Parallel Resistor Calculator
Find the total resistance of resistors wired in parallel, plus the current through each branch. A live 3D circuit and charts show why total resistance always drops below the smallest resistor.
Reviewed by the ToolNestr Editorial Team — July 2026
Enter 2 to 4 resistor values (Ω). Leave unused rows blank. Supply voltage is optional.
Two ideas that trip students up
1. Parallel branches share two rails
Each resistor connects the same top and bottom rail, so every branch sees the same voltage. Adding a branch just adds another path — it never removes one.
2. R_total always beats the smallest resistor
The short indigo bar is R_total for three parallel resistors; the taller grey bars are the individual resistors. R_total is always shorter than every one of them.
Parallel resistance graphs
How it works
The core idea in one line: in a parallel circuit every resistor shares the same voltage, so adding branches only adds more paths for current — total resistance always falls below the smallest individual resistor.
1/Rtotal = 1/R₁ + 1/R₂ + 1/R₃ + …
reciprocals add for any number of parallel resistors
Rtotal = (R₁ × R₂) / (R₁ + R₂)
shortcut for exactly two resistors
Ii = V / Ri
current through branch i, same V across every branch
Rearranged, the reciprocal sum handles any number of branches: compute 1/R for each resistor, add them, then invert the sum to get R_total. For exactly two resistors, the algebra simplifies to the handy product-over-sum shortcut Rtotal = (R₁R₂)/(R₁+R₂). Once R_total is known, the current drawn from the supply is I = V/R_total, and it splits between branches in inverse proportion to their resistance.
Worked example 1 — two resistors (product-over-sum)
Given: A 100 Ω resistor and a 300 Ω resistor are connected in parallel. Find the total resistance.
75 Ω is less than both 100 Ω and 300 Ω — the hallmark of a parallel combination.
Worked example 2 — three resistors with branch currents
Given: Resistors of 100 Ω, 200 Ω and 300 Ω are connected in parallel across a 12 V supply. Find R_total, each branch current, and the total current.
Check: I = V/R_total = 12 / 54.5 ≈ 0.22 A — matches the sum of branch currents.
Series vs parallel resistor rules
The two combination types behave as opposites for resistance, voltage, and current.
| Quantity | Series | Parallel |
|---|---|---|
| Total resistance | Rtotal = R₁ + R₂ + … | 1/Rtotal = 1/R₁ + 1/R₂ + … |
| Compared to individual R | Always greater than the largest R | Always less than the smallest R |
| Voltage | Divides across resistors | Same across every resistor |
| Current | Same through every resistor | Divides across branches |
Adding a resistor in series always increases R_total; adding one in parallel always decreases it.
Where parallel resistance actually matters
🏠 Household electrical wiring
Wall outlets and light fixtures on a circuit are wired in parallel so each device sees the same full supply voltage (e.g. 120 V or 230 V) and can be switched independently without affecting the others.
🔋 Parallel battery banks
Connecting batteries in parallel keeps the voltage the same as a single cell while combining their current capacity — the pack behaves like one larger battery with lower internal resistance.
🧩 Multi-path circuit design
Engineers use parallel branches to give current redundant paths, distribute load across components, and fine-tune an equivalent resistance that no single off-the-shelf resistor provides.
Common misconceptions
"Adding more resistors in parallel increases total resistance."
It always decreases (or at worst leaves unchanged in the limiting case) R_total. Each extra branch gives current another path, so the combination always conducts current more easily than any single branch alone.
"Voltage is different across each parallel branch."
Voltage is identical across every resistor in a parallel group — they all connect between the same two nodes. It is current, not voltage, that differs between branches.
"You can just average the resistances."
Averaging only works for identical resistors (R_total = R/n). For different values you must add reciprocals: 1/R_total = 1/R1 + 1/R2 + …, then invert.
"Parallel and series total resistance are calculated the same way."
They are opposites: series resistances add directly, while parallel resistances add as reciprocals, which is why parallel combinations always end up smaller than any individual resistor.
Formula sources & further reading
The formulas here are standard, traceable to:
- • OpenStax, University Physics Volume 2 — Chapter 10, Direct-Current Circuits, resistors in parallel (free, peer-reviewed). openstax.org
- • Halliday, Resnick & Walker, Fundamentals of Physics — Chapter 27, Circuits, resistors in parallel.
- • Serway & Jewett, Physics for Scientists and Engineers — Direct Current Circuits chapter.
1/R_total = sum of reciprocals for parallel resistors; branch current I = V/R with a shared supply voltage. Results are rounded for display.
How to use this calculator
Enter your resistors
Fill in 2 to 4 resistor values in ohms; leave any unused rows blank.
Add a supply voltage (optional)
Enter volts to also see current per branch and total current drawn.
Explore the 3D circuit
Drag the sliders to see R_total drop as resistors change, live in 3D.
Related tools
Frequently asked questions
What happens to voltage across resistors in parallel?
Voltage is the same across every resistor in a parallel combination — each branch connects to the same two nodes, so each sees the full supply voltage. This is the defining feature of a parallel connection.
What happens to current in a parallel circuit?
Current splits between the branches. Each branch carries I = V/R for its own resistance, so branches with lower resistance carry more current. The branch currents add up to the total current drawn from the supply.
Why is total resistance always less than the smallest resistor?
Adding a parallel branch gives current an extra path, so the combination always conducts at least as well as the best single branch. Mathematically, 1/R_total = 1/R1 + 1/R2 + ... is always bigger than 1/R_smallest alone, so R_total is always smaller than the smallest R.
How is parallel different from series?
In series, resistances add directly (R_total = R1+R2+...) and current is the same through every resistor while voltage divides. In parallel, reciprocals add and voltage is the same across every resistor while current divides.
Can I mix series and parallel resistors?
Yes — real circuits often combine both. Solve parallel sub-groups down to a single equivalent resistance first, then add that equivalent in series with the rest of the circuit (or vice versa), working from the innermost combination outward.