Magnification calculator for microscopy

Magnification is how many times bigger an image is than the real object: magnification = image size ÷ actual size, with both sizes in the same unit. A cell that measures 30 mm in a photo but is really 60 µm across is magnified 30,000 ÷ 60 = ×500. This magnification calculator finds the magnification, the image size or the actual size from the other two, takes each size in cm, mm, µm or nm and converts for you, and calibrates an eyepiece graticule against a stage micrometer.

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Magnification Calculator

Link image size, actual size and magnification across units

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How to use the magnification calculator

1. Open the Magnification Calculator and choose Magnification, Image size, Actual size or Graticule.
2. Type the two values you know, and pick each size's unit: cm, mm, µm or nm. The image can be in millimetres and the cell in micrometres; the calculator converts them before dividing.
3. Read the answer with its working. Sizes come out in the unit that reads best, with the same length listed in mm, µm and nm underneath.
4. For practice questions on photographs, scale bars and graticules, press Random problem.

The magnification formula

Rearranged, I = M × A and A = I ÷ M. A formula triangle with I on top and M and A underneath gives all three. Magnification has no units, because the units cancel, so it is written as ×500, not 500 mm.

Unit conversions

Most mistakes in magnification questions are unit mistakes. Change both sizes to micrometres first and they rarely go wrong.

Worked examples you can check in the calculator

Example 1: finding the magnification

A cheek cell is 30 mm across in a photograph and 60 µm across in real life. Choose Magnification, type 30 with mm and 60 with µm.

The magnification is ×500.

Example 2: finding the actual size

A drawing of a red blood cell is 24 mm wide at ×3,000. Choose Actual size: A = 24 mm ÷ 3,000 = 0.008 mm = 8 µm.

Example 3: finding the image size

A mitochondrion 2 µm long is photographed at ×15,000. Choose Image size: I = 15,000 × 2 µm = 30,000 µm = 30 mm.

Example 4: an electron micrograph

A virus is 12 mm across in an electron micrograph at ×100,000. A = 12 mm ÷ 100,000 = 120 nm, which the calculator gives in nanometres because that reads best. Something that small is beyond a light microscope, whose resolution is about 200 nm; electron microscopes can reach ×100,000 and far finer detail.

Example 5: using a scale bar

A micrograph has a scale bar 20 mm long labelled 5 µm. The bar's image size is 20 mm and its actual size is 5 µm, so M = 20,000 µm ÷ 5 µm = ×4,000. Type those two into Magnification. Then use the magnification to find the actual size of anything else in the picture.

Example 6: an eyepiece graticule

An eyepiece graticule is a scale in the eyepiece with no units of its own, so it has to be calibrated for each objective lens. Line it up with a stage micrometer, a tiny ruler on a slide. Say 10 stage divisions, each 10 µm, line up with 25 eyepiece units, and a cell measures 18 eyepiece units. Choose Graticule and type 10, 10, 25 and 18:

The cell is 72 µm long. Change to a higher-power objective and one eyepiece unit is worth less, so you calibrate again.

Total magnification of a light microscope

A light microscope has two lenses: the eyepiece and the objective. The total magnification is the eyepiece magnification multiplied by the objective magnification: a ×10 eyepiece with a ×40 objective gives ×400. The calculator doesn't do this step, but it is a single multiplication. Laboratory light microscopes magnify up to about ×400, or ×1,000 with oil immersion. The microscope diagram guide shows where each lens is.

Common mistakes

• Mixed units. Dividing 30 mm by 60 µm without converting gives 0.5, not 500.
• Dividing the wrong way round. Magnification is image ÷ actual, and it is usually bigger than 1.
• Giving magnification a unit. Write ×500, not 500 µm.
• Measuring the scale bar's label instead of its length. Measure the bar with a ruler for the image size.
• Using an old graticule calibration. Each objective lens needs its own.

Read next

Biology · CellsVirtual microscope: focus, magnify and measure cellsFree virtual microscope: focus on onion cells, blood, a leaf and live pond water, switch objectives from ×4 to ×100 and measure cells with a scale bar.