{
  "id": "microscope-magnification",
  "version": "1b5568c517c4",
  "status": "published",
  "name": "Microscope Magnification Calculator",
  "question": "What is microscope magnification?",
  "summary": "Finds a compound microscope’s total magnification from the eyepiece and objective, the field of view from the field number, the field of view at another magnification, a specimen’s actual size from its image, or the magnification of an image.",
  "category": "biology",
  "subcategory": "lab",
  "url": "https://www.acalculator.org/biology/microscope-magnification-calculator",
  "markdown": "https://www.acalculator.org/biology/microscope-magnification-calculator.md",
  "kind": "function",
  "method": "Total magnification = eyepiece × objective; field of view = field number ÷ objective; FOV₂ = FOV₁ × M₁ ÷ M₂; actual size = image size ÷ magnification; magnification = image size ÷ actual size.",
  "assumptions": [
    "A compound light microscope with no extra magnification between the objective and the eyepiece (no zoom or magnification changer).",
    "The field of view scales with the objective when the eyepiece stays the same, so total magnifications compare the same way."
  ],
  "inputs": {
    "$schema": "https://json-schema.org/draft/2020-12/schema",
    "type": "object",
    "properties": {
      "find": {
        "title": "Find",
        "description": "Total magnification, field of view at another magnification, actual size, or an image’s magnification.",
        "type": "string",
        "enum": [
          "total",
          "fov",
          "actual",
          "mag"
        ]
      },
      "e": {
        "title": "Eyepiece (ocular) power (×)",
        "description": "The eyepiece lens magnification, usually 10×.",
        "type": "number",
        "minimum": 1,
        "maximum": 100
      },
      "o": {
        "title": "Objective power (×)",
        "description": "The objective lens in use: 4×, 10×, 40× or 100× on most microscopes.",
        "type": "number",
        "minimum": 0.1,
        "maximum": 1000
      },
      "fn": {
        "title": "Eyepiece field number (mm)",
        "description": "The field number printed on the eyepiece, such as 18, 20 or 22 mm; leave empty to skip the field of view.",
        "type": "number",
        "minimum": 0.1,
        "maximum": 100
      },
      "f1": {
        "title": "Field of view you know",
        "description": "The field of view measured at one magnification.",
        "type": [
          "number",
          "string"
        ],
        "x-quantity": "length",
        "minimum": 1e-15,
        "maximum": 1000
      },
      "m1": {
        "title": "Its total magnification (×)",
        "description": "The total magnification at which you know the field of view.",
        "type": "number",
        "minimum": 0.1,
        "maximum": 1000000000
      },
      "m2": {
        "title": "New total magnification (×)",
        "description": "The total magnification for the new field of view, with the same eyepiece.",
        "type": "number",
        "minimum": 0.1,
        "maximum": 1000000000
      },
      "i": {
        "title": "Image size",
        "description": "The size of the image: measured on a drawing or photo, or on the screen.",
        "type": [
          "number",
          "string"
        ],
        "x-quantity": "length",
        "minimum": 1e-15,
        "maximum": 1000
      },
      "m": {
        "title": "Magnification (×)",
        "description": "The magnification of the image.",
        "type": "number",
        "minimum": 0.000001,
        "maximum": 1000000000
      },
      "a": {
        "title": "Actual size",
        "description": "The real size of the specimen.",
        "type": [
          "number",
          "string"
        ],
        "x-quantity": "length",
        "minimum": 1e-15,
        "maximum": 1000
      }
    }
  },
  "outputs": {
    "result": {
      "label": "Answer",
      "description": "The magnification, field of view or actual size worked out.",
      "format": "text"
    },
    "magnification": {
      "label": "Magnification (×)",
      "description": "The total magnification, or the image’s magnification.",
      "format": "number"
    },
    "fovMm": {
      "label": "Field of view (mm)",
      "description": "The diameter of the circle you see, in millimeters.",
      "format": "number"
    },
    "fovUm": {
      "label": "Field of view (µm)",
      "description": "The diameter of the circle you see, in micrometers.",
      "format": "number"
    },
    "sizeUm": {
      "label": "Actual size (µm)",
      "description": "The specimen’s real size in micrometers.",
      "format": "number"
    },
    "sizeMm": {
      "label": "Actual size (mm)",
      "description": "The specimen’s real size in millimeters.",
      "format": "number"
    }
  },
  "defaultAnswer": {
    "inputs": {
      "find": "total",
      "e": 10,
      "o": 40,
      "fn": 20,
      "f1": "4.5 mm",
      "m1": 40,
      "m2": 400,
      "i": "50 mm",
      "m": 2000,
      "a": "25 µm"
    },
    "outputs": {
      "result": "400×; field of view 0.5 mm (500 µm)",
      "magnification": 400,
      "fovMm": 0.5,
      "fovUm": 500
    },
    "text": "400×; field of view 0.5 mm (500 µm)."
  },
  "examples": [
    {
      "given": {
        "find": "total",
        "e": 10,
        "o": 40,
        "fn": 20
      },
      "expect": {
        "magnification": 400,
        "fovMm": 0.5,
        "fovUm": 500,
        "result": "400×; field of view 0.5 mm (500 µm)"
      },
      "source": "OpenStax, Microbiology, §2.3 Instruments of Microscopy (total magnification = ocular × objective; 10× ocular with a 40× objective is 400×), https://openstax.org/books/microbiology/pages/2-3-instruments-of-microscopy; Nikon, Glossary of Microscopy Terms: field of view (field number ÷ objective magnification, in mm), https://www.microscope.healthcare.nikon.com/resources/glossary/field-of-view: 20 ÷ 40 = 0.5 mm; Python 3"
    },
    {
      "given": {
        "find": "total",
        "e": 10,
        "o": 100
      },
      "expect": {
        "magnification": 1000,
        "result": "1,000×"
      },
      "source": "OpenStax, Microbiology, §2.3 Instruments of Microscopy (total magnification = ocular × objective; 10× ocular with a 40× objective is 400×), https://openstax.org/books/microbiology/pages/2-3-instruments-of-microscopy: objectives from 4× to 100×, oculars usually 10×; hand calculation in content.mdx"
    },
    {
      "given": {
        "find": "fov",
        "f1": 0.0045,
        "m1": 40,
        "m2": 400
      },
      "expect": {
        "fovMm": 0.45,
        "fovUm": 450
      },
      "source": "Nikon, Glossary of Microscopy Terms: field of view (field number ÷ objective magnification, in mm), https://www.microscope.healthcare.nikon.com/resources/glossary/field-of-view: the field of view is the field number ÷ the objective, so it scales as 1 ÷ magnification; hand calculation in content.mdx"
    },
    {
      "given": {
        "find": "actual",
        "i": 0.05,
        "m": 2000
      },
      "expect": {
        "sizeUm": 25,
        "sizeMm": 0.025,
        "result": "Actual size 25 µm (0.025 mm)"
      },
      "source": "OpenStax, University Physics Volume 3, §2.4 Thin Lenses (m = h_i ÷ h_o, equation 2.22), https://openstax.org/books/university-physics-volume-3/pages/2-4-thin-lenses: object size = image size ÷ m; hand calculation in content.mdx"
    },
    {
      "given": {
        "find": "mag",
        "i": 0.05,
        "a": 0.000025
      },
      "expect": {
        "magnification": 2000,
        "result": "Magnification 2,000×"
      },
      "source": "OpenStax, University Physics Volume 3, §2.4 Thin Lenses (m = h_i ÷ h_o, equation 2.22), https://openstax.org/books/university-physics-volume-3/pages/2-4-thin-lenses; hand calculation in content.mdx: 50,000 µm ÷ 25 µm"
    }
  ],
  "sources": [
    "OpenStax, Microbiology, §2.3 Instruments of Microscopy: total magnification is the ocular magnification times the objective magnification (40× objective with a 10× ocular: 400×); oculars usually 10×, objectives 4× to 100×; brightfield images sharp up to about 1,000×. https://openstax.org/books/microbiology/pages/2-3-instruments-of-microscopy (retrieved 2026-10-19)",
    "Nikon, Glossary of Microscopy Terms: field of view, the diameter of the area seen, found by dividing the field number by the magnification of the objective (mm). https://www.microscope.healthcare.nikon.com/resources/glossary/field-of-view (retrieved 2026-10-19)",
    "OpenStax, University Physics Volume 3, §2.4 Thin Lenses: magnification m = h_i ÷ h_o (equation 2.22). https://openstax.org/books/university-physics-volume-3/pages/2-4-thin-lenses (retrieved 2026-10-19)",
    "OpenStax, Biology 2e, §4.1 Studying Cells: light microscopes magnify up to about 400 times, about 1,000 times with oil immersion. https://openstax.org/books/biology-2e/pages/4-1-studying-cells (retrieved 2026-10-19)"
  ],
  "related": [
    "centrifuge",
    "serial-dilution",
    "tm",
    "reverse-complement"
  ],
  "changelog": []
}