Parallel Circuit Calculator

This calculator solves a fixed-resistance, DC-style parallel circuit using Ohm’s Law and the parallel-resistance (conductance) relationship. It is intended for concept verification, training worksheets, and preliminary component arithmetic — for example, checking how current divides across resistive branches or confirming an equivalent resistance value before deeper design work.

The tool assumes purely resistive branches under a single DC (or resistive-equivalent) source voltage. It does not perform AC impedance analysis (reactance, phase angle, or power factor), does not select or size components, and does not produce an installation or code-compliance result. Any application to a real circuit — including conductor sizing, overcurrent protection, or load calculations — must be verified separately against the NEC edition adopted by the local Authority Having Jurisdiction (AHJ).

Formulas

For resistors \(R_1, R_2, \dots, R_n\) connected in parallel across a common source voltage ( V ):

Branch current (Ohm’s Law): \(I_k = \frac{V}{R_k}\)

Total conductance: \(G_{total} = \frac{1}{R_1} + \frac{1}{R_2} + \dots + \frac{1}{R_n}\)

Equivalent resistance: \(R_{eq} = \frac{1}{G_{total}}\)

Total current: \(I_{total} = I_1 + I_2 + \dots + I_n = \frac{V}{R_{eq}}\)

Key properties of a resistive parallel network: voltage is identical across every branch \(\text{V}_1 = \text{V}_2 = \dots = \text{V}_n\), current divides inversely with each branch’s resistance, and the equivalent resistance is always smaller than the smallest individual branch resistance.

Worked Example

Inputs: \(V = 120\text{ V}\), \(R_1 = 30\ \Omega\), \(R_2 = 60\ \Omega\), \(R_3 = 90\ \Omega\)

Step 1 — Branch currents (Ohm’s Law, (I = V/R)):

• \(I_1 = 120 / 30 = 4.0000\text{ A}\)
• \(I_2 = 120 / 60 = 2.0000\text{ A}\)
• \(I_3 = 120 / 90 = 1.3333\text{ A}\)

Step 2 — Total conductance: \(G_{total} = \frac{1}{30} + \frac{1}{60} + \frac{1}{90} = 0.033333 + 0.016667 + 0.011111 = 0.0611\text{ S}\)

Step 3 — Equivalent resistance: \(R_{eq} = \frac{1}{0.0611} = 16.3636\ \Omega\)

Step 4 — Total current \(cross-check via sum of branch currents and via \(V / R_{eq}\)\): \(I_{total} = 4 + 2 + 1.3333 = 7.3333\text{ A} \quad \text{and} \quad I_{total} = \frac{120}{16.3636} = 7.3333\text{ A}\)

Both methods agree, confirming internal consistency of the result set: total conductance 0.0611 S, equivalent resistance 16.3636 Ω, total current 7.3333 A, with branch currents of 4 A, 2 A, and 1.3333 A through R1, R2, and R3 respectively.

NEC Context: Parallel Circuits vs. Parallel Conductors

The “parallel circuit” concept in this calculator (multiple resistive branches sharing one source voltage) is a general electrical theory model, not the same thing as “conductors installed in parallel” under the NEC — a distinct code term for running two or more conductors of the same length, material, size, insulation, and termination in parallel to carry a single circuit’s current, typically for large ampacity loads (e.g., service feeders).

Under NEC 2023 §310.10(H) — Conductors in Parallel, parallel conductor sets must generally be 1/0 AWG or larger, matched in length and characteristics, and terminated to divide current equally. Overcurrent protection, ampacity (Article 310/Table 310.16), and conduit fill (Chapter 9, Table 1) calculations for such installations are governed separately and are outside the scope of this calculator’s resistive math.

The NEC 2026 edition, released by NFPA on August 20, 2025 and effective September 9, 2025, has been adopted so far only by a limited number of jurisdictions (e.g., Massachusetts, Texas), while most states as of mid-2026 continue to enforce NEC 2023. Any code references — including §310.10(H) — should be confirmed against the specific NEC edition your local AHJ has adopted before being applied to a real installation.