Parallel Resistors
With r1 100 ohm, r2 220 ohm, r3 0 ohm, r4 0 ohm and 1 more field, parallel resistors comes to 68.750 ohm — parallel resistance. It is reached in 6 steps, the last of which is 1 / 0.0145455, and each one is printed on the page with its numbers filled in. The formula is the one published by NIST SP 811, not an approximation fitted to it.
Up to four resistors in parallel or series, with the current each one takes and the power it has to dissipate — which is what decides the rating.
Formula and sources checked · How we check
R1 100 ohm, R2 220 ohm, Voltage across the network 12 V
68.750 ohm
Parallel resistance for the example below. Editing a field recomputes the calculator below; this figure holds the answer the page was loaded with.
It is written into the HTML rather than drawn by a script, so a search engine reading this page without running JavaScript still finds an answer.
- In parallel
1 / 0.014545568.75 ohm- In series
100 + 220 + 0 + 0320 ohm- Total current, in parallel
12 * 0.01454550.175 A- Current through R1
12 / 1000.12 A- Power in R1
12 * 12 / 1001.44 W- Total power, in parallel
12 * 12 * 0.01454552.095 W
Worked example
100 ohms and 220 ohms in parallel is 68.75 ohms — below the smaller of the two, which is always true and is the quickest check that a parallel answer is not upside down. In series they would be 320.
How to work it out yourself
- 1.Enter the resistors you have and leave the unused fields at zero. A zero is read as an open circuit rather than as a short, so it drops out of the parallel sum instead of collapsing it.
- 2.The parallel result is always smaller than the smallest resistor. If an answer comes out larger, the reciprocals were added the wrong way round.
- 3.Set the voltage to see the currents and the power. The power figure is what picks the physical resistor: a quarter-watt part in a circuit dissipating 0.4 W runs hot and drifts.
- 4.For two resistors the shortcut is product over sum: 100 × 220 ÷ 320 = 68.75. It only works for two, which is why the reciprocal form is the one worth learning.
Two 100 ohm resistors, second one varied
| R2 (ohm) | Parallel resistance | In series |
|---|---|---|
| 10 | 9.091 ohm | 110 ohm |
| 22 | 18.033 ohm | 122 ohm |
| 47 | 31.973 ohm | 147 ohm |
| 100 | 50.000 ohm | 200 ohm |
| 150 | 60.000 ohm | 250 ohm |
| 220 | 68.750 ohm | 320 ohm |
| 330 | 76.744 ohm | 430 ohm |
| 470 | 82.456 ohm | 570 ohm |
| 1000 | 90.909 ohm | 1,100 ohm |
| 4700 | 97.917 ohm | 4,800 ohm |
| 10000 | 99.010 ohm | 10,100 ohm |
The parallel value is always smaller than the smallest resistor in the set, and adding a much larger resistor barely moves it: 100 in parallel with 10,000 is 99.0 ohms. That is the sanity check on any parallel answer.
The formula
- In parallel
1 / 0.0145455 - In series
100 + 220 + 0 + 0 - Total current, in parallel
12 * 0.0145455 - Current through R1
12 / 100 - Power in R1
12 * 12 / 100 - Total power, in parallel
12 * 12 * 0.0145455
Source: NIST SP 811 — the ohm and the siemens, IEC 60063 — preferred number series for resistors (E6, E12, E24)
Questions people actually ask
- What is the formula for resistors in parallel?
- 1/R = 1/R1 + 1/R2 + … , so R is the reciprocal of the sum of the reciprocals. For exactly two, the shortcut R1 × R2 ÷ (R1 + R2) gives the same answer and is easier by hand.
- Why is the parallel resistance smaller than either resistor?
- Because each extra path gives the current somewhere else to go. Two 100 ohm resistors side by side present half the opposition of one, so 50 ohms. The rule holds for any number: the total is always below the smallest member.
- What about resistors in series?
- They add directly: 100 + 220 is 320 ohms. The same current passes through each, and the voltage divides between them in proportion to their resistance — which is what a voltage divider is.
- How do I get a value I do not have?
- Two in parallel or in series. Two 100 ohm resistors make 50 or 200; a 100 and a 220 make 68.75 or 320. Standard E12 values were chosen so that combinations cover the gaps, and matching within 5% is usually enough because that is the tolerance of the part anyway.
- How do I pick the power rating?
- Compute the power each resistor dissipates — V²/R for that resistor — and choose a part rated at least double. A resistor run at its full rating reaches well over 100 °C, drifts in value and cooks whatever sits next to it on the board.
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