Ideal resistors assumed. Real values vary by the tolerance band, and each resistor must be rated for the power shown with a safety margin.
Formula and breakdown
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This parallel resistor calculator works out the equivalent resistance of up to 20 resistors connected in parallel or in series, for students, electronics hobbyists, makers and technicians in the UK, Europe and elsewhere. Add a supply voltage to see the current, voltage and power in every resistor, or enter a target value to find the extra resistor you need and the nearest standard part.
Quick answer: A parallel resistor calculator adds the reciprocal of each resistance and takes the reciprocal of the total: 1/Req = 1/R1 + 1/R2 + 1/R3. For two resistors, product over sum gives the same answer. The result is always below the smallest resistor, so 100, 220 and 470 ohms in parallel give about 60 ohms.
What Is a Parallel Resistor Calculator?
A parallel resistor calculator is a tool that replaces a group of resistors with the single resistance that would draw the same current from the same voltage. In plain words: for parallel resistors, add one divided by each resistance, then take one divided by that sum; for series resistors, simply add the values.
The Wikipedia article on series and parallel circuits sets out both rules and notes that two parallel parts are often written with the parallel operator, as R1 || R2. Parallel resistors share the same voltage and split the current; series resistors share the same current and split the voltage. The parallel resistor calculator handles both, so you can check each half of a mixed network one step at a time.
How Do You Use the Parallel Resistor Calculator?
- Choose Parallel or Series.
- Enter each resistor value and pick ohms, kilohms or megohms for that row. Use Add resistor for more rows and Remove for unused ones.
- Optionally enter the voltage across the whole network to see total current, total power and the current, voltage and power in each resistor.
- Optionally enter a target total resistance to find the extra resistor needed and the nearest E24 standard value.
- Open Formula and breakdown to see the sum with your own numbers, then copy the result if you need it.
How Do You Calculate Resistors in Parallel?
Add the reciprocals and invert the total: for 100, 220 and 470 ohms, 1/100 + 1/220 + 1/470 = 0.01667, and 1 / 0.01667 = 59.98 ohms. The reciprocal of resistance is conductance, measured in siemens, so the same step can be read as “conductances add in parallel”. The parallel resistor calculator shows that total conductance in millisiemens.
For exactly two resistors the shortcut is product over sum, R1 x R2 / (R1 + R2). For identical resistors divide one value by how many there are. If you only need one resistance from a voltage and current, the Ohm’s law calculator is quicker.
What Do Common Resistor Combinations Give?
Two equal resistors in parallel always give half the value, and a large resistor in parallel with a small one barely changes the small one. The table lists some combinations worked out with the parallel formula.
| Resistors in parallel | Equivalent resistance | Note |
|---|---|---|
| 100 ohms and 100 ohms | 50 ohms | Equal values halve |
| 3 x 100 ohms | 33.33 ohms | R divided by 3 |
| 4 x 10 kilohms | 2.5 kilohms | R divided by 4 |
| 220 ohms and 330 ohms | 132 ohms | Product over sum |
| 1 kilohm and 2.2 kilohms | 687.5 ohms | Product over sum |
| 4.7 kilohms and 10 kilohms | 3.197 kilohms | Not an E24 value |
| 47 ohms and 100 ohms | 31.97 ohms | Close to E24 30 ohms |
| 1 kilohm and 1 megohm | 999 ohms | Large value barely matters |
How Is Current and Power Shared Between Parallel Resistors?
Each parallel resistor carries the supply voltage divided by its own resistance, so the lowest value carries the most current and gets hottest. With 12 V across 100, 220 and 470 ohms, the branches carry 120 mA, 54.5 mA and 25.5 mA, and dissipate 1.44 W, 0.65 W and 0.31 W, for a total of 2.4 W.
Power in each resistor is V x V / R in parallel and I x I x R in series. Choose parts whose rated power sits comfortably above the figure shown, following the derating curve in the manufacturer’s datasheet, because a resistor near its rating runs very hot. Spreading the load across identical resistors in parallel divides the heat equally. To turn a circuit’s power into current at mains or battery voltage, use the watts to amps calculator.
When Is a Target Resistance Impossible?
In parallel you can only lower the resistance, so a target above the existing value cannot be reached by adding another resistor; in series you can only raise it. The calculator explains which case applies. When a target is reachable it gives the exact missing value, then rounds to the nearest E24 preferred value and shows the total that part actually produces.
The E series are defined in IEC 60063. According to the Wikipedia summary of E series preferred numbers, the E12 range is associated with 10% tolerance and the E24 range with 5%, with E24 values per decade of 1.0, 1.1, 1.2, 1.3, 1.5, 1.6, 1.8, 2.0, 2.2 and so on up to 9.1. Pairing two standard values in parallel or series is a common way to reach a value the range does not contain, such as the resistor for an LED.
Does This Apply to Mains Wiring and Heating Elements?
The formulas apply to any resistive load, including heating elements, but working on mains circuits is a job for a qualified electrician, and in the UK the work must meet BS 7671. Use the calculator for understanding and for low-voltage electronics. For long cable runs, conductor resistance matters too, which the voltage drop calculator covers.
Worked Example: Reaching 75 Ohms From Standard Parts
Example: a 12 V low-voltage test load needs 75 ohms, and a 100 ohm resistor is already fitted. Enter 100 ohms, choose Parallel, set the voltage to 12 V and the target to 75 ohms.
- Missing resistor: 1 / (1/75 minus 1/100) = 1 / (0.013333 minus 0.01) = 1 / 0.003333 = 300 ohms.
- 300 ohms is an E24 value, so the nearest standard part gives exactly 75 ohms: 100 x 300 / 400 = 75.
- Total current: 12 / 75 = 0.16 A, total power 12 x 0.16 = 1.92 W.
- Per resistor: the 100 ohm part carries 120 mA and dissipates 1.44 W; the 300 ohm part carries 40 mA and dissipates 0.48 W.
The 100 ohm resistor takes three quarters of the heat, so it needs the higher power rating. Using two 150 ohm resistors instead would also give 75 ohms and split the 1.92 W evenly at 0.96 W each.
Frequently Asked Questions
How do you calculate two resistors in parallel?
Multiply the two values and divide by their sum, known as product over sum. A 1 kilohm and a 2.2 kilohm resistor give 1,000 x 2,200 / 3,200 = 687.5 ohms. For three or more resistors, add the reciprocals and take the reciprocal of the total instead.
Why is resistance in parallel always lower than the smallest resistor?
Each resistor in parallel adds another path for current, so the network conducts more easily than any single branch. In terms of conductance, the conductances add up, and a larger total conductance means a smaller total resistance. That is why the result always falls below the lowest value.
What is the resistance of identical resistors in parallel?
Divide one resistor’s value by the number of resistors. Two 100 ohm resistors give 50 ohms, three give about 33.3 ohms and four 10 kilohm resistors give 2.5 kilohms. Identical parts also share the current and the heat equally, which is useful for spreading power.
How is current shared between resistors in parallel?
Every branch sees the same voltage, so each resistor carries a current equal to the voltage divided by its own resistance. The smallest resistor carries the most current and dissipates the most power. With 12 V across 100 ohms and 470 ohms, the branches carry 120 mA and about 25.5 mA.
How do I find the resistor needed to reach a target value?
In parallel, the missing resistor is 1 / (1/target minus 1/existing), which only works when the target is below the existing value. In series, subtract the existing total from the target. The calculator then suggests the nearest E24 preferred value and shows the total it gives.
Does resistor tolerance change the parallel result?
Yes. The calculator uses nominal values, but each real resistor can sit anywhere within its tolerance, such as 5% for the E24 range. If every part in a parallel group is within 5%, the combined resistance also stays within 5% of the nominal result.
Checked October 2026 by the Solaxyra Editorial Team. Sources: Wikipedia, Series and parallel circuits, Wikipedia, E series of preferred numbers.