Quickly calculate the total equivalent resistance of multiple resistors connected in parallel. Includes the 1/R formula, unit conversions, and a quick reference table.
The Parallel Resistor Formula
Calculating the total (or equivalent) resistance of a parallel circuit is different from a series circuit. In parallel, adding more resistors actually decreases the total resistance. The general formula for any number of resistors is:
1 / RTotal = 1 / R1 + 1 / R2 + 1 / R3 + … + 1 / Rn
The “Product Over Sum” Shortcut (For 2 Resistors)
If you are only working with exactly two resistors in parallel, you can use a much simpler mathematical shortcut known as the “product over sum” formula:
RTotal = (R1 × R2) / (R1 + R2)
Quick Reference Table
Here are some of the most common parallel resistor combinations you will encounter on breadboards and PCB designs.
| Resistor 1 | Resistor 2 | Resistor 3 | Equivalent Resistance |
|---|---|---|---|
| 100 Ω | 100 Ω | – | 50 Ω |
| 1 kΩ (1000 Ω) | 1 kΩ (1000 Ω) | – | 500 Ω |
| 100 Ω | 100 Ω | 100 Ω | 33.33 Ω |
| 330 Ω | 470 Ω | – | 193.87 Ω |
| 10 kΩ | 100 kΩ | – | 9.09 kΩ |
Pro-Tip: When two resistors of the exact same value are in parallel, the total resistance is simply half of one resistor’s value.
Contextual Information
Why does resistance decrease in parallel?
A common point of confusion for students is why adding more components lowers the total resistance. Think of a highway: if you have a one-lane road, traffic gets congested (high resistance). If you build a second parallel lane, traffic flows more easily. Even if the new lane is narrow and slow (a high-value resistor), it still provides an extra path for the current to take, making the overall flow of electricity easier than it was with just one lane.
What happens if a resistor is 0 Ohms?
If you place a wire with no resistance (0 Ohms) in parallel with other resistors, all the electrical current will take the path of least resistance. This bypasses the other resistors entirely, resulting in an equivalent resistance of 0 Ohms. In electronics, this is called a short circuit.
Rules of Thumb for Parallel Circuits
- The equivalent resistance will always be lower than the smallest individual resistor in the parallel network.
- Voltage is the same across all components connected in parallel.
- Current splits across the parallel branches based on their resistance (lower resistance paths carry more current).