Parallel Resistor Calculator | Equivalent Resistance
Calculate the equivalent resistance of up to 10 resistors connected in parallel (1/R = 1/R1+1/R2+...).
How to Use
- Enter resistance values (in Ω) for each parallel resistor.
- Click 'Add Resistor' to add more parallel branches (up to 10).
- Optionally enter a supply voltage to calculate total current and per-branch currents.
- Click 'Calculate' to get the equivalent resistance using 1/R = 1/R1 + 1/R2 + ...
- The equivalent resistance is always less than the smallest individual resistor.
- For two equal resistors in parallel, the result is exactly half of one resistor.
About Parallel Resistors
Parallel Resistance Formula
In a parallel circuit, all resistors share the same voltage but each carries a different current. The equivalent resistance is found using the reciprocal formula: 1/R_eq = 1/R1 + 1/R2 + ... + 1/Rn. For two resistors, this simplifies to R_eq = (R1 × R2) / (R1 + R2), known as the 'product over sum' formula. Parallel resistance is always less than the smallest resistor in the group.
Current Division in Parallel Circuits
Each parallel branch carries current inversely proportional to its resistance: I_n = V / R_n. Branches with lower resistance carry more current. The total current from the source equals the sum of all branch currents (Kirchhoff's Current Law). This current-sharing behavior makes parallel circuits ideal for providing multiple load paths while maintaining the same voltage.
Comparing Series and Parallel
In series circuits, resistances add directly (Rtotal increases), voltage divides, and current is the same everywhere. In parallel circuits, resistances combine reciprocally (Rtotal decreases), voltage is the same across all branches, and current divides. Real circuits often combine both configurations (series-parallel networks) to achieve complex impedance behavior and signal routing.
Practical Parallel Resistor Uses
Parallel resistors are used to: (1) achieve resistance values not available in standard series, (2) increase current-handling capacity by sharing power between multiple resistors, (3) reduce the overall resistance when lower values are needed, and (4) provide redundancy in critical circuits. High-power current shunts often use parallel resistor combinations to handle large currents.
Key Features
- Supports up to 10 resistors in parallel
- Uses reciprocal formula: 1/R = 1/R1 + 1/R2 + ...
- Optional voltage input for current calculation per branch
- Dynamically add or remove parallel branches
Common Applications
- Achieving lower resistance values with available components
- Distributing power across multiple resistors to manage heat
- Current shunt design for high-current measurement
- Load balancing in parallel power supply configurations
- Circuit analysis and educational exercises