{
  "id": "frequency",
  "version": "4e5c0d39b0f3",
  "status": "published",
  "name": "Frequency Calculator",
  "question": "What is the frequency?",
  "summary": "Finds a frequency in hertz from the period (f = 1/T), from a wave’s speed and wavelength (f = v/λ), or from the angular frequency (f = ω/2π), with the period, angular frequency and cycles per minute.",
  "category": "physics",
  "subcategory": "mechanics",
  "url": "https://www.acalculator.org/physics/frequency-calculator",
  "markdown": "https://www.acalculator.org/physics/frequency-calculator.md",
  "kind": "function",
  "method": "f = 1 ÷ T; f = v ÷ λ; f = ω ÷ 2π.",
  "assumptions": [
    "The motion repeats at a steady rate (periodic motion), and the wave speed is the speed in the medium the wave travels through.",
    "Exact unit sizes: 1 ms = 0.001 s; 1 mph = 0.44704 m/s; 1 km/h = 1/3.6 m/s; 1 ft = 0.3048 m; 1 in = 0.0254 m."
  ],
  "inputs": {
    "$schema": "https://json-schema.org/draft/2020-12/schema",
    "type": "object",
    "properties": {
      "from": {
        "title": "Find the frequency from",
        "description": "Work out the frequency from the period, from a wave’s speed and wavelength, or from the angular frequency.",
        "type": "string",
        "enum": [
          "period",
          "wave",
          "angular"
        ]
      },
      "T": {
        "title": "Period",
        "description": "The time for one full cycle.",
        "type": [
          "number",
          "string"
        ],
        "x-quantity": "time",
        "minimum": 1e-15,
        "maximum": 1000000000
      },
      "v": {
        "title": "Wave speed",
        "description": "How fast the wave travels: about 343 m/s for sound in air at 20 °C.",
        "type": [
          "number",
          "string"
        ],
        "x-quantity": "speed",
        "minimum": 0.000001,
        "maximum": 299792458
      },
      "l": {
        "title": "Wavelength",
        "description": "The distance between two crests of the wave.",
        "type": [
          "number",
          "string"
        ],
        "x-quantity": "length",
        "minimum": 1e-15,
        "maximum": 1000000000
      },
      "w": {
        "title": "Angular frequency (rad/s)",
        "description": "The angular frequency ω in radians per second.",
        "type": "number",
        "minimum": 1e-9,
        "maximum": 1000000000000000000
      }
    }
  },
  "outputs": {
    "hz": {
      "label": "Frequency (Hz)",
      "description": "The frequency in hertz: cycles per second.",
      "format": "number"
    },
    "khz": {
      "label": "Frequency (kHz)",
      "description": "The same frequency in kilohertz.",
      "format": "number"
    },
    "period": {
      "label": "Period (s)",
      "description": "The time for one cycle, T = 1 ÷ f, in seconds.",
      "format": "number"
    },
    "omega": {
      "label": "Angular frequency (rad/s)",
      "description": "ω = 2π f, in radians per second.",
      "format": "number"
    },
    "perMinute": {
      "label": "Cycles per minute",
      "description": "f × 60, the same as rpm for something that turns.",
      "format": "number"
    }
  },
  "defaultAnswer": {
    "inputs": {
      "from": "period",
      "T": "20 ms",
      "v": "343 m/s",
      "l": "0.78 m",
      "w": 314.159
    },
    "outputs": {
      "hz": 50,
      "khz": 0.05,
      "period": 0.02,
      "omega": 314.1592653589793,
      "perMinute": 3000
    },
    "text": "The frequency is 50 Hz, one cycle every 0.02 s."
  },
  "examples": [
    {
      "given": {
        "from": "period",
        "T": 0.02
      },
      "expect": {
        "hz": 50,
        "perMinute": 3000,
        "omega": 314.1592653589793
      },
      "source": "OpenStax, University Physics Volume 1, §15.1 Simple Harmonic Motion (f = 1 ÷ T; ω = 2πf), https://openstax.org/books/university-physics-volume-1/pages/15-1-simple-harmonic-motion; hand calculation in content.mdx: f = 1 ÷ 0.02 s = 50 Hz; ω = 2π × 50 = 314.159 rad/s"
    },
    {
      "given": {
        "from": "wave",
        "v": 343,
        "l": 0.78
      },
      "expect": {
        "hz": 439.7435897435897
      },
      "source": "OpenStax, University Physics Volume 1, §16.1 Traveling Waves (v = λ ÷ T = λ f), https://openstax.org/books/university-physics-volume-1/pages/16-1-traveling-waves; hand calculation in content.mdx: f = 343 ÷ 0.78 = 439.744 Hz"
    },
    {
      "given": {
        "from": "period",
        "T": 2
      },
      "expect": {
        "hz": 0.5,
        "perMinute": 30
      },
      "source": "OpenStax, University Physics Volume 1, §15.1 Simple Harmonic Motion (f = 1 ÷ T; ω = 2πf), https://openstax.org/books/university-physics-volume-1/pages/15-1-simple-harmonic-motion; hand calculation in content.mdx: f = 1 ÷ 2 s = 0.5 Hz = 30 per minute"
    },
    {
      "given": {
        "from": "angular",
        "w": 314.1592653589793
      },
      "expect": {
        "hz": 50,
        "T": 0.02
      },
      "source": "OpenStax, University Physics Volume 1, §15.1 Simple Harmonic Motion (f = 1 ÷ T; ω = 2πf), https://openstax.org/books/university-physics-volume-1/pages/15-1-simple-harmonic-motion; hand calculation in content.mdx: f = ω ÷ 2π = 100π ÷ 2π = 50 Hz"
    }
  ],
  "sources": [
    "OpenStax, University Physics Volume 1, §15.1 Simple Harmonic Motion (f = 1 ÷ T; ω = 2π f). https://openstax.org/books/university-physics-volume-1/pages/15-1-simple-harmonic-motion (retrieved 2026-10-03)",
    "OpenStax, University Physics Volume 1, §16.1 Traveling Waves (v = λ ÷ T = λ f). https://openstax.org/books/university-physics-volume-1/pages/16-1-traveling-waves (retrieved 2026-10-03)"
  ],
  "related": [
    "wavelength",
    "rpm",
    "speed"
  ],
  "changelog": []
}