{
    "name": "Resistors in Series and Parallel Calculator",
    "url": "https://calculators.geekmidst.com/calculators/resistor-series-parallel-calculator",
    "markdown": "https://calculators.geekmidst.com/calculators/resistor-series-parallel-calculator.md",
    "category": "Science & engineering",
    "description": "Enter any list of resistor values to get the equivalent resistance in series and in parallel, using R = R₁ + R₂ + … and 1/R = 1/R₁ + 1/R₂ + ….",
    "summary": "Resistances in series add; in parallel their reciprocals add, so the result is always smaller than the smallest resistor. Paste a list of values to see both.",
    "also_called": [
        "Parallel resistance calculator",
        "Equivalent resistance calculator"
    ],
    "applies_to": "Worldwide",
    "last_updated": "2026-10-29",
    "computation": "Results are computed in the visitor’s browser on the HTML page. This API describes the calculator; it does not compute results.",
    "inputs": [
        {
            "name": "mode",
            "label": "Connection",
            "type": "segmented",
            "default": "parallel",
            "options": {
                "series": "Series",
                "parallel": "Parallel"
            }
        },
        {
            "name": "resistors",
            "label": "Resistor values",
            "type": "textarea",
            "default": "100, 220, 470"
        }
    ],
    "outputs": [
        {
            "key": "total",
            "label": "Equivalent resistance",
            "format": "number"
        },
        {
            "key": "series",
            "label": "If connected in series",
            "format": "number"
        },
        {
            "key": "parallel",
            "label": "If connected in parallel",
            "format": "number"
        },
        {
            "key": "count",
            "label": "Number of resistors",
            "format": "integer"
        }
    ],
    "formula": {
        "text": "Series: R = R₁ + R₂ + … + Rₙ;  Parallel: 1/R = 1/R₁ + 1/R₂ + … + 1/Rₙ",
        "variables": {
            "R₁ … Rₙ": "individual resistances in ohms"
        }
    },
    "worked_example": {
        "inputs": {
            "mode": "parallel",
            "resistors": "100, 220, 470"
        },
        "steps": [
            "Series: 100 + 220 + 470 = 790 Ω.",
            "Parallel: 1/100 + 1/220 + 1/470 = 0.0100 + 0.004545 + 0.002128 = 0.016673 S.",
            "R = 1 ÷ 0.016673 = 59.98 Ω."
        ],
        "result": "100 Ω, 220 Ω and 470 Ω give 59.98 Ω in parallel and 790 Ω in series."
    },
    "interpretation": "For mixed networks, reduce the circuit step by step: combine each parallel group, then add the groups in series.",
    "assumptions": [
        "Ideal resistors at their nominal values."
    ],
    "limitations": [
        "Tolerance (±1% or ±5%) and temperature drift are not included; use the Resistor Calculator to read colour bands."
    ],
    "rules": null,
    "faqs": [
        {
            "question": "Why is parallel resistance smaller than any single resistor?",
            "answer": "Each extra path lets more current flow for the same voltage, which is what lower resistance means."
        },
        {
            "question": "Two equal resistors in parallel?",
            "answer": "Half of one: two 100 Ω resistors in parallel make 50 Ω."
        }
    ],
    "sources": [],
    "related": [
        {
            "name": "Resistor Calculator",
            "url": "https://calculators.geekmidst.com/calculators/resistor-calculator"
        },
        {
            "name": "Ohm’s Law Calculator",
            "url": "https://calculators.geekmidst.com/calculators/ohms-law-calculator"
        },
        {
            "name": "Voltage Drop Calculator",
            "url": "https://calculators.geekmidst.com/calculators/voltage-drop-calculator"
        }
    ],
    "disclaimer": null,
    "publisher": "GM¹X CalcVerse"
}