Parallel Resistors Calculator
Calculate the equivalent resistance of up to 4 resistors connected in parallel.
Also calculates current through each resistor if voltage is known.
When resistors are connected in parallel, the equivalent resistance is:
1/R_total = 1/R₁ + 1/R₂ + 1/R₃ + 1/R₄
Or equivalently: R_total = 1 / (1/R₁ + 1/R₂ + 1/R₃ + 1/R₄)
Key properties of parallel connections:
- The equivalent resistance is always less than the smallest individual resistor
- All resistors share the same voltage across their terminals
- Total current = sum of currents through each resistor
- Adding more resistors in parallel always decreases the equivalent resistance
Special cases:
- Two equal resistors in parallel: R_total = R/2
- n equal resistors in parallel: R_total = R/n
- Two resistors: R_total = (R₁ × R₂)/(R₁ + R₂) — the “product over sum” formula
Why parallel connections matter:
Household electrical wiring uses parallel connections. Every appliance you plug in is connected in parallel with the others. This way, each appliance gets the full supply voltage (120V or 230V), and one appliance failing does not cut power to the others.
Current distribution: Each branch current is inversely proportional to its resistance: I_n = V / R_n
where V is the common voltage across all parallel branches.