Parallel resistance calculator
When resistors are connected in parallel, they share the same voltage across their terminals and the current splits between them. Adding more parallel paths makes the network conduct more easily — the equivalent resistance is always lower than the smallest individual resistor. This calculator takes any number of resistor values and returns the equivalent (total) resistance instantly.
How it works
The reciprocal rule comes from Kirchhoff’s current law: the total current entering the parallel junction equals the sum of the currents through each branch. Since current through each resistor is V/R, summing them and factoring out V gives:
1/Rt = 1/R1 + 1/R2 + ... + 1/Rn
Rt = 1 ÷ (sum of reciprocals)Equivalently, each resistor’s conductance G = 1/R (measured in siemens) adds directly in parallel, and the equivalent resistance is the reciprocal of the total conductance. The tool sums the reciprocals, inverts, and returns the result.
Why the result is always smaller than the smallest resistor
Adding another parallel branch gives current an additional route through the circuit. Even a very large resistor in parallel reduces total resistance slightly — more paths always means lower overall opposition to current flow. If you add a 1 MΩ resistor in parallel with a 100 Ω resistor, the result is about 99.99 Ω, barely changed but always lower.
The special case of two equal resistors in parallel is worth memorising: the equivalent is exactly half the individual value (R/2). Three equal resistors give R/3, and n equal resistors give R/n.
Worked examples
Three standard E24 values in parallel:
100 Ω, 220 Ω, and 470 Ω:
- 1/100 + 1/220 + 1/470 = 0.010000 + 0.004545 + 0.002128 = 0.016673 S
- Rt = 1 ÷ 0.016673 ≈ 59.98 Ω
| Resistors (Ω) | Equivalent (Ω) | Notes |
|---|---|---|
| 100, 100 | 50 | Equal-value shortcut: R/2 |
| 100, 220, 470 | 59.98 | Standard E24 mix |
| 1000, 1000, 1000 | 333.33 | Three equal: R/3 |
| 47, 10000 | 46.78 | High-value barely changes low |
Practical uses
Increasing current capacity: when a single resistor’s power rating is insufficient, two resistors of double the value in parallel share the dissipation between them, doubling effective power handling.
Achieving non-standard values: parallel combinations let you hit resistance values not available in standard E12/E24/E96 series. For example, 330 Ω and 680 Ω in parallel gives approximately 220 Ω — useful for a spot value that may be unavailable in stock.
Pull-up/pull-down networks: in digital circuits, multiple pull-up resistors in parallel reduce the effective pull-up resistance and speed up rise times on slow signal lines.
Enter values in the same unit (ohms, kilohms, or megohms) and the result is in the same unit — the reciprocal formula is unit-agnostic. All calculation happens locally in your browser.