Parallel Resistor Calculator
Calculate the total equivalent resistance of resistors connected in parallel. Add as many resistors as needed — the calculator handles any number of parallel resistors. See also our Series Resistor Calculator and Ohm's Law Calculator.
How to Calculate Parallel Resistance
When resistors are connected in parallel, they share the same voltage across their terminals but carry different currents (unless they have equal resistance). The total equivalent resistance is always less than the smallest individual resistor in the parallel combination. This is because adding more parallel paths increases the total current flow for a given voltage, which by Ohm's Law means lower total resistance.
To calculate parallel resistance, take the reciprocal of the sum of reciprocals of each individual resistance. For two resistors, there is a simplified formula: Rt = (R1 × R2) / (R1 + R2). For equal resistors in parallel, the total resistance is simply one resistor value divided by the number of resistors.
Parallel Resistance Formula
General Formula (n resistors):
1/Rt = 1/R1 + 1/R2 + 1/R3 + ... + 1/Rn
Two Resistors (simplified):
Rt = (R1 × R2) / (R1 + R2)
Equal Resistors:
Rt = R / n (where n = number of equal resistors)
Current Division:
I1 = Itotal × (Rt / R1)
I2 = Itotal × (Rt / R2)
Example Calculation
Calculate the total resistance of 100Ω and 200Ω resistors in parallel:
Method 1 (reciprocal formula):
1/Rt = 1/100 + 1/200 = 0.01 + 0.005 = 0.015
Rt = 1/0.015 = 66.67 Ω
Method 2 (product over sum):
Rt = (100 × 200) / (100 + 200) = 20000 / 300 = 66.67 Ω
Verification: Rt (66.67Ω) < smallest resistor (100Ω) ✓
If 12V is applied across this parallel combination, the total current is I = 12/66.67 = 0.18A. The 100Ω resistor carries 12/100 = 0.12A and the 200Ω resistor carries 12/200 = 0.06A. The sum of branch currents (0.12 + 0.06 = 0.18A) equals the total current, confirming Kirchhoff's Current Law.
Parallel Resistance Reference Table
| R1 | R2 | Total (Ω) |
|---|---|---|
| 100Ω | 100Ω | 50.00 Ω |
| 100Ω | 200Ω | 66.67 Ω |
| 100Ω | 1000Ω | 90.91 Ω |
| 220Ω | 330Ω | 132.00 Ω |
| 470Ω | 470Ω | 235.00 Ω |
| 1kΩ | 1kΩ | 500.00 Ω |
| 1kΩ | 2.2kΩ | 687.50 Ω |
| 4.7kΩ | 10kΩ | 3,197 Ω |
| 10kΩ | 10kΩ | 5,000 Ω |
| 10kΩ | 47kΩ | 8,246 Ω |
| 47kΩ | 100kΩ | 31,973 Ω |
| 100kΩ | 100kΩ | 50,000 Ω |
Frequently Asked Questions
Why is parallel resistance always less than the smallest resistor?
Each parallel resistor provides an additional path for current to flow. More paths mean more total current for the same voltage, which by Ohm's Law (R = V/I) means lower resistance. Even adding a very large resistor in parallel slightly reduces the total because it still adds some current capacity.
What happens when one parallel resistor is much larger than the other?
The total resistance approaches the value of the smaller resistor. For example, 100Ω in parallel with 1MΩ gives 99.99Ω — the large resistor has negligible effect. This is why a short circuit (0Ω) in parallel with any resistance gives 0Ω total.
How do I create a non-standard resistance value using parallel resistors?
Use the product-over-sum formula in reverse. If you need Rt and have R1, then R2 = (R1 × Rt) / (R1 - Rt). For example, to make 75Ω from standard values: 100Ω ∥ 300Ω = (100×300)/(100+300) = 75Ω. This technique is common when exact resistor values are unavailable.
Do parallel resistors share power equally?
No, unless they have equal resistance. Power dissipation in each resistor is P = V²/R. Since all parallel resistors share the same voltage, the smaller resistor dissipates more power. For example, with 12V across 100Ω ∥ 200Ω: P₁ = 144/100 = 1.44W, P₂ = 144/200 = 0.72W.
When should I use parallel resistors instead of a single resistor?
Use parallel resistors when: you need a non-standard value, you need to distribute power dissipation across multiple components (each resistor handles less power), you need lower resistance than available single resistors, or you need to fine-tune a resistance value by adding a large parallel resistor.
How does parallel resistance apply to real-world circuits?
Household electrical outlets are wired in parallel — each outlet sees the full 120V regardless of other loads. Speaker systems use parallel wiring to reduce impedance (two 8Ω speakers in parallel = 4Ω). In PCB design, parallel resistors are used for current sharing in power circuits and for achieving precise resistance values.
Current Division in Parallel Circuits
In a parallel circuit, the total current divides among the branches inversely proportional to their resistance. The branch with the lowest resistance carries the most current. The current divider rule states: I₁ = Itotal × (R2/(R1+R2)) for two resistors. This is the dual of the voltage divider rule for series circuits. Understanding current division is essential for designing current-sharing circuits, parallel battery configurations, and load balancing in power distribution systems.
Practical Applications
- Power distribution: Parallel resistors share current, reducing power dissipation per component
- Precision values: Combine standard resistors to achieve non-standard resistance values
- Current sensing: Low-value parallel shunt resistors measure high currents with minimal voltage drop
- Speaker systems: Parallel speakers reduce impedance (two 8Ω = 4Ω, four 8Ω = 2Ω)
- LED arrays: Parallel strings with individual current-limiting resistors ensure uniform brightness
- Fault tolerance: If one parallel path opens, others continue to function (at higher total resistance)