Resistors combine in two basic ways. In series they share one current path, so their resistances simply add. In parallel they share the same two nodes, so their conductances add and the total drops. This calculator handles both from a single list of values, shows the current, voltage and power in every resistor when you give it a voltage, and can work backwards to the one resistor you need to hit a target value.
How to use the series and parallel resistor calculator
- Choose Series or Parallel. Both totals are always shown; the choice sets the headline result, the per-resistor table and the drawing.
- Type the resistor values, separated by commas, spaces or new lines. You can write prefixes (4.7k, 2.2M) or the printed RKM code used on schematics (4k7, 2R2, R47).
- Pick the unit for plain numbers. A bare 10 means 10 Ω, 10 kΩ or 10 MΩ depending on this setting; values with their own prefix ignore it.
- Optionally enter the voltage across the network to see each resistor’s voltage, current and power.
- Optionally enter a target total to find the resistor to add.
Series and parallel formulas
The reciprocal of resistance is conductance, measured in siemens (S). Parallel branches add conductance in the same way series parts add resistance, which is why the calculator shows the conductance sum in its steps.
| Combination | Series total | Parallel total |
|---|---|---|
| Two equal resistors R | 2R | R/2 |
| n equal resistors R | nR | R/n |
| 1 kΩ and 10 kΩ | 11 kΩ | 909.1 Ω |
| 100 Ω, 220 Ω, 470 Ω | 790 Ω | 59.98 Ω |
Worked example
100 Ω, 220 Ω and 470 Ω in parallel across 12 V (the default)
1/R = 1/100 + 1/220 + 1/470 = 0.01 + 0.0045455 + 0.0021277 = 0.0166731 S, so R = 59.98 Ω.
Each branch sees the full 12 V: 120 mA through 100 Ω (1.44 W), 54.55 mA through 220 Ω (654.5 mW) and 25.53 mA through 470 Ω (306.4 mW). The total is 200.1 mA and 2.401 W.
Switch to Series and the same three parts total 790 Ω. Now 15.19 mA flows through all of them, and the voltage divides in proportion to resistance: 1.519 V, 3.342 V and 7.139 V.
Hitting a target. Suppose you have two 100 Ω resistors in parallel (50 Ω) but need 40 Ω. Enter 40 as the target and the calculator returns 1 ÷ (1/40 − 1/50) = 200 Ω to add in parallel, which is itself a standard E24 value.
Power ratings and practical limits
Total power is shared unevenly, so check each resistor against its own rating rather than the total. A common rule is to keep each part below half its rated wattage; the Ohm’s law calculator suggests a rating for a single resistor. In the example above, the 100 Ω branch dissipates 1.44 W and needs a 3 W part by that rule, and even the 470 Ω branch, at 306 mW, calls for 1 W. A common quarter-watt resistor would overheat in any of the three positions.
Real resistors also carry tolerance. Two ±5% parts in series or parallel still give roughly a ±5% total, so combining parts does not improve accuracy, but it does let you reach values that are not stocked. Read existing parts with the resistor color code calculator, and use the voltage divider calculator when two series resistors are meant to produce an output voltage.
For low-voltage electronics. Resistors on mains-powered or high-energy circuits must be rated for the voltage as well as the power; follow your local electrical code and use a licensed electrician for installations.
Frequently asked questions
How do you calculate resistors in parallel?
Add the reciprocals of the resistances and take the reciprocal of the sum: 1/R = 1/R1 + 1/R2 + … For 100 Ω, 220 Ω and 470 Ω, 1/R = 0.01 + 0.004545 + 0.002128 = 0.016673 S, so R ≈ 59.98 Ω.
Is the parallel total always smaller than the smallest resistor?
Yes. Every resistor added in parallel opens another path for current, so the combination conducts better than any single branch. Two equal resistors in parallel give exactly half of one, and n equal resistors give one nth.
What is the product-over-sum rule?
For exactly two resistors in parallel, R = (R1 × R2) ÷ (R1 + R2). It is the reciprocal formula rearranged, and handy for mental math: 100 Ω and 100 Ω give 10,000 ÷ 200 = 50 Ω. For three or more resistors, use the reciprocal sum or apply the rule pairwise.
How do I make a non-standard resistance from standard parts?
Enter the resistors you have and a target total. If the target is above your current total, the calculator gives the resistor to add in series; if it is below, it gives the resistor to add in parallel, along with the nearest E24 value.
Which resistor gets the most power?
In series, the same current flows through each part, so the largest resistor drops the most voltage and dissipates the most power. In parallel, every branch sees the same voltage, so the smallest resistor carries the most current and runs hottest.