Parallel Circuit Calculator

Parallel Circuit Calculator
1/RT = 1/R₁ + 1/R₂ + …
IT = V / RT
In = V / Rn
Parallel Circuit — Enter Source & Resistors
V Source Voltage
I Or Total Current (optional)
Enter voltage and resistors
Parallel Circuit Results
RTotal
—
Ω
Total Current IT
—
A
Total Power
—
W
Parallel Circuit: Same Voltage, Current Splits Vs R₁ R₂ Rn I₁ I₂ In 1/RT = 1/R₁ + 1/R₂ + …  |  IT = I₁ + I₂ + …

Figure 1: In a parallel circuit, all branches share the same voltage. Current divides between branches inversely proportional to resistance — smaller resistors carry more current.

Table of Contents
Fundamentals
  1. What Is a Parallel Circuit?
  2. Parallel Circuit Rules
Worked Examples
  1. Two Equal Resistors
  2. Three Mixed Branches
  3. Finding the Missing Branch
Deep Dive
  1. Kirchhoff’s Current Law
  2. Power in Parallel Circuits
  3. Shortcuts for Two Resistors
Reference
  1. Frequently Asked Questions
  2. Related Circuit Analysis Calculators

What Is a Parallel Circuit?

A parallel circuit connects components between two common nodes so every branch experiences the same voltage. Current from the source splits at the first node, flows through each branch independently, and recombines at the second node. If one branch fails open, the others continue to operate normally — this is a major advantage over series circuits.

Household wiring is the most familiar example: every outlet and appliance is connected in parallel across the mains supply. Each device sees the full 230 V regardless of how many others are connected. The Current Divider Calculator provides a specialised tool for finding how current splits between branches.

Parallel Circuit Rules

Voltage: The same voltage V appears across every branch.
Current: IT = I₁ + I₂ + … + In (branch currents add).
Resistance: 1/RT = 1/R₁ + 1/R₂ + … + 1/Rn.
RT is always less than the smallest branch resistance.

Worked Example — Two Equal Resistors

Given: V = 12 V, R₁ = R₂ = 1 kΩ

RT = (1000 × 1000) / (1000 + 1000) = 500 Ω

IT = 12 / 500 = 24 mA

Each branch carries 12 mA — exactly half the total.

For n equal resistors in parallel, RT = R/n. Two 1 kΩ resistors give 500 Ω, three give 333 Ω, and so on.

Worked Example — Three Mixed Branches

Given: V = 5 V, R₁ = 100 Ω, R₂ = 220 Ω, R₃ = 470 Ω

1/RT = 1/100 + 1/220 + 1/470 = 0.01 + 0.00455 + 0.00213 = 0.01668

RT = 1/0.01668 = 59.96 Ω

I₁ = 5/100 = 50 mA (59.9%), I₂ = 5/220 = 22.7 mA (27.2%), I₃ = 5/470 = 10.6 mA (12.7%)

IT = 50 + 22.7 + 10.6 = 83.4 mA

The 100 Ω resistor carries the most current because it has the lowest resistance. The total resistance (59.96 Ω) is less than the smallest branch (100 Ω). The Circuit Current Calculator can verify any of these current values independently.

Worked Example — Finding the Missing Branch

Given: RT = 500 Ω, R₁ = 1 kΩ. Find R₂.

1/R₂ = 1/RT − 1/R₁ = 1/500 − 1/1000 = 0.001

R₂ = 1000 Ω

Kirchhoff’s Current Law

Kirchhoff’s Current Law (KCL) states that the total current entering a node equals the total current leaving it. In a parallel circuit, this means IT = I₁ + I₂ + … + In. This law is the foundation of nodal analysis and is applied in the KCL Circuit Calculator for more complex multi-node circuits.

Power in Parallel Circuits

Each branch dissipates Pn = V²/Rn. Since the voltage is the same across all branches, the branch with the lowest resistance dissipates the most power. Total power PT = V × IT = V²/RT. The Power Dissipation Calculator helps check that each component stays within its power rating.

Shortcuts for Two Resistors

For exactly two resistors in parallel, the product-over-sum formula is faster: RT = (R₁ × R₂) / (R₁ + R₂). If the two are equal, RT = R/2. These shortcuts are widely used in circuit design for quick mental calculations.

Frequently Asked Questions

Can parallel resistance be higher than the individual values?
No. The total parallel resistance is always less than the smallest individual resistor. Adding more parallel paths always reduces total resistance because you are providing more paths for current.
What if one branch is a short circuit (0 Ω)?
A 0 Ω branch means RT = 0 regardless of other resistors. All current flows through the short circuit. This is why fuses or circuit breakers protect parallel circuits from shorts.
Why is household wiring in parallel?
Parallel wiring ensures every appliance gets the same voltage (230V) and can operate independently. Turning off one light doesn’t affect others. Adding or removing loads changes total current but not the supply voltage.
How many branches can I have?
In theory, unlimited. In practice, the supply source must provide enough current for all branches combined. This calculator handles up to 6 branches. For more complex networks, use the Thevenin or Norton equivalent approach.
How does this relate to the Wheatstone Bridge?
A Wheatstone Bridge is a combination of series and parallel elements. The Wheatstone Bridge Calculator analyses this specific configuration to determine bridge balance and unknown resistance.
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Last updated: March 2026