Microscope Magnification & Actual Size Calculator
Magnification, actual size in µm or nm, field of view, scale bars and resolution limits.
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Scale bars at this magnification
At other wavelengths
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About the Microscope Magnification & Actual Size Calculator
Five microscope calculations in one place, each with its working shown the way exams expect it:
- Magnification: total magnification = objective × eyepiece (× any zoom or changer), checked against the useful range of the objective’s numerical aperture.
- Actual size: the magnification triangle, magnification = image size ÷ actual size, solved for whichever of the three you need, with the lengths converted between mm, µm and nm and the answer in standard form.
- Field of view: its diameter from the eyepiece’s field number and the objective, or scaled from one you measured at another magnification, and the size of a cell from how many fit across.
- Scale bars: the magnification of a picture from its scale bar and the actual size of an object in it, or how long to draw a bar.
- Resolution: the smallest detail the objective can separate, d = λ ÷ 2NA (Abbe) and 0.61λ ÷ NA (Rayleigh).
With a Pro pass, copy the result or download it as a CSV, or unlock this one result. Without a pass the free preview shows the magnification, actual size, field of view or resolution in full, with the first rows of each table and the first working step; other figures are hidden.
How to use it
- Choose the calculation: magnification, actual size, field of view, scale bar or resolution.
- Enter what you know, each length with its unit: measure drawings and photographs with a ruler in millimetres.
- For actual size, pick what to work out; the calculator converts every length to one unit before dividing.
- Read the answer, the table and the working. Copy the result or download the CSV with a Pro pass, or after unlocking this result.
Examples
Image 25 mm long at ×400
25 mm = 25,000 µm; 25,000 ÷ 400 = 62.5 µm = 6.25 × 10⁻⁵ m
A 2 µm bacterium drawn 50 mm long
50,000 µm ÷ 2 µm = ×25,000 (an electron micrograph)
Objective ×40, eyepiece ×10, NA 0.65
×400, within the useful range ×325 to ×650
Field number 18 mm, objective ×40; 10 cells across
0.45 mm = 450 µm across; each cell about 45 µm
A 20 mm bar labelled 10 µm; the cell measures 35 mm
Magnification ×2,000; the cell is 17.5 µm
Green light 550 nm, oil objective NA 1.25
Abbe 220 nm, Rayleigh 268 nm; useful magnification ×625 to ×1,250
Common uses
- GCSE, A-level and IB biology: actual size and magnification questions with the unit conversions shown
- Lab practicals: the field of view at each objective, cell sizes from counts across the field, and scale bars for drawings
- Choosing an objective and eyepiece that stay within the useful magnification range
- Explaining why light microscopes cannot resolve the smallest structures in a cell and electron microscopes can
The formulas
- Total magnification = objective × eyepiece × any other lens in the light path
- Magnification = image size ÷ actual size, so actual size = image size ÷ magnification and image size = actual size × magnification; both lengths must be in the same unit
- Units: 1 m = 1,000 mm, 1 mm = 1,000 µm, 1 µm = 1,000 nm; the answer in standard form is a number from 1 to 10 times a power of ten, such as 6.25 × 10⁻⁵ m
- Field of view = field number ÷ (objective × any lens between them); the eyepiece’s magnification is not in the formula, because the field number already belongs to the eyepiece. A field of view measured at one magnification shrinks in proportion at a higher one
- Scale bar: magnification = the bar’s length on the picture ÷ the length it stands for
- Resolution: d = λ ÷ 2NA (Abbe), r = 0.61λ ÷ NA (Rayleigh), r = 1.22λ ÷ (NA_objective + NA_condenser) with the condenser
- Useful magnification = 500 to 1,000 × the objective’s NA; above it, magnification is “empty” and shows no more detail
Magnification and resolution
Magnification makes an image bigger; resolution is the smallest distance between two points that can still be told apart. With green light (550 nm) and an oil-immersion objective of NA 1.4, a light microscope resolves about 0.2 µm (550 ÷ 2.8 = 196 nm), however much it magnifies. Smaller structures need an electron microscope, which has much higher magnification and resolving power than a light microscope and is what revealed the sub-cellular structures of cells.
Sources
- AQA, GCSE Biology (8461) specification, 4.1.1.5 Microscopy: magnification = size of image ÷ size of real object, prefixes and standard form, light and electron microscopes
- Nikon MicroscopyU: Field of View (field number ÷ objective), Resolution (λ ÷ 2NA, 0.61λ ÷ NA, 1.22λ ÷ (NA_obj + NA_cond)) and Useful Magnification Range (500 to 1,000 × NA)
- E. Abbe’s diffraction limit, d = λ ÷ 2NA
Limitations
- Resolution figures are theoretical limits for a well-aligned microscope; contrast, staining and illumination decide what you actually see.
- Sizes estimated by counting cells across the field are rough; an eyepiece graticule calibrated with a stage micrometer is accurate.
- Lengths measured from a picture are only as good as the ruler and the print: measure the scale bar and the object on the same copy.
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Frequently asked questions
What do I get without a pass?
Without a pass, Microscope Magnification & Actual Size Calculator shows the magnification, actual size, field of view or resolution in full, with the first rows of each table and the first working step; other figures are hidden. Until you unlock it, the result can’t be downloaded or copied. A Pro, Premium or Ultimate pass, a one-time payment that never renews, unlocks the full result. The pricing page lists the passes and their prices.
How do I calculate the actual size of a cell?
Divide the image size by the magnification, with both in the same unit. A cell 25 mm long in a picture at ×400: 25 mm = 25,000 µm, and 25,000 ÷ 400 = 62.5 µm.
How do I calculate magnification?
Magnification = image size ÷ actual size. A 2 µm bacterium that is 50 mm long in a drawing: 50 mm = 50,000 µm, so the magnification is 50,000 ÷ 2 = ×25,000. For a microscope, the total magnification is the objective times the eyepiece: ×40 × ×10 = ×400.
How do I convert mm to µm and nm?
Multiply by 1,000 for each step down: 1 mm = 1,000 µm = 1,000,000 nm. So 0.0625 mm = 62.5 µm = 62,500 nm, or 6.25 × 10⁻⁵ m in standard form.
How do I find the field of view?
Divide the eyepiece’s field number (printed on it, in mm) by the objective’s magnification: 18 mm ÷ 40 = 0.45 mm. If you measured the field at low power with a ruler, scale it: 4.5 mm at ×40 is 4.5 × 40 ÷ 400 = 0.45 mm at ×400.
What is the difference between magnification and resolution?
Magnification is how much bigger the image is; resolution is the smallest gap between two points that can still be seen as separate. Magnifying beyond about 1,000 times the objective’s numerical aperture adds no detail: the limit is resolution, d = λ ÷ 2NA.