Resistor Series & Parallel Calculator
Calculate equivalent resistance for resistors in series, parallel, or mixed configurations. Add or remove resistors dynamically and see the result instantly.
Equivalent Resistance (series)
320 Ω
What Is the Resistor Series & Parallel Calculator?
When resistors are connected in series, current flows through each one in sequence and the total resistance is simply the sum. When connected in parallel, the voltage across each resistor is equal and the combined resistance is always less than the smallest individual resistor. This calculator handles both configurations and allows up to 10 resistors with standard SI prefixes (Ω, kΩ, MΩ).
Formula
How to Use
Select Series or Parallel mode. Add resistors by entering their values and clicking Add. Use the unit selector for Ω, kΩ, or MΩ. The total equivalent resistance updates automatically. Remove individual resistors with the × button. The calculator also shows the current through each resistor for a given supply voltage.
Example Calculation
Three resistors in parallel: 100 Ω, 220 Ω, 470 Ω. R_total = 1/(1/100 + 1/220 + 1/470) = 1/(0.01 + 0.00455 + 0.00213) = 1/0.01667 ≈ 59.9 Ω.
Understanding Resistor Series & Parallel
Resistor networks are fundamental in electronics. Every circuit divides voltage and controls current through the strategic placement of resistors. Ohm's Law (V = IR) and Kirchhoff's laws are the foundations; series and parallel combination rules are their most immediate application.
Voltage dividers (two series resistors) are used to create reference voltages, scale signals for ADC inputs, and bias transistors. The output voltage of a resistor divider is V_out = V_in × R₂/(R₁+R₂).
Parallel combinations appear in current dividers, load combinations, and LED arrays. LEDs connected in parallel need matched resistors to ensure equal current sharing, since small manufacturing variations in forward voltage cause unequal current distribution.
The E-series (E12, E24, E48, E96) of preferred resistor values were designed so that consecutive values in the same decade overlap within manufacturing tolerance — minimising the number of distinct values while covering all practical requirements.
Frequently Asked Questions
Why is parallel resistance always less than the smallest resistor?
Adding a parallel path gives current an additional route to flow. Even a very large parallel resistor contributes some current, increasing total conductance (1/R). Since R = 1/conductance, total R decreases.
What is the equivalent resistance of two equal resistors in parallel?
Two equal resistors R in parallel give R/2. Three give R/3, and n resistors give R/n. This only applies when all resistors are identical.
How do I handle mixed series-parallel circuits?
Reduce the circuit stepwise: identify groups of purely series or purely parallel resistors, replace each group with its equivalent, and repeat until you have one total resistance. This calculator handles one group at a time.
What is the difference between resistance and impedance?
Resistance (R) applies to DC and purely resistive AC circuits. Impedance (Z) is the AC generalisation that includes the frequency-dependent effects of capacitors (reactance 1/ωC) and inductors (reactance ωL). This calculator handles pure resistance only.