Parallel Resistance Calculator
Parallel equivalent for 2-4 resistors, with series sum.
What it does
Parallel resistors share voltage and split current, so their combination always reads below the smallest branch. A 1k resistor beside a 2k gives 666.67 ohms, less than either alone. Add more branches and the total keeps falling toward zero.
The tool above handles two to four resistors with a series comparison beside. Enter ohms per branch with 0 for unused slots, and it prints the parallel equivalent, the series sum, and how many times lower parallel runs. Defaults give 666.67 against 3,000, a 4.5x gap.
University treatments derive the same rules. HyperPhysics builds series and parallel equivalents from Ohm law with branch currents, and MIT 6.002 teaches resistive network analysis with superposition and Thevenin methods. The two-resistor shortcut, product over sum, falls straight out.
Tolerance keeps meter readings near, not on, these ideals. A 5 % band on each resistor moves the equivalent a few percent, and heat shifts values under load. Size power ratings from branch currents, then confirm critical dividers by measurement.
How to use
- Enter the first two resistors in ohms.
- Add third and fourth, or leave 0.
- Read parallel equivalent first.
- Read the series sum beside it.
- Read how many times lower parallel runs.
- Check power ratings separately.
Formula
- R1-R4
- Branch resistors in ohms, 0 marks unused.
- Rt
- Equivalent parallel resistance.
- series
- Straight sum for comparison.
Follows from Ohm law with common voltage across branches (HyperPhysics) and MIT 6.002 network analysis. Zeros mark unused slots.
Worked example
Example: 1k parallel with 2k
Defaults: 1k and 2k resistors.
- Inputs: 1,000 and 2,000 ohms.
- Reciprocals: 1/1000 + 1/2000 = 3/2000.
- Invert: 2000 / 3 = 666.67 ohms.
- Series check: 1,000 + 2,000 = 3,000.
- Ratio: 3,000 / 666.67 = 4.5. Tool shows 666.67 ohms, 3,000 ohms, 4.5x lower.
Reference table
| Resistors | Parallel | Series |
|---|---|---|
| 1000, 2000 | 666.67 | 3,000 |
| 100, 200, 300 | 54.55 | 600 |
| 100, 200, 300, 400 | 48.00 | 1,000 |
Limits
- Ideal resistors only. Tolerance and heat shift readings.
- DC resistive only. Reactive AC networks differ.
- At least two positive branches required.
- Power ratings need separate current math.
Common mistakes
- Averaging instead of reciprocals.
- Adding parallel like series.
- Leaving one branch and expecting magic.
- Ignoring tolerance on precision builds.
- Forgetting heat drift under load.
Try it yourself
Quick checks. Answers sit tucked under each question.
100, 200, 300 in parallel?
1/100+1/200+1/300 = 11/600. Rt = 600/11 = 54.55 ohms. Series 600, 11x lower.
100, 200, 300, 400 in parallel?
Twelfths: 12+6+4+3 = 25/1200 = 1/48. Rt = 48 ohms. Series 1,000, 20.83x lower.
Questions
How is parallel resistance figured?
Invert the sum of reciprocals: 1/(1/1000 + 1/2000) = 666.67 ohms. Two resistor shortcut: (1000x2000)/3000.
What is the series total?
Series adds: 1,000 + 2,000 = 3,000 ohms. Parallel always lands below the smallest branch.
Can I use two resistors only?
Yes. Enter 0 for unused third and fourth slots; the tool uses only positive values.
What about 100, 200, 300 together?
54.55 ohms: 1/100+1/200+1/300 = 11/600, inverted. Series 600, so 11x lower.
And with 400 added?
48 ohms exact: twelfths sum 12+6+4+3 = 25/1200 = 1/48. Series 1,000, so 20.83x lower.
Are real readings exact?
No. Real resistors carry tolerance bands, so meter readings vary a few percent around these ideals.
Sources
- Georgia State HyperPhysics: Resistor Combinations
- Georgia State HyperPhysics: DC Parallel Circuit
- MIT OCW 6.002: Circuits and Electronics (resistive networks)