Parallel Resistor Calculator
Calculate equivalent resistance for resistors in parallel or series. Find missing resistor values and calculate current distribution. Supports 2-10 resistors with automatic unit conversion.
Two 1kΩ resistors in parallel = 500Ω
Formula: 1/Req = 1/R1 + 1/R2 + ... | Parallel resistance is always less than the smallest resistor
⚡ Resistors in Parallel
Parallel Circuit
├── R₂ ──┤
└── Rₙ ──┘
📊 Equivalent Resistance
Equivalent Resistance (Req)
Formula Used:
1/Req = 1/R1 + 1/R2
📋 Input Values
📊 Series vs Parallel Comparison
| Property | Series Circuit | Parallel Circuit |
|---|---|---|
| Total Resistance | RT = R₁ + R₂ + R₃... | 1/RT = 1/R₁ + 1/R₂ + 1/R₃... |
| Result | Increases total resistance | Decreases total resistance |
| Current | Same through all resistors | Divides among resistors |
| Voltage | Divides among resistors | Same across all resistors |
| Example: 100Ω + 100Ω | 200Ω | 50Ω |
⚡ Understanding Parallel Resistors
When resistors are connected in parallel, they share the same two nodes, meaning the voltage across each resistor is identical. However, the current divides among the parallel paths. This configuration is fundamental in electronics for power distribution, voltage regulation, and creating specific resistance values.
Why Parallel Resistance Decreases
Adding resistors in parallel creates additional paths for current flow. Think of it like adding lanes to a highway — more lanes allow more traffic (current) to flow with less congestion (resistance). Even adding a very high resistance in parallel will slightly decrease the total resistance because it still provides an additional current path.
The Parallel Resistance Formula
The formula for calculating equivalent resistance of parallel resistors is:
For just two resistors, a simplified "product over sum" formula can be used:
Practical Applications
- Creating non-standard values: Combine standard resistors to achieve a specific resistance value not available commercially.
- Power distribution: Spread power dissipation across multiple resistors to prevent overheating.
- Current limiting: In LED circuits, parallel resistors can handle higher currents than a single resistor.
- Redundancy: If one resistor fails open in a parallel circuit, the others continue to function.
⚡ Quick Examples
1kΩ ∥ 1kΩ = 500Ω
100Ω ∥ 100Ω = 50Ω
1kΩ ∥ 2kΩ = 667Ω
10kΩ ∥ 10kΩ ∥ 10kΩ = 3.33kΩ
∥ symbol means "in parallel with"
📋 E24 Standard Values
1.0, 1.1, 1.2, 1.3, 1.5, 1.6, 1.8, 2.0, 2.2, 2.4, 2.7, 3.0, 3.3, 3.6, 3.9, 4.3, 4.7, 5.1, 5.6, 6.2, 6.8, 7.5, 8.2, 9.1
Multiply by 10, 100, 1k, 10k, etc.
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Frequently Asked Questions
For resistors in parallel, the formula is: 1/Req = 1/R1 + 1/R2 + 1/R3 + ... + 1/Rn. To find the equivalent resistance, calculate the sum of the reciprocals of all resistor values, then take the reciprocal of that sum. For two resistors, you can use the simplified formula: Req = (R1 × R2) / (R1 + R2). The equivalent resistance of parallel resistors is always less than the smallest individual resistor.
For 3 resistors in parallel, use: 1/Req = 1/R1 + 1/R2 + 1/R3. For example, with R1=100Ω, R2=200Ω, R3=300Ω: 1/Req = 1/100 + 1/200 + 1/300 = 0.01 + 0.005 + 0.00333 = 0.01833. Therefore, Req = 1/0.01833 = 54.55Ω. Notice how the equivalent resistance (54.55Ω) is less than the smallest resistor (100Ω).
Parallel resistance is always lower because adding resistors in parallel creates additional paths for current to flow. Think of it like adding more lanes to a highway — more lanes mean less traffic resistance. Each parallel resistor provides an additional path, allowing more total current to flow for the same voltage. Even adding a very high resistance in parallel will slightly reduce the total resistance because it still provides one more path for current.
To find a missing resistor value in a parallel circuit when you know the target equivalent resistance: Rearrange the parallel formula to solve for the unknown. For two resistors: Rx = (Req × R1) / (R1 - Req). For example, if you need Req = 500Ω and have R1 = 1kΩ, then Rx = (500 × 1000) / (1000 - 500) = 500000/500 = 1000Ω. Use our 'Find Missing Resistor' tab for automatic calculation.
In a parallel circuit, voltage is the same across all resistors, but current divides inversely proportional to resistance. Using Ohm's Law (I = V/R), lower resistance carries more current. For example, with 12V across 100Ω and 200Ω in parallel: I1 = 12/100 = 0.12A (120mA), I2 = 12/200 = 0.06A (60mA). Total current = 0.18A. The 100Ω resistor carries twice the current because it has half the resistance.
In SERIES: Resistors are connected end-to-end, current is the same through all, voltage divides, total resistance ADDS (Rtotal = R1 + R2 + R3). In PARALLEL: Resistors share the same two nodes, voltage is the same across all, current divides, total resistance is LESS than the smallest resistor (1/Rtotal = 1/R1 + 1/R2 + 1/R3). Series increases resistance; parallel decreases it.
E24 is a standard series of preferred resistor values with 24 values per decade (±5% tolerance). The E24 values are: 1.0, 1.1, 1.2, 1.3, 1.5, 1.6, 1.8, 2.0, 2.2, 2.4, 2.7, 3.0, 3.3, 3.6, 3.9, 4.3, 4.7, 5.1, 5.6, 6.2, 6.8, 7.5, 8.2, 9.1. These values repeat in each decade (×10, ×100, ×1k, etc.). When designing circuits, use these standard values for easier component sourcing.
⚡ Disclaimer: This calculator is for educational and reference purposes only. Always verify calculations for critical applications. Results assume ideal resistors without tolerance variations. For precision circuits, account for resistor tolerance (±1%, ±5%, etc.).