{
  "id": "wavelength",
  "version": "bc2188c51789",
  "status": "published",
  "name": "Wavelength Calculator",
  "question": "What is the wavelength?",
  "summary": "Finds the wavelength from the frequency and the wave speed (λ = v ÷ f), or the frequency or the speed, for light, sound in air or any wave, with the period and the photon energy.",
  "category": "physics",
  "subcategory": "energy",
  "url": "https://www.acalculator.org/physics/wavelength-calculator",
  "markdown": "https://www.acalculator.org/physics/wavelength-calculator.md",
  "kind": "function",
  "method": "v = f × λ, so λ = v ÷ f and f = v ÷ λ; T = 1 ÷ f; for light E = h × f.",
  "assumptions": [
    "Light travels at exactly 299,792,458 m/s in a vacuum; in glass or water it is slower (type that speed instead).",
    "Sound travels at 343 m/s in dry air at 20 °C; it is faster in warmer air.",
    "Each value is read as the exact decimal you typed, so the results have no rounding error before they are shown."
  ],
  "inputs": {
    "$schema": "https://json-schema.org/draft/2020-12/schema",
    "type": "object",
    "properties": {
      "find": {
        "title": "Find",
        "description": "Which of the three to work out from the other two.",
        "type": "string",
        "enum": [
          "wavelength",
          "frequency",
          "speed"
        ]
      },
      "wave": {
        "title": "Wave",
        "description": "Light in a vacuum (299,792,458 m/s), sound in air at 20 °C (343 m/s), or a speed you type.",
        "type": "string",
        "enum": [
          "light",
          "sound",
          "custom"
        ]
      },
      "v": {
        "title": "Wave speed (m/s)",
        "description": "The speed of the wave in metres per second.",
        "type": "number",
        "minimum": 1e-15,
        "maximum": 1e+21
      },
      "f": {
        "title": "Frequency",
        "description": "The number of waves per second, in the unit chosen below.",
        "type": "number",
        "minimum": 1e-15,
        "maximum": 1e+21
      },
      "fu": {
        "title": "Frequency unit",
        "description": "The unit of the frequency.",
        "type": "string",
        "enum": [
          "Hz",
          "kHz",
          "MHz",
          "GHz",
          "THz",
          "PHz"
        ]
      },
      "l": {
        "title": "Wavelength",
        "description": "The distance from one crest to the next, in the unit chosen below.",
        "type": "number",
        "minimum": 1e-15,
        "maximum": 1e+21
      },
      "lu": {
        "title": "Wavelength unit",
        "description": "The unit of the wavelength.",
        "type": "string",
        "enum": [
          "pm",
          "nm",
          "µm",
          "mm",
          "cm",
          "m",
          "km"
        ]
      }
    }
  },
  "outputs": {
    "result": {
      "label": "Answer",
      "description": "The value found, in the unit that puts it from 1 to 1,000, to 10 significant figures.",
      "format": "text"
    },
    "wavelength": {
      "label": "Wavelength λ (m)",
      "description": "The wavelength in metres.",
      "format": "number"
    },
    "frequency": {
      "label": "Frequency f (Hz)",
      "description": "The frequency in hertz (waves per second).",
      "format": "number"
    },
    "speed": {
      "label": "Wave speed v (m/s)",
      "description": "The speed of the wave in metres per second.",
      "format": "number"
    },
    "period": {
      "label": "Period T (s)",
      "description": "The time for one full wave: 1 ÷ f.",
      "format": "number"
    },
    "energy": {
      "label": "Photon energy (J)",
      "description": "For light: the energy of one photon, E = h × f, in joules.",
      "format": "number"
    },
    "ev": {
      "label": "Photon energy (eV)",
      "description": "The photon energy in electronvolts: E ÷ 1.602176634 × 10⁻¹⁹.",
      "format": "number"
    }
  },
  "defaultAnswer": {
    "inputs": {
      "find": "wavelength",
      "wave": "light",
      "v": 1500,
      "f": 100,
      "fu": "MHz",
      "l": 500,
      "lu": "nm"
    },
    "outputs": {
      "result": "λ = 2.99792458 m",
      "wavelength": 2.99792458,
      "frequency": 100000000,
      "speed": 299792458,
      "period": 1e-8,
      "energy": 6.62607015e-26,
      "ev": 4.135667697e-7
    },
    "text": "For this wave, λ = 2.99792458 m."
  },
  "examples": [
    {
      "given": {
        "find": "wavelength",
        "wave": "light",
        "f": 100,
        "fu": "MHz"
      },
      "expect": {
        "result": "λ = 2.99792458 m",
        "wavelength": 2.99792458,
        "period": 1e-8
      },
      "source": "hand calculation in content.mdx: 299,792,458 ÷ 100,000,000 = 2.99792458 m; OpenStax, University Physics Volume 1, §16.1 Traveling Waves: v = λ ÷ T = λf (https://openstax.org/books/university-physics-volume-1/pages/16-1-traveling-waves, retrieved 2026-10-02); NIST CODATA: c = 299 792 458 m/s, h = 6.626 070 15 × 10⁻³⁴ J/Hz, e = 1.602 176 634 × 10⁻¹⁹ C, all exact (https://physics.nist.gov/cgi-bin/cuu/Value?h, retrieved 2026-10-02)"
    },
    {
      "given": {
        "find": "frequency",
        "wave": "light",
        "l": 500,
        "lu": "nm"
      },
      "expect": {
        "result": "f = 599.584916 THz",
        "frequency": 599584916000000,
        "energy": 3.972891714e-19,
        "ev": 2.479683969
      },
      "source": "hand calculation in content.mdx: 299,792,458 ÷ 5 × 10⁻⁷ = 5.99584916 × 10¹⁴ Hz; E = h f; NIST CODATA: c = 299 792 458 m/s, h = 6.626 070 15 × 10⁻³⁴ J/Hz, e = 1.602 176 634 × 10⁻¹⁹ C, all exact (https://physics.nist.gov/cgi-bin/cuu/Value?h, retrieved 2026-10-02)"
    },
    {
      "given": {
        "find": "wavelength",
        "wave": "sound",
        "f": 440,
        "fu": "Hz"
      },
      "expect": {
        "result": "λ = 779.5454545 mm",
        "wavelength": 0.7795454545
      },
      "source": "hand calculation in content.mdx: 343 ÷ 440 = 0.779545… m; OpenStax, University Physics Volume 1, §17.2 Speed of Sound: 343 m/s in air at 20.0 °C (https://openstax.org/books/university-physics-volume-1/pages/17-2-speed-of-sound, retrieved 2026-10-02)"
    },
    {
      "given": {
        "find": "speed",
        "f": 2,
        "fu": "Hz",
        "l": 2.5,
        "lu": "m"
      },
      "expect": {
        "result": "v = 5 m/s",
        "speed": 5,
        "period": 0.5
      },
      "source": "OpenStax, University Physics Volume 1, §16.1 Traveling Waves: v = λ ÷ T = λf (https://openstax.org/books/university-physics-volume-1/pages/16-1-traveling-waves, retrieved 2026-10-02): waves at 2.00 Hz with λ = 2.50 m travel at 5.00 m/s"
    }
  ],
  "sources": [
    "OpenStax, University Physics Volume 1, §16.1 Traveling Waves (v = λ ÷ T = λf; a 2.00 Hz wave with λ = 2.50 m moves at 5.00 m/s), CC BY 4.0, retrieved 2026-10-02. https://openstax.org/books/university-physics-volume-1/pages/16-1-traveling-waves",
    "OpenStax, University Physics Volume 1, §17.2 Speed of Sound (343 m/s in air at 20.0 °C), CC BY 4.0, retrieved 2026-10-02. https://openstax.org/books/university-physics-volume-1/pages/17-2-speed-of-sound",
    "NIST CODATA 2022: Planck constant h = 6.626 070 15 × 10⁻³⁴ J Hz⁻¹ (exact), retrieved 2026-10-02. https://physics.nist.gov/cgi-bin/cuu/Value?h",
    "NIST CODATA 2022: speed of light in vacuum c = 299 792 458 m s⁻¹ (exact), retrieved 2026-10-02. https://physics.nist.gov/cgi-bin/cuu/Value?c",
    "NIST CODATA 2022: elementary charge e = 1.602 176 634 × 10⁻¹⁹ C (exact; 1 eV = e joules), retrieved 2026-10-02. https://physics.nist.gov/cgi-bin/cuu/Value?e"
  ],
  "related": [
    "speed",
    "power",
    "ohms-law"
  ],
  "changelog": []
}