Resistors in Parallel Calculator

Calculate total resistance for parallel resistors using 1/R = 1/R₁ + 1/R₂ + ... plus branch currents and total power.

⚡ Circuits📐 1/R = Σ(1/Rᵢ)🔌 Parallel

Enter up to 5 resistor values and supply voltage.

R₁ (Ω)
R₂ (Ω)
R₃ (Ω)
R₄ (Ω)
R₅ (Ω)
Supply voltage (V)
⚠️ Enter at least one resistance value.

What Is Resistors in Parallel?

In a parallel circuit, all components share the same voltage. The equivalent resistance is found using the reciprocal formula: 1/R_total = 1/R₁ + 1/R₂ + 1/R₃ + .... Adding resistors in parallel always decreases total resistance — the more parallel paths, the easier current can flow.

Each branch of a parallel network draws its own current independently: Iᵢ = V / Rᵢ. The total current drawn from the supply equals the sum of all branch currents (Kirchhoff's Current Law): I_total = I₁ + I₂ + ... This is also found from I_total = V / R_total.

Special case: two identical resistors in parallel give R_total = R/2. Two different resistors: R_total = R₁R₂/(R₁+R₂) — the 'product over sum' formula that avoids the reciprocal step. More than two: use the full reciprocal formula or calculate iteratively.

Parallel resistors are ubiquitous: household outlets wire appliances in parallel (each gets full mains voltage). Car battery terminals can be replaced with paralleled batteries (doubling current capacity). In electronics, biasing resistors, current mirrors, and filter networks all use parallel combinations.

Formula Reference Table

Solve ForFormulaNotes
Total resistance1/R_total = 1/R₁ + 1/R₂ + ...R_total always < smallest Rᵢ
Two resistorsR_total = R₁·R₂/(R₁+R₂)Product over sum shortcut
Branch currentIᵢ = V / RᵢEach branch has same V, different I
Total current (KCL)I_total = I₁ + I₂ + ...KCL: currents sum at node
Total current (Ohm)I_total = V / R_totalEquivalent to KCL result
Power (each branch)Pᵢ = V² / RᵢLower R → more power dissipated

3 Worked Examples

Example 1
Two Parallel Resistors

100 Ω and 150 Ω in parallel at 12 V.

  • R_total = (100×150)/(100+150) = 15,000/250 = 60 Ω
  • I_total = 12/60 = 0.2 A = 200 mA
  • I₁ = 12/100 = 120 mA; I₂ = 12/150 = 80 mA
  • Check: 120 + 80 = 200 mA ✓
✓ R_total = 60 Ω; I_total = 200 mA
Example 2
Three Parallel Resistors

100 Ω, 200 Ω, 500 Ω in parallel.

  • 1/R = 1/100 + 1/200 + 1/500 = 0.01 + 0.005 + 0.002 = 0.017
  • R_total = 1/0.017 = 58.8 Ω
  • Note: less than the smallest (100 Ω) ✓
✓ R_total = 58.8 Ω
Example 3
Household Appliances — Total Current

TV (200 Ω load), lamp (500 Ω), phone charger (120 Ω) on 240 V.

  • 1/R = 1/200 + 1/500 + 1/120 = 0.005 + 0.002 + 0.00833 = 0.01533
  • R_total = 65.2 Ω; I_total = 240/65.2 = 3.68 A
  • P_total = 240 × 3.68 = 883 W
✓ R_total = 65.2 Ω; I_total = 3.68 A; P = 883 W

Real-World Applications

🏠
Household Wiring
All household appliances wire in parallel — each device gets the full 120/240 V. Adding more devices doesn't reduce their voltage, but increases total current drawn from the supply (and service panel capacity).
🔋
Battery Paralleling
Connecting batteries in parallel: same voltage, summed current capacity. Two 100 Ah batteries in parallel = one 200 Ah battery at the same voltage. This doubles runtime for high-current loads.
🖥️
PCB Decoupling
Multiple bypass capacitors are placed in parallel near IC power pins to provide different frequency responses. Similarly, parallel resistors fine-tune impedance values when exact resistance values aren't available.
⚡
Fuse Protection
Each parallel branch in household wiring has its own fuse or breaker. A fault in one branch only trips that branch's protection, not affecting other parallel branches — the safety benefit of parallel distribution.
🎵
Speaker Wiring
Multiple speakers are wired in parallel to share the amplifier's load. 4 Ω wired in parallel with another 4 Ω gives 2 Ω total impedance — amplifiers must handle the lower impedance without overheating.

Common Mistakes to Avoid

⚠️
Adding parallel resistance to get more

Adding resistors in parallel ALWAYS decreases total resistance. If R_total > any individual R, recheck your calculation.

⚠️
Misremembering which formula is which

Series: add directly. Parallel: add RECIPROCALS (then invert). A memory aid: parallel resistors share the voltage, series resistors share the current.

⚠️
Forgetting to invert at the end

1/R_total = sum of reciprocals → R_total = 1/(sum of reciprocals). Stopping at the sum gives 1/R_total, not R_total.

⚠️
Branch currents differ

Each branch carries different current (I = V/R). Higher-resistance branches carry LESS current. Unlike series circuits where I is the same everywhere.

⚠️
Voltage is the same across all parallel branches

All parallel branches share the same terminal voltage V. This is the defining characteristic of a parallel connection.

Frequently Asked Questions

Why is total R less than any individual R? ▾
Each additional parallel path provides another route for current to flow, reducing the total opposition. 1/R_total = Σ(1/Rᵢ): adding more positive terms to the right side makes the total larger, so R_total (= 1/larger number) gets smaller.
What is Kirchhoff's Current Law (KCL)? ▾
KCL states that the sum of currents entering a node equals the sum leaving: ΣI_in = ΣI_out. For a parallel junction, I_source = I₁ + I₂ + ... This is derived from charge conservation — charge cannot accumulate at a node.
What is the 'product over sum' formula? ▾
For exactly two resistors: R_total = R₁×R₂/(R₁+R₂). This is derived from 1/R = 1/R₁ + 1/R₂ = (R₁+R₂)/(R₁R₂), inverted. It only works for exactly two resistors. For three or more, use the reciprocal formula directly.
How do I combine series and parallel networks? ▾
Solve step by step: identify series groups (same current path) and parallel groups (same terminal voltage). Simplify each group using the appropriate formula. Repeat until the network reduces to a single equivalent R. This iterative reduction handles any resistor network.
Why are household circuits parallel? ▾
Parallel wiring ensures each appliance receives the full supply voltage regardless of other loads. If appliances were wired in series, they'd share the voltage (most would get too little), current would be the same through all (sized to the smallest), and turning off one would break the circuit for all.
What is a Norton equivalent circuit? ▾
Norton's theorem says any linear network can be replaced by a current source I_N in parallel with a resistance R_N. R_N is found by zeroing all sources and calculating the equivalent resistance. This is the parallel dual of Thévenin's theorem (voltage source in series with R_Th).
How do skin effect and frequency affect parallel resistance? ▾
At high frequencies, AC current flows near the conductor surface (skin effect), effectively increasing resistance. Parallel conductor bundles increase the effective surface area, reducing high-frequency resistance. This is why power lines use stranded or bundled conductors.
When would you deliberately use parallel resistors in a design? ▾
To achieve non-standard resistance values (series/parallel combination). To increase power rating (each R handles part of the power). To improve reliability (failure of one still leaves others conducting). To tune filter networks. To match impedances in antenna systems.

Related Physics Calculators

🔌 Series Resistors ⚡ Ohm's Law 🔋 Voltage Divider 💡 Electrical Power 📻 RC Time Constant

Formula Explorer connections

Interpretation: This formula links charge, voltage, current, resistance, capacitance, power or circuit time response. Assumption: Confirm DC versus AC conditions, RMS versus peak values, component topology and steady-state versus transient behavior. Ideal components may be assumed.

Resistors in Series Calculator →RL Time Constant Calculator →Thévenin & Norton Equivalent Calculator →Physics Formula Explorer →