{
  "id": "rc-time-constant",
  "slug": "rc-time-constant-calculator",
  "url": "https://electronics.tools/tools/rc-time-constant-calculator/",
  "name": "RC Time Constant Calculator",
  "group": "cap-ind",
  "summary": "τ = R C. 10 kΩ and 100 µF is 1 s; E = 1.25 mJ.",
  "formulas": [
    {
      "id": "tau",
      "label": "Time constant",
      "plain": "τ = R C",
      "mathml": "<math display=\"block\" xmlns=\"http://www.w3.org/1998/Math/MathML\" aria-label=\"τ = R C\"><mrow><mi>τ</mi><mo>=</mo><mi>R</mi><mi>C</mi></mrow></math>",
      "symbols": [
        "R",
        "C"
      ],
      "sources": [
        "rc"
      ]
    },
    {
      "id": "charge",
      "label": "Charging exponential",
      "plain": "Vc(t) = V (1 − e^(−t/τ))",
      "mathml": "<math display=\"block\" xmlns=\"http://www.w3.org/1998/Math/MathML\" aria-label=\"Vc(t) = V (1 − e^(−t/τ))\"><mrow><msub><mi>V</mi><mi>c</mi></msub><mrow><mo>(</mo><mi>t</mi><mo>)</mo></mrow><mo>=</mo><mi>V</mi><mrow><mo>(</mo><mrow><mn>1</mn><mo>-</mo><msup><mi>e</mi><mrow><mo>-</mo><mi>t</mi><mo>/</mo><mi>τ</mi></mrow></msup></mrow><mo>)</mo></mrow></mrow></math>",
      "symbols": [
        "V",
        "C"
      ],
      "sources": [
        "rc"
      ]
    },
    {
      "id": "energy",
      "label": "Stored energy",
      "plain": "E = ½ C V²",
      "mathml": "<math display=\"block\" xmlns=\"http://www.w3.org/1998/Math/MathML\" aria-label=\"E = ½ C V²\"><mrow><mi>E</mi><mo>=</mo><mfrac><mn>1</mn><mn>2</mn></mfrac><mi>C</mi><msup><mi>V</mi><mn>2</mn></msup></mrow></math>",
      "symbols": [
        "E",
        "C",
        "V"
      ],
      "sources": [
        "rc"
      ]
    }
  ],
  "variables": [
    {
      "symbol": "R",
      "name": "Resistance",
      "unit": "Ω",
      "role": "input",
      "precision": {
        "sig": 4
      },
      "range": {
        "min": 0
      },
      "default": 10000,
      "urlParam": "r"
    },
    {
      "symbol": "C",
      "name": "Capacitance",
      "unit": "F",
      "role": "input",
      "precision": {
        "sig": 4
      },
      "range": {
        "min": 0
      },
      "default": 0.0001,
      "urlParam": "c"
    },
    {
      "symbol": "V",
      "name": "Voltage",
      "unit": "V",
      "role": "input",
      "precision": {
        "sig": 4
      },
      "default": 5,
      "urlParam": "v"
    },
    {
      "symbol": "tau",
      "name": "Time constant",
      "unit": "s",
      "role": "output",
      "precision": {
        "sig": 4
      }
    },
    {
      "symbol": "E",
      "name": "Stored energy",
      "unit": "J",
      "role": "output",
      "precision": {
        "sig": 4
      }
    },
    {
      "symbol": "Q",
      "name": "Charge",
      "unit": "1",
      "role": "output",
      "precision": {
        "sig": 4
      }
    },
    {
      "symbol": "fc",
      "name": "Cutoff frequency",
      "unit": "Hz",
      "role": "output",
      "precision": {
        "sig": 4
      }
    }
  ],
  "examples": [
    {
      "id": "10k-100u-5v",
      "title": "10 kΩ, 100 µF, 5 V",
      "input": [
        {
          "symbol": "R",
          "value": 10000,
          "unit": "Ω",
          "display": "10 kΩ"
        },
        {
          "symbol": "C",
          "value": 0.0001,
          "unit": "F",
          "display": "100 µF"
        },
        {
          "symbol": "V",
          "value": 5,
          "unit": "V",
          "display": "5 V"
        }
      ],
      "output": [
        {
          "symbol": "tau",
          "value": 1,
          "unit": "s",
          "display": "1 s"
        },
        {
          "symbol": "E",
          "value": 0.00125,
          "unit": "J",
          "display": "1.25 mJ"
        },
        {
          "symbol": "Q",
          "value": 0.0005,
          "unit": "1",
          "display": "0.0005"
        },
        {
          "symbol": "fc",
          "value": 0.15915494309189535,
          "unit": "Hz",
          "display": "0.1592 Hz"
        }
      ],
      "computedBy": "rcNetwork"
    },
    {
      "id": "1m-1u-12v",
      "title": "1 MΩ, 1 µF, 12 V",
      "input": [
        {
          "symbol": "R",
          "value": 1000000,
          "unit": "Ω",
          "display": "1 MΩ"
        },
        {
          "symbol": "C",
          "value": 0.000001,
          "unit": "F",
          "display": "1 µF"
        },
        {
          "symbol": "V",
          "value": 12,
          "unit": "V",
          "display": "12 V"
        }
      ],
      "output": [
        {
          "symbol": "tau",
          "value": 1,
          "unit": "s",
          "display": "1 s"
        },
        {
          "symbol": "E",
          "value": 0.000072,
          "unit": "J",
          "display": "72 µJ"
        }
      ],
      "computedBy": "rcNetwork"
    }
  ],
  "sources": [
    {
      "title": "RC time constant (Wikipedia, textbook identity)",
      "url": "https://en.wikipedia.org/wiki/RC_time_constant",
      "retrieved": "2026-11-02"
    }
  ],
  "datePublished": "2026-11-02T00:00:00+08:00",
  "dateModified": "2026-11-02T00:00:00+08:00",
  "author": {
    "name": "Jasper",
    "url": "https://electronics.tools/about/#jasper"
  },
  "relatedTools": [
    "https://electronics.tools/tools/capacitor-energy-calculator/",
    "https://electronics.tools/tools/capacitor-discharge-calculator/",
    "https://electronics.tools/tools/555-timer-calculator/",
    "https://electronics.tools/tools/series-parallel-capacitor-calculator/"
  ]
}