Calculation Results
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Step-by-Step Solution
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Branch Results
| Branch | Entered Value | Resistance | Reciprocal | Conductance | Current | Power | Current Share |
|---|---|---|---|---|---|---|---|
| Branch details will appear here. | |||||||
Preferred Resistor Comparison
Choose an E-series to compare the calculated resistance.
Calculator Settings
Parallel Resistor Branches
Each branch can use a different resistance unit and tolerance.
Solve a Missing Parallel Resistor
Known resistors
Equal Resistors in Parallel
Optional Electrical Analysis
Parallel Circuit Diagram
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Calculation History
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Formula Used
1 / Rₜ = 1 / R₁ + 1 / R₂ + ... + 1 / RₙParallel branches share the same voltage across both connection nodes. Their conductances add before converting back into resistance. The total stays below the smallest valid branch resistance.
For two resistors: Rₜ = (R₁ × R₂) / (R₁ + R₂)The two-resistor shortcut gives the same result as reciprocals. It is convenient for quick checks and manual calculations. Mixed units must be converted before using this formula.
Equal resistors: Rₜ = R / nHow to Use
- Select the required calculation mode.
- Enter each resistor and choose its unit.
- Add voltage and tolerance values when needed.
- Select precision, notation, and output units.
- Press Calculate Parallel Resistance to view results.
- Copy, print, or export the completed calculation.
Worked Example
| Branch | Resistance | Reciprocal | Conductance |
|---|---|---|---|
| R1 | 1 kΩ | 0.001 Ω⁻¹ | 1 mS |
| R2 | 2.2 kΩ | 0.0004545 Ω⁻¹ | 0.4545 mS |
| R3 | 4.7 kΩ | 0.0002128 Ω⁻¹ | 0.2128 mS |
| Total conductance | 1.6673 mS | ||
| Equivalent resistance | 599.77 Ω | ||
Frequently Asked Questions
Why is parallel resistance always smaller?
Adding branches creates more paths for current. More conductance means lower equivalent resistance. The result remains below the smallest positive branch.
Can I mix resistance units?
Yes, each resistor may use a different unit. The calculator converts every value into ohms internally. Results can use any selected output unit.
How are equal resistors calculated?
Divide one resistor value by the resistor count. Four equal 1 kΩ resistors produce 250 Ω. This method only applies to identical resistance values.
How does current divide between branches?
Every branch receives the same applied voltage. Lower resistance branches carry more current. Branch current follows Ohm's law directly.
What happens when one branch opens?
An open branch carries no current. The remaining branches still operate across the source. Equivalent resistance increases after removing that branch.
What happens during a short circuit?
A zero-ohm branch creates an ideal short circuit. Current may become dangerously large in real circuits. This calculator rejects zero resistance inputs.
How does tolerance affect equivalent resistance?
Each resistor can vary inside its tolerance band. The calculator evaluates minimum and maximum branch values. Those limits create the total resistance range.
Can parallel resistors increase power capacity?
Parallel parts can share total power dissipation. Unequal resistors do not share power equally. Always check every resistor's individual wattage requirement.
What is conductance?
Conductance is the reciprocal of resistance. Its SI unit is the siemens. Parallel conductances add directly together.
How many resistors can I enter?
The interface supports many dynamic resistor branches. Browser performance sets the practical limit. Typical engineering calculations need far fewer branches.
Can this calculator analyse AC circuits?
It handles purely resistive AC branches using RMS voltage. Reactive components require complex impedance calculations. Capacitors and inductors need another calculator.