Series and Parallel Resistor: formula
Select two or three included resistors and enter their values in ohms. Choosing two excludes the third field. An included zero-ohm resistor remains a branch: in parallel it shorts the network.
Negative resistance is outside this passive-component model.
Series and Parallel Resistor: worked example
| Resistor 1 (ohms) | 100 |
|---|---|
| Resistor 2 (ohms) | 220 |
| Resistors included | Three |
| Resistor 3 (ohms) | 330 |
| Series resistance (ohms) | 650 |
| Parallel resistance (ohms) | 56.9 |
Real resistors have tolerance, so the combination varies by the same percentages. Wires and connections add small resistance. In parallel the current splits unevenly, so the smaller resistor carries more.
Power ratings apply to each part, not the total.
Series and Parallel Resistor: changing Resistor 1 (ohms)
| Resistor 1 (ohms) | Series resistance (ohms) | Parallel resistance (ohms) |
|---|---|---|
| 80 | 630 | 49.8 |
| 90 | 640 | 53.5 |
| 100 (example) | 650 | 56.9 |
| 110 | 660 | 60 |
| 120 | 670 | 62.9 |
Series and Parallel Resistor: compare input ranges
| Input | Tested from | To | Series resistance (ohms): low input | Series resistance (ohms): high input | Swing |
|---|---|---|---|---|---|
| Resistors included | Two | Three | 320 | 650 | 330 (51%) |
| Resistor 3 (ohms) | 297 | 363 | 617 | 683 | 66 (10%) |
| Resistor 2 (ohms) | 198 | 242 | 628 | 672 | 44 (6.8%) |
| Resistor 1 (ohms) | 90 | 110 | 640 | 660 | 20 (3.1%) |
Series and Parallel Resistor: individual input comparisons
| Input | Value | Series resistance (ohms) | Parallel resistance (ohms) |
|---|---|---|---|
| Resistor 1 (ohms) | 80 | 630 | 49.8 |
| 90 | 640 | 53.5 | |
| 100 | 650 | 56.9 | |
| 110 | 660 | 60 | |
| 120 | 670 | 62.9 | |
| Resistor 2 (ohms) | 176 | 606 | 53.4 |
| 198 | 628 | 55.3 | |
| 220 | 650 | 56.9 | |
| 242 | 672 | 58.3 | |
| 264 | 694 | 59.5 | |
| Resistors included | Two | 320 | 68.8 |
| Three | 650 | 56.9 | |
| Resistor 3 (ohms) | 264 | 584 | 54.5 |
| 297 | 617 | 55.8 | |
| 330 | 650 | 56.9 | |
| 363 | 683 | 57.8 | |
| 396 | 716 | 58.6 |
Series and Parallel Resistor: combined input changes
| Resistor 1 (ohms) / Resistor 2 (ohms) | 176 | 220 | 264 |
|---|---|---|---|
| 80 | 586 | 630 | 674 |
| 90 | 596 | 640 | 684 |
| 100 | 606 | 650 | 694 |
| 110 | 616 | 660 | 704 |
| 120 | 626 | 670 | 714 |
Series and Parallel Resistor: which assumptions move the result?
Series and Parallel Resistor: values and definitions
| Quantity and definition | Value used |
|---|---|
| Resistor 1 (ohms) | 100 |
| Resistor 2 (ohms) | 220 |
| Resistors included — Choose whether resistor 3 is included. | Three |
| Resistor 3 (ohms) — Choose two resistors to omit this position. An included zero-ohm branch is a short circuit. | 330 |
| Series resistance (ohms) | 650 |
| Parallel resistance (ohms) | 56.9 |
Common error: Adding resistances in parallel like a series chain. The result is always larger than any single part, which cannot be true when current has extra paths.
Read the component code and its tolerance
Treat the selected tolerance as a manufacturing range around the nominal resistance, rather than another color digit. For an explicitly assumed 4,700-ohm nominal part at five percent, that range is 4,465 through 4,935 ohms. A measured value within the interval does not establish the component’s power rating or behavior at another temperature.
Four-band and five-band codes allocate different numbers of significant digits, so identify the format before combining the digit and multiplier bands. A circuit calculation still needs the resistance and power requirements separately.
Science & Electronics calculators: LED Resistor Calculator, Watts to Amps Calculator, Resistor Color Code Calculator, Voltage Divider Calculator, RC Time Constant Calculator, Combined Gas Law Calculator.
Resistors add in series and combine in reverse in parallel. Three resistors of 100, 220 and 330 ohms make 650 ohms in a chain, but only about 57 ohms side by side, less than the smallest one. Current takes every path it can, so more paths always lower the total resistance.
That is the reason a parallel branch can never raise resistance.
Confirm how the parts are wired. A resistor in line with the current is in series, and one connected across the same two points is in parallel.
See the voltage across resistors on the voltage divider calculator, current and power on the Ohm's law page, LED resistors on the LED resistor page and color bands on the resistor color code calculator. The RC time constant calculator adds a capacitor, and the voltage drop page covers wires.
Does entering zero mean a resistor is absent?
No. Use the count selector to omit resistor 3. An included zero-ohm branch is a short circuit.
Can a zero vector or open circuit be represented by zero ohms?
No. An open circuit is infinite resistance. Zero ohms represents a conducting short, not an absent connection.
How do I calculate resistors in parallel?
Add the reciprocals of the resistances and take the reciprocal of the sum. Two equal resistors in parallel give half the value of one.
Why is parallel resistance lower than any single resistor?
Because each added path gives current another route, so the total opposition to current falls below that of the smallest single resistor.
What is resistor tolerance?
The allowed deviation from the marked value, commonly 5% or 1%, shown by the last color band.