Parallel Resistor Calculator

What does this quantity describe?

In a parallel connection, the reciprocals of the branch resistances add to give the reciprocal of the equivalent resistance: 1/R_total = 1/R₁ + 1/R₂ + 1/R₃. Every branch sees the same voltage, while total current splits across the branches.

Outlets, lights and appliances in a home are wired in parallel: each device sits directly across the full mains voltage and works independently of the others. Switching off or unplugging one device leaves all the rest unaffected — in a series connection, the entire circuit would instead be broken.

Formula and variables

1/Rtotal = 1/R1 + 1/R2 + 1/R3

• 1/Rtotal = 1/R1 + 1/R2 + 1/R3
• Rtotal = (R1·R2)/(R1+R2) for two resistors

Choose the inputs correctly

Enter the known branch resistances; a value of 0 Ω means that branch is not connected. The calculator computes the equivalent resistance or solves for a missing branch resistor.

How to use the calculator

Enter the known branch resistors and read off the equivalent resistance, or enter the equivalent resistance and known branch resistors to find the missing one.

Worked example

Given R₁ = 10 Ω and R₂ = 5 Ω (R₃ not connected), substitution gives 1/R_total = 1/10 + 1/5 = 0.3, so R_total = 1/0.3 ≈ 3.33 Ω.

Understand the result and units

An equivalent resistance of 3.33 Ω is lower than either individual resistor (10 Ω and 5 Ω). This is a general feature of parallel connections: every added branch opens another current path, lowering total resistance.

Resistance is given in ohms (Ω), larger values in kΩ or MΩ. The reciprocal formula 1/R_total = 1/R₁+1/R₂+1/R₃ requires consistent units across all resistors.

Why is the equivalent resistance always lower than the smallest branch resistor?

Every added parallel branch gives current another, independent path. Since the branches' conductances (reciprocal resistances) add, total conductance rises with each additional branch — and equivalent resistance, the reciprocal of total conductance, falls accordingly. It can therefore never exceed the smallest individual branch resistance, since that branch alone already passes at least as much current as the whole parallel combination.

Typical applications

Parallel connections are used in household and building wiring, for parallel battery cells to increase capacity, in current-sensing shunts, and to share load across several identical components.

Assumptions, limits and common mistakes

The formula applies to ideal, linear resistors with no contact or lead resistance between branches. Real parallel connections with long leads to individual branches can deviate slightly from the ideal result due to additional lead resistance.

Common mistake: Do not confuse parallel with series connection: in parallel, reciprocals add, not the resistances themselves. A common calculation error is leaving the reciprocal intermediate result 1/R_total as the final answer instead of inverting it again at the end.