Parallel Circuit Calculator
Enter at least two branch resistances to calculate equivalent resistance. Add a source voltage to also compute branch currents, total current, and total power.
What Is a Parallel Circuit?
A parallel circuit has multiple current paths connected across the same voltage source. Each branch sees the same voltage, but current splits across branches based on resistance. Lower resistance branches carry more current, and higher resistance branches carry less.
This is why a parallel circuit is common in homes and electronics: if one branch opens, the others can still operate. Understanding equivalent resistance and branch currents is essential for safe design and troubleshooting.
How the Parallel Resistance Formula Works
Core Relationship
In a parallel resistor network, conductances add. Conductance is the inverse of resistance, so:
1 / Req = Σ(1 / Ri)
After summing inverse resistances, invert the result to get equivalent resistance:
Req = 1 / [Σ(1 / Ri)]
Because conductances add, equivalent resistance in parallel is always smaller than the smallest branch resistance.
How to Use This Circuit Parallel Calculator
- Enter resistance values for each branch (in ohms).
- Use + Add Branch for larger networks.
- Optionally enter source voltage to compute currents and power.
- Click Calculate to see full results.
- Use Reset to start over quickly.
Worked Example
Suppose three resistors are in parallel: 10 Ω, 20 Ω, and 30 Ω with a 12 V source.
- 1 / Req = 1/10 + 1/20 + 1/30 = 0.18333...
- Req ≈ 5.45 Ω
- Total current Itotal = V / Req = 12 / 5.45 ≈ 2.20 A
- Branch currents: 1.20 A, 0.60 A, and 0.40 A
Notice that branch currents add to total current, which is exactly what Kirchhoff’s Current Law predicts.
Common Mistakes to Avoid
- Mixing units: Keep resistance in ohms and voltage in volts.
- Using zero or negative resistance: Physical resistor values must be positive.
- Confusing series and parallel formulas: Series adds resistance directly; parallel adds inverse resistance.
- Ignoring power limits: Large branch currents can exceed resistor wattage ratings.
Practical Use Cases
This tool is useful when designing sensor pull-ups, LED resistor branches, load-sharing circuits, and equivalent load calculations for power supplies. It is also a quick learning aid for students in physics, electronics, and electrical engineering classes.
Quick FAQ
Can I calculate branch current without voltage?
Not exactly. You can calculate equivalent resistance without voltage, but branch current requires a known voltage across the parallel network.
Does this work for AC circuits?
For pure resistors, yes. For AC circuits with reactance, use impedance (complex values), not simple resistance.
Can this calculator handle two branches only?
Yes. Two-branch and multi-branch networks are both supported.