{
    "name": "RL Time Constant Calculator",
    "url": "https://calculators.geekmidst.com/calculators/rl-time-constant-calculator",
    "markdown": "https://calculators.geekmidst.com/calculators/rl-time-constant-calculator.md",
    "category": "Science & engineering",
    "description": "Calculate the time constant τ = L ÷ R of a resistor–inductor circuit, the inductor current at any time as it rises or decays, and the RL cut-off frequency.",
    "summary": "Current through an inductor cannot change instantly: it rises towards V ÷ R with time constant τ = L ÷ R, reaching about 63% after one τ.",
    "also_called": [
        "L/R time constant 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": "inductance",
            "label": "Inductance",
            "type": "number",
            "default": "100"
        },
        {
            "name": "inductance_unit",
            "label": "Inductance unit",
            "type": "select",
            "default": "mH",
            "options": {
                "uH": "µH",
                "mH": "mH",
                "H": "H"
            }
        },
        {
            "name": "resistance",
            "label": "Total series resistance",
            "type": "number",
            "default": "10"
        },
        {
            "name": "resistance_unit",
            "label": "Resistance unit",
            "type": "select",
            "default": "ohm",
            "options": {
                "ohm": "Ω",
                "kohm": "kΩ",
                "Mohm": "MΩ"
            }
        },
        {
            "name": "mode",
            "label": "Current is",
            "type": "segmented",
            "default": "rise",
            "options": {
                "rise": "Rising",
                "decay": "Decaying"
            }
        },
        {
            "name": "voltage",
            "label": "Supply voltage",
            "type": "number",
            "default": "12",
            "unit": "V",
            "optional": true
        },
        {
            "name": "time",
            "label": "Time after switching",
            "type": "number",
            "default": "10",
            "optional": true
        },
        {
            "name": "time_unit",
            "label": "Time unit",
            "type": "select",
            "default": "ms",
            "options": {
                "ns": "ns",
                "us": "µs",
                "ms": "ms",
                "s": "s"
            }
        }
    ],
    "outputs": [
        {
            "key": "tau",
            "label": "Time constant τ",
            "format": "text"
        },
        {
            "key": "tau_seconds",
            "label": "τ in seconds",
            "format": "text"
        },
        {
            "key": "five_tau",
            "label": "5τ (≈ 99.3% settled)",
            "format": "text"
        },
        {
            "key": "i_max",
            "label": "Steady-state current V ÷ R",
            "format": "number"
        },
        {
            "key": "i_t",
            "label": "Current at that time",
            "format": "number"
        },
        {
            "key": "pct",
            "label": "Share of the steady-state current",
            "format": "percent"
        },
        {
            "key": "cutoff",
            "label": "Cut-off frequency R/(2πL)",
            "format": "text"
        }
    ],
    "formula": {
        "text": "τ = L ÷ R;  I = V ÷ R;  rising: i(t) = I × (1 − e^(−t/τ));  decaying: i(t) = I × e^(−t/τ);  f_c = R ÷ (2πL)",
        "variables": {
            "L": "inductance in henries",
            "R": "total series resistance in ohms",
            "V": "supply voltage",
            "I": "steady-state current",
            "t": "time since the switch"
        }
    },
    "worked_example": {
        "inputs": {
            "inductance": "100",
            "inductance_unit": "mH",
            "resistance": "10",
            "resistance_unit": "ohm",
            "mode": "rise",
            "voltage": "12",
            "time": "10",
            "time_unit": "ms"
        },
        "steps": [
            "τ = 0.1 H ÷ 10 Ω = 0.01 s = 10 ms.",
            "Steady-state current I = 12 ÷ 10 = 1.2 A.",
            "After 10 ms = 1τ: i = 1.2 × (1 − e⁻¹) ≈ 0.7585 A."
        ],
        "result": "A 100 mH coil with 10 Ω in series has τ = 10 ms; 10 ms after switching on 12 V the current is about 0.76 A of its final 1.2 A."
    },
    "interpretation": "Use τ to estimate how quickly a relay, solenoid or motor winding reaches full current, and how long the current takes to die away when switched off (which is why inductive loads need a flyback path).",
    "assumptions": [
        "Ideal inductor (no core saturation) in series with the resistance entered, switched by a step from a stiff voltage source.",
        "Decaying current starts from V ÷ R and flows through the same resistance."
    ],
    "limitations": [
        "Iron-cored inductors saturate, so L falls at high current and the real rise is faster than calculated."
    ],
    "rules": null,
    "faqs": [
        {
            "question": "Why does the decay need a path?",
            "answer": "Interrupting inductor current abruptly produces a large voltage spike (V = L di/dt). A diode or snubber lets the current decay with the time constant instead."
        },
        {
            "question": "Is the coil resistance included?",
            "answer": "Only if you add it. Enter the total of the external resistor and the winding resistance."
        }
    ],
    "sources": [],
    "related": [
        {
            "name": "RC Time Constant Calculator",
            "url": "https://calculators.geekmidst.com/calculators/rc-time-constant-calculator"
        },
        {
            "name": "Ohm’s Law Calculator",
            "url": "https://calculators.geekmidst.com/calculators/ohms-law-calculator"
        },
        {
            "name": "Resistor Calculator",
            "url": "https://calculators.geekmidst.com/calculators/resistor-calculator"
        }
    ],
    "disclaimer": null,
    "publisher": "GM¹X CalcVerse"
}