Parallel Circuit Resistance Calculator
Two resistors in parallel are easy. Six of them, plus a supply voltage and a per-branch current check, are where hand math starts to slip. This calculator finds the total (equivalent) resistance of 2 to 6 resistors in parallel, and when you add a voltage it also works out the total current, the total power, and how the current splits across each branch.
Quick Answer
For two resistors, Rtotal = (R1 × R2) / (R1 + R2). A 100 Ω and a 200 Ω resistor in parallel give 66.6667 Ω, which is less than either branch. For any number of branches, add the reciprocals: 1/Rtotal = 1/R1 + 1/R2 + … The calculator above runs 2 to 6 branches and, with a voltage entered, also reports total current, total power and each branch current.
How to use this calculator
Pick the number of resistors (2 to 6), type each resistance in ohms, and press Calculate. The fields come pre-filled with the worked example below, and nothing computes until you click, so you can study the inputs first. Add an applied voltage only when you also want current and power: the calculator then shows total current, total power, and a per-branch current breakdown. Reset restores the 100 Ω and 200 Ω example. Every resistor value must be greater than zero; anything else shows an inline error instead of a number.
Parallel resistance formula
The general rule is a reciprocal sum. Conductances (1/R) add in parallel, so the equivalent resistance is the reciprocal of the summed conductances:
1/Rtotal = 1/R1 + 1/R2 + 1/R3 + …
For exactly two resistors this collapses to the product-over-sum shortcut, which is what most quick mental math uses:
Rtotal = (R1 × R2) / (R1 + R2)
Worked example
Put 100 Ω and 200 Ω in parallel with a 12 V supply, exactly as the calculator is pre-filled (voltage left for you to add):
- Reciprocal sum: 1/100 + 1/200 = 0.01 + 0.005 = 0.015 S, so conductance is 0.0150 S.
- Total resistance: 1 / 0.015 = 66.6667 Ω, less than the 100 Ω branch.
- Total current at 12 V: 12 / 66.6667 = 0.1800 A.
- Total power: 12 × 0.18 = 2.1600 W.
- Branch currents: 12/100 = 0.1200 A through the 100 Ω resistor and 12/200 = 0.0600 A through the 200 Ω resistor. They add to 0.1800 A, which checks the arithmetic.
Press Calculate with 12 in the voltage field and the tool returns these exact figures.
Equal resistors shortcut
When every branch is the same value, the reciprocal math simplifies to one division: Rtotal = R / n. Three 100 Ω resistors in parallel are 33.3333 Ω, and six are 16.6667 Ω. Two identical resistors always give exactly half of one, so paralleling two 100 Ω parts is the classic way to get 50 Ω from the parts bin.
Solving for a missing resistor
Sometimes you know the total you want and one resistor you already own. Rearranging the two-resistor formula gives the partner value directly:
R2 = (R1 × Rtotal) / (R1 − Rtotal)
Example: you have a 470 Ω resistor and want about 150 Ω. R2 = (470 × 150) / (470 − 150) = 70,500 / 320 = 220.3125 Ω. The nearest standard value, 220 Ω, in parallel with 470 Ω gives 149.8551 Ω, close enough for almost any non-critical circuit. Note the denominator: the target must be smaller than R1, because parallel resistance can never exceed the smallest branch.
Why the total is always lower
Adding a parallel branch adds another path for current, which is the same as adding conductance. More conductance at the same voltage means more total current, and by Ohm’s law more current at the same voltage means lower equivalent resistance. That is why the total can never reach even the smallest branch value: a 47 Ω, 100 Ω and 220 Ω combination gives 27.9158 Ω, under the 47 Ω floor. If your result ever exceeds your smallest resistor, you added resistances directly by mistake.
Parallel vs series at a glance
| Property | Parallel | Series |
|---|---|---|
| Formula | 1/Rt = Σ(1/Ri) | Rt = R1 + R2 + … |
| Total resistance | Always less than the smallest branch | Always greater than the largest resistor |
| Voltage | Same across every branch | Divides across resistors |
| Current | Divides among branches | Same through every resistor |
| One branch fails open | Rest keep working (home wiring) | Whole chain goes dead (old string lights) |
How the current splits
At 12 V across the worked example, the branch currents are 0.1200 A and 0.0600 A. The smaller resistor always hogs the larger share, in exact inverse proportion to the resistances:
This is why the tool lists each branch separately: in power circuits you need to know whether the hottest branch stays within its wattage rating. Once you have the total current, an amps to watts calculator converts it to power draw at your supply voltage, and an electrical cable size calculator tells you what wire gauge that current needs. For three-phase distribution boards, a three-phase current calculator handles the per-phase split.
What competing calculators miss
The top results for this keyword each do one slice of the job well and stop there:
- CoolConversion: a clean parallel tool with worked examples, but resistance only, no current or power, and no branch breakdown.
- Starting Electronics: excellent formula teaching with scientific-calculator keystrokes, but the worked examples stop at two resistors and there is no interactive multi-branch tool.
- CalculatorDoc: up to five fixed fields with unused ones defaulting to infinity, which silently changes the meaning of a blank field instead of flagging it.
- Engineering Toolbox: solid series/parallel theory with a hand-worked current example, but the current math is text you must repeat yourself.
- RedCrab: semicolon-separated entry and good special-case formulas, yet no voltage mode and no per-branch results.
- Utmel and ReversePCB: combined series/parallel tools, but the parallel side returns a single resistance number with no conductance, current or power.
- The gap this page fills: 2 to 6 branches with an explicit resistor count, a conductance readout, an optional voltage that unlocks total current, total power and per-branch currents in one result table, a pre-filled worked example that reproduces to the fourth decimal, and copy/share for lab notes.
Common mistakes to avoid
- Adding the resistances directly. That is the series formula. In parallel, 100 + 200 = 300 Ω is wrong; the answer is 66.6667 Ω.
- Forgetting to take the final reciprocal. The sum 1/100 + 1/200 = 0.015 is the conductance in siemens, not the resistance. Invert it.
- Mixing units. This tool takes ohms only. Convert kilohms to ohms first (1 kΩ = 1000 Ω); a 1 kΩ entered as 1 gives a nonsense answer.
- Entering 0 for a short circuit. A true 0 Ω branch is a short: all current bypasses the other branches and the equivalent resistance is 0. The tool rejects zero to avoid a divide-by-zero, so model a near-short with a tiny value such as 0.001 Ω instead.
- Assuming equal current in each branch. Current splits in inverse proportion to resistance, so the 100 Ω branch here carries twice the current of the 200 Ω branch.
Takeaways
- Parallel resistance is always less than the smallest branch resistor.
- Two resistors: Rt = (R1 × R2) / (R1 + R2); equal resistors: R/n.
- Voltage is identical across branches; current divides in inverse proportion to resistance.
- Add a voltage to get total current, total power and per-branch currents, not just ohms.
Frequently asked questions
Add the reciprocals: 1/Rt = 1/R1 + 1/R2 + 1/R3 and so on, then take the reciprocal of the sum. For two resistors only, the shortcut Rt = (R1 × R2) / (R1 + R2) gives the same answer with less arithmetic.
Each added branch is another path for current, which adds conductance. More conductance at the same voltage means more total current, and by Ohm’s law more current at fixed voltage means lower equivalent resistance. The total therefore sits below even the smallest branch.
Use the reciprocal sum for all branches: 1/Rt = 1/R1 + 1/R2 + 1/R3 + … For example, 4, 6 and 12 ohms give 1/4 + 1/6 + 1/12 = 0.5 S, so Rt = 2.0000 ohms. The calculator above handles 2 to 6 branches directly.
That is a short circuit: all current takes the zero-resistance path, the equivalent resistance drops to zero, and the other branches are bypassed. This tool rejects zero to avoid dividing by zero, so enter a tiny value like 0.001 ohms to model a near-short.
No. Voltage is optional. Without it you get total resistance and conductance. With it, the calculator also returns total current, total power and the current through each individual resistor.
In inverse proportion to the resistances, because every branch sees the same voltage and I = V/R. In the worked example at 12 V, the 100 ohm branch carries 0.1200 A and the 200 ohm branch carries 0.0600 A, exactly a 2:1 split.
Convert first: the tool assumes every entry is in ohms. Multiply kilohm values by 1000 before entering them. A 1 kilohm resistor entered as 1 would silently produce a wrong answer.
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References
- All About Circuits. Parallel Circuits and the Application of Ohm’s Law. Accessed October 23, 2026.
- All About Circuits. Resistance in Parallel Networks. Accessed October 23, 2026.
- LibreTexts Physics. Parallel Circuits. Accessed October 23, 2026.
- Engineering ToolBox. Electrical Resistance in Serial and Parallel Networks. Accessed October 23, 2026.
- Starting Electronics. Resistors in Parallel: Add and Calculate Parallel Resistance. Accessed October 23, 2026.