Parallel Resistance Calculator
Equivalent resistance of resistors connected side by side: 1/RT = 1/R₁ + 1/R₂ + … + 1/Rₙ.
Inputs
Drag the handle (or focus it and press ↑/↓) to reorder. Leave unused resistors blank; blank ones are ignored. Scientific notation such as 4.7e3 is accepted. Pick any unit; conversion is automatic.
Results
Enter values and press Calculate. Your answer will appear here.
Total resistance as branches are added
Each teal bar is the total resistance after that branch is connected. The amber dot is the resistance of the branch just added. The bar is always lower than every dot, because adding a parallel path can only lower the total.
What is being calculated
Reference values
| Equal resistors in parallel | Each | Total RT |
|---|
With equal resistors the total is the value divided by the count.
Common pairs, R₁ ∥ R₂
| R₁ | R₂ | RT = R₁·R₂ / (R₁ + R₂) |
|---|
Series vs. parallel
| Property | Series | Parallel |
|---|---|---|
| Total resistance | RT = R₁ + R₂ + … | 1/RT = 1/R₁ + 1/R₂ + … |
| Current | Same through every resistor | Splits between branches |
| Voltage | Splits between resistors | Same across every branch |
| Total compared with the parts | Larger than the largest | Smaller than the smallest |
E12 preferred values (one decade, ±10%)
| Series | Values (multiply by 1, 10, 100 … for other decades) |
|---|---|
| E12 | 10 · 12 · 15 · 18 · 22 · 27 · 33 · 39 · 47 · 56 · 68 · 82 |
Unit conversions
| Quantity | Conversion |
|---|---|
| Resistance | 1 kΩ = 1,000 Ω · 1 MΩ = 10⁶ Ω · 1 GΩ = 10⁹ Ω · 1 Ω = 1,000 mΩ |
| Conductance | G = 1/R · 1 S (siemens) = 1 Ω⁻¹ · 1 mS = 1,000 µS |
| Current | 1 A = 1,000 mA = 10⁶ µA |
| Power | 1 W = 1,000 mW · P = V²/R = V·I |
Formula
- RT: equivalent (total) resistance (Ω)
- R₁ … Rₙ: the branch resistors (Ω)
- G = 1/RT = 1/R₁ + 1/R₂ + …: conductances simply add (S)
- Iₖ = V / Rₖ: current in branch k, and I = V / RT is the sum of all Iₖ
Example: 100 Ω and 220 Ω in parallel give RT = 100 × 220 ÷ (100 + 220) = 68.75 Ω. On a 12 V supply the total current is 12 ÷ 68.75 ≈ 174.5 mA.
Rearranged: a missing branch is Rₓ = 1 / (1/RT − 1/R₁ − 1/R₂ − …), which only exists when RT is smaller than the parallel total of the resistors you already have. Power in each branch is P = V²/R and the total is P = V²/RT. With equal tolerance t on every resistor, RT lies between RT·(1 − t) and RT·(1 + t). RT is always smaller than the smallest branch, and a 0 Ω branch (a short) makes RT = 0. The rule assumes ideal resistors and negligible wire resistance.
References
- Wikipedia, Series and parallel circuits: resistors in parallel and the two-resistor shortcut
- OpenStax University Physics Vol. 2, Resistors in Series and Parallel: derivation and worked examples
- HyperPhysics, Parallel resistors: equivalent resistance and branch currents
- Wikipedia, Current divider: how current splits between branches
How to Use This Tool
- Pick a preset, or enter R₁ and R₂ with their units. Add R₃ and R₄ if you need them.
- Leave unused resistor boxes blank.
- In Advanced, add up to six branches, a supply voltage, a tolerance, or solve for a missing branch from a known total.
- Click Calculate.
- Read RT in the highlighted result, then check the branch table and the chart.
What This Tool Offers
- Basic and Advanced modes on one calculation engine
- Resistance entered in mΩ, Ω, kΩ, MΩ or GΩ with automatic conversion
- Total resistance, conductance, and the series total of the same resistors
- Branch currents, power, current shares, tolerance range, and a missing-branch solver (Advanced)
- Running-total chart and a labelled parallel-circuit diagram
- Reorderable inputs, presets and a mobile-friendly layout
Variables
| Symbol | Quantity | Unit |
|---|---|---|
| R | Resistance | Ohms |
What it means
When resistors are connected in parallel, the reciprocal of the total resistance equals the sum of the reciprocals of the individual resistances. The formula is 1/R_T = 1/R1 + 1/R2 + ... + 1/Rn. The total resistance is always less than the smallest individual resistance because parallel branches provide additional paths for current. This is a direct consequence of KCL: the total current is the sum of branch currents, and each branch voltage is the same. Parallel resistors are used to increase the current capacity of a circuit, to create current dividers, and to provide redundancy. In practical applications, parallel resistors help achieve non‑standard resistance values by combining standard ones. The equivalent resistance of two parallel resistors can be found using the product‑over‑sum formula: R_T = (R1*R2)/(R1+R2). Parallel resistance also appears in transmission lines and loudspeaker systems. Understanding parallel resistance is crucial for power distribution, circuit design, and fault analysis. Example: Two resistors of 4Ω and 6Ω in parallel give 1/R_T = 1/4 + 1/6 = 5/12, so R_T = 2.4Ω, which is less than both 4Ω and 6Ω.
Worked example
Parallel Resistance – Practical Example
Real‑World| Parameter | Value |
|---|---|
| R₁ (speaker 1) | 8 Ω |
| R₂ (speaker 2) | 8 Ω |
| Formula | 1/RT = 1/R₁ + 1/R₂ |
Common mistakes
- Reciprocals: Do not add resistances directly – use 1/R_T = 1/R₁ + 1/R₂.
- Result: The total parallel resistance is always < the smallest individual resistor.
- Two‑resistor shortcut: R_T = (R₁·R₂)/(R₁+R₂) works only for two resistors.
- Conductances: Use G = 1/R and add conductances for parallel.
- Power: Total power is the sum; current divides inversely with resistance.
Applications
Parallel resistance is the reciprocal sum of the reciprocals of individual branch resistances, resulting in a total that is always smaller than the smallest individual resistor. This formula is essential for designing parallel circuits where loads share the same voltage but draw different currents. Engineers use it to combine resistors in power supplies, to design current‑sharing networks, and to calculate the equivalent resistance of complex networks. In home wiring, parallel connections allow multiple appliances to operate independently at the same voltage. By computing equivalent parallel resistance, professionals can determine the total current drawn from a source and ensure that protection devices are adequately rated. Understanding parallel resistance is fundamental for practical circuit design and analysis.
- Load sharing in parallel‑connected devices
- Current divider design for measurement circuits
- Equivalent resistance calculation for complex networks
- Home and industrial wiring – parallel circuits
- Power supply output impedance calculation
Related calculators · Circuit Analysis
Recently updated formulas
Suggest an improvement
Found a mistake? Have a better example? Let us know.
You may send up to 3 suggestions per 24 hours.