Calculation history
Formula used
1 / RT = 1 / R1 + 1 / R2 + ... + 1 / Rn
RT = (R1 × R2) / (R1 + R2)
RT = R / n and GT = G1 + G2 + ... + Gn
How to use this calculator
- Select the required calculation mode.
- Add every active parallel resistor branch.
- Choose the unit and tolerance for each resistor.
- Enter supply voltage for current and power analysis.
- Add power ratings to receive overload warnings.
- Select output precision and the preferred result unit.
- Press Calculate and review the complete solution.
- Copy, export, print, or save the calculated result.
An open branch has extremely high resistance and contributes little conductance. A shorted branch approaches zero resistance and dominates the network. Real circuits also include wiring, temperature, and contact effects.
Example data
| Example | Branch values | Voltage | Expected result |
|---|---|---|---|
| Two equal resistors | 100 Ω, 100 Ω | 10 V | 50 Ω, 0.2 A total |
| Mixed values | 100 Ω, 220 Ω, 330 Ω | 12 V | About 56.90 Ω |
| Mixed units | 1 kΩ, 500 Ω, 0.002 MΩ | 5 V | About 285.71 Ω |
| Identical network | Four 1 kΩ resistors | 24 V | 250 Ω |
Understanding parallel resistor networks
Each parallel branch receives the same applied voltage. Branch current increases when resistance decreases. Total current equals every branch current added together.
Conductance measures how easily current can flow. Parallel conductances add directly across the network. Equivalent resistance is the reciprocal of total conductance.
Tolerance creates a possible resistance range around nominal values. Minimum branch values produce the minimum equivalent resistance. Maximum branch values produce the maximum equivalent resistance.
Power equals voltage squared divided by branch resistance. A practical rating should include a safety margin. This calculator recommends twice the calculated branch power.
Frequently asked questions
Why is parallel resistance always smaller?
Adding a branch creates another current path. Total conductance therefore increases. Greater conductance means lower equivalent resistance.
Can different resistance units be mixed?
Yes. Each branch can use its own unit. Values are converted to ohms before calculation.
How are branch currents calculated?
Every branch receives the same source voltage. Current equals voltage divided by branch resistance. The calculator sums all branch currents.
What happens when one resistor is zero?
An ideal zero-ohm branch is a short circuit. Equivalent resistance approaches zero. Real sources may supply dangerous current.
What represents an open circuit?
An open branch has extremely high resistance. Its conductance and current approach zero. Other active branches still determine total resistance.
How does resistor tolerance affect the result?
Each resistor may vary around its nominal value. The calculator evaluates minimum and maximum branch values. These produce a total resistance range.
How is a missing resistor found?
The known branch conductances are subtracted from target conductance. The remaining conductance is inverted. A positive remaining value is required.
How many identical resistors are required?
Divide one resistor value by the target resistance. Round upward to a whole resistor count. The actual result may be slightly lower.
Why include a power safety margin?
Temperature and ventilation affect safe resistor operation. Continuous operation near maximum rating reduces reliability. A larger rating improves thermal margin.
Are ideal calculations exact in practice?
No. Leads, connections, temperature, and measurement accuracy add error. Use measured values for critical engineering work.