Three Resistors in Series
Enter 100, 200, and 300 ohms in series. Result: 100 + 200 + 300 = 600 Ω. Now switch to parallel: 1/R_total = 1/100 + 1/200 + 1/300 = 0.01 + 0.005 + 0.00333 = 0.01833. R_total = 1/0.01833 ≈ 54.55 Ω.
Voltage and Current Dividers
Enter a source voltage (for series) or source current (for parallel) to see how voltage or current divides across each component. For series resistors, voltage across each is V_n = V_source × R_n / R_total. For parallel, current through each is I_n = I_source × (1/R_n) / sum(1/R_i).
RC and RL Time Constants
When you calculate a resistor and the source section contains another resistor value, the calculator notes the RC time constant τ = R × C. For a 1 kΩ resistor and 100 μF capacitor, τ = 1000 × 0.0001 = 0.1 seconds. The capacitor reaches full charge in approximately 0.5 seconds (5τ).
For a detailed walkthrough, see our guide: How Electric Circuits Work.
FAQ
How do resistors combine in series vs. parallel?
In series, resistances add directly: R_total = R1 + R2 + R3. Total resistance is always greater than any individual resistor. In parallel, the reciprocal of total resistance equals the sum of reciprocals: 1/R_total = 1/R1 + 1/R2 + 1/R3. Total resistance is always less than the smallest individual resistor.
How do capacitors combine differently from resistors?
Capacitors combine in the opposite way from resistors. Series capacitors: 1/C_total = 1/C1 + 1/C2 (like parallel resistors). Parallel capacitors: C_total = C1 + C2 (like series resistors). This is because capacitors store energy in electric fields between their plates — adding plates in parallel increases total capacitance.
What is the RC time constant?
The RC time constant τ = R × C (in seconds) determines how quickly a capacitor charges or discharges through a resistor. After one time constant, the capacitor reaches 63.2% of its final voltage. After 5 time constants (5τ), it's considered fully charged (99.3%). This tool calculates τ when you enter both R and C values.
What is the RL time constant?
The RL time constant τ = L/R (in seconds) determines how quickly current builds up in an inductor through a resistor. After one τ, the current reaches 63.2% of its final value. Inductors resist rapid changes in current, just as capacitors resist rapid changes in voltage.
Is this tool free?
Yes, completely free with no signup required. All calculations run locally in your browser.
How is this different from the capacitor-series-parallel calculator in electronics?
This is a unified physics calculator that handles all three component types (R, C, and L) in one interface, designed for physics students. The electronics/capacitor-series-parallel-calculator is focused on capacitor-only applications in electronics design contexts.
What is a voltage divider?
A voltage divider uses two series resistors to produce a fraction of the source voltage. If R1 and R2 are in series with voltage V, the voltage across R2 is V2 = V × R2 / (R1 + R2). This is fundamental in electronics for biasing transistors and creating reference voltages.