Series and Parallel Resistor Calculator
Resistors connected in series simply add together, while resistors in parallel combine by the reciprocal rule. This calculator accepts up to 8 resistor values and computes total equivalent resistance for either configuration. Series circuits are common in simple current-limiting applications; parallel circuits appear in household wiring and anywhere multiple loads share the same voltage source. Enter each resistor value in ohms (or consistently in kilohms or megohms) and select your circuit type. The result is displayed in the same unit you entered.
Resistor combination formulas
Series: R_total = R1 + R2 + R3 + ...
Parallel: 1/R_total = 1/R1 + 1/R2 + 1/R3 + ...
For series circuits, total resistance equals the arithmetic sum. For parallel circuits, total resistance equals the reciprocal of the sum of reciprocals. Two equal resistors in parallel give exactly half the resistance of one resistor.
Practical applications
- Series resistors are used to limit current, create voltage dividers, and set LED brightness.
- Parallel resistors are used to increase current capacity and combine standard values to hit a non-standard target resistance.
- The NEC (NFPA 70) requires correctly sized conductors and protection; resistor selection affects heat dissipation and circuit safety.
- When resistors are in series, the one with the highest wattage rating determines maximum power handling if they are equal resistance values.
Frequently asked questions
How do you add resistors in series?
In a series circuit, total resistance is simply the sum of all individual resistors: R_total = R1 + R2 + R3 + ... The current through each resistor is the same, and voltages add up.
How do you combine resistors in parallel?
For parallel resistors, the reciprocal of the total resistance equals the sum of the reciprocals: 1/R_total = 1/R1 + 1/R2 + 1/R3 + ... The voltage across each resistor is the same, and currents add up.
Why is parallel resistance always less than the smallest resistor?
Because parallel paths give current more routes to flow through, reducing total opposition. Even adding a very large resistor in parallel slightly decreases total resistance below the smallest value.
What units should I use?
Enter all resistors in the same unit (ohms, kilohms, or megohms). The result will be in the same unit. For example, if you enter values in kilohms, the result is in kilohms.
Can I mix series and parallel resistors?
This calculator handles a single configuration at a time. For mixed networks, break the circuit into sub-groups, calculate each group separately, then combine those results as series or parallel as needed.
Official sources
- NIST: NIST SP 811, Guide for SI Units.
- IEEE: IEEE Standards Association.
- NFPA 70 (National Electrical Code): NFPA 70.
Reviewed by the CalculatorHub team, edited by James Graham, 15 June 2026. See our methodology.