{
    "name": "RC Time Constant Calculator",
    "url": "https://calculators.geekmidst.com/calculators/rc-time-constant-calculator",
    "markdown": "https://calculators.geekmidst.com/calculators/rc-time-constant-calculator.md",
    "category": "Science & engineering",
    "description": "Find the time constant τ = R × C of a resistor–capacitor circuit, the capacitor voltage at any time while charging or discharging, and the RC cut-off frequency.",
    "summary": "A capacitor charging through a resistor reaches about 63% of the supply voltage after one time constant, τ = R × C, and is treated as fully charged after about 5τ.",
    "also_called": [
        "Capacitor charge time 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": "resistance",
            "label": "Resistance",
            "type": "number",
            "default": "10"
        },
        {
            "name": "resistance_unit",
            "label": "Resistance unit",
            "type": "select",
            "default": "kohm",
            "options": {
                "ohm": "Ω",
                "kohm": "kΩ",
                "Mohm": "MΩ"
            }
        },
        {
            "name": "capacitance",
            "label": "Capacitance",
            "type": "number",
            "default": "100"
        },
        {
            "name": "capacitance_unit",
            "label": "Capacitance unit",
            "type": "select",
            "default": "uF",
            "options": {
                "pF": "pF",
                "nF": "nF",
                "uF": "µF",
                "mF": "mF",
                "F": "F"
            }
        },
        {
            "name": "mode",
            "label": "Capacitor is",
            "type": "segmented",
            "default": "charge",
            "options": {
                "charge": "Charging",
                "discharge": "Discharging"
            }
        },
        {
            "name": "voltage",
            "label": "Supply (or starting) voltage",
            "type": "number",
            "default": "5",
            "unit": "V",
            "optional": true
        },
        {
            "name": "time",
            "label": "Time after switching",
            "type": "number",
            "default": "1",
            "optional": true
        },
        {
            "name": "time_unit",
            "label": "Time unit",
            "type": "select",
            "default": "s",
            "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": "vc",
            "label": "Capacitor voltage at that time",
            "format": "number"
        },
        {
            "key": "pct",
            "label": "Share of the final change",
            "format": "percent"
        },
        {
            "key": "cutoff",
            "label": "Cut-off frequency 1/(2πRC)",
            "format": "text"
        }
    ],
    "formula": {
        "text": "τ = R × C;  charging: V(t) = V × (1 − e^(−t/τ));  discharging: V(t) = V × e^(−t/τ);  f_c = 1 ÷ (2πRC)",
        "variables": {
            "R": "resistance in ohms",
            "C": "capacitance in farads",
            "τ": "time constant in seconds",
            "V": "supply voltage (charging) or starting voltage (discharging)",
            "t": "time since the switch"
        }
    },
    "worked_example": {
        "inputs": {
            "resistance": "10",
            "resistance_unit": "kohm",
            "capacitance": "100",
            "capacitance_unit": "uF",
            "mode": "charge",
            "voltage": "5",
            "time": "1",
            "time_unit": "s"
        },
        "steps": [
            "τ = 10,000 Ω × 0.0001 F = 1 s.",
            "After t = 1 s = 1τ: V = 5 × (1 − e⁻¹) = 5 × 0.63212 = 3.1606 V.",
            "f_c = 1 ÷ (2π × 1) ≈ 0.1592 Hz."
        ],
        "result": "A 10 kΩ resistor with a 100 µF capacitor has τ = 1 s; after one second the capacitor has charged to 3.16 V of 5 V."
    },
    "interpretation": "After 1τ the capacitor has covered 63.2% of the change, after 3τ 95%, and after 5τ 99.3%, which is the usual “fully charged” rule. The same τ sets the −3 dB corner of a first-order RC filter.",
    "assumptions": [
        "Ideal resistor and capacitor driven by a step from a stiff voltage source.",
        "Discharging starts from the voltage entered and decays towards zero."
    ],
    "limitations": [
        "Capacitor leakage, ESR, source resistance and tolerance (often ±10–20% for electrolytics) change the real timing."
    ],
    "rules": null,
    "faqs": [
        {
            "question": "Why 63%?",
            "answer": "After one time constant the remaining gap is e⁻¹ ≈ 36.8% of the original, so 63.2% of the change has happened."
        },
        {
            "question": "How long until the capacitor is fully charged?",
            "answer": "Mathematically never, but after 5τ it is within 0.7% of the final voltage, which is treated as complete in practice."
        }
    ],
    "sources": [],
    "related": [
        {
            "name": "RL Time Constant Calculator",
            "url": "https://calculators.geekmidst.com/calculators/rl-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"
}