Magnification Formula and Calculations

The formula

magnification = image size ÷ actual size

The same relationship rearranges to give either length directly, and it is worth being able to produce both rearrangements without hesitating under exam pressure:

actual size = image size ÷ magnification
image size = magnification × actual size

Magnification is a ratio, so it carries no unit of its own — it is written as ×.... Image size and actual size are both lengths, so both must always be given with a unit. Before dividing one by the other, check that they are already expressed in the same unit; if they are not, convert first.

Worked examples, all in millimetres

Calculating magnification

An image of a cell is 36 mm long. The actual cell is 0.06 mm long.

magnification = 36 mm ÷ 0.06 mm = 600, so the answer is ×600. The millimetre units cancel each other out because magnification itself has no unit.

Calculating actual size

An image is 48 mm wide and has a magnification of ×800.

actual size = 48 mm ÷ 800 = 0.06 mm.

Calculating image size

A specimen is 0.15 mm long and is shown at ×200.

image size = 200 × 0.15 mm = 30 mm.

Measuring an image accurately

When a question asks you to measure part of a diagram or photograph, identify the exact dimension being asked for — length, width or diameter — and measure precisely that dimension with a ruler, using the intended endpoints of the structure rather than the edges of the whole picture. Do not include arrowheads, labels or surrounding white space in the measurement, and record the image size in millimetres before you touch the formula. Measuring the size of the whole picture when a question actually wants the size of one structure inside it is a common way to produce a confidently wrong answer.

Reasonableness checks

An enlarged image should almost always give a magnification greater than 1. If a calculated actual size comes out larger than a clearly enlarged image, or a calculated magnification comes out as a fraction below 1, that is a strong sign the formula has been applied the wrong way round rather than a genuinely surprising result — go back and check which value was divided by which.

Where marks are actually lost

The formula only ever runs one way: image size ÷ actual size, never actual size divided by image size. If your answer for a clearly enlarged specimen comes out below 1, you have inverted the formula — redo the calculation rather than accepting the number. Do not mix units before dividing, either; dividing a value in mm by a value in µm produces a meaningless number, so convert first and divide second. And do not attach a unit to a magnification value — it is a ratio, so write ×200, never “200 mm” and never “200%”. It is also worth knowing that magnification is not the same idea as resolution: magnification is about apparent size, resolution is about the ability to distinguish fine detail, and resolution is not part of what is required here.

Supplement: converting between millimetres and micrometres

This section is required for Extended candidates only. Microscopic specimens are frequently given in micrometres, written µm, and a magnification calculation cannot mix an image measurement in millimetres with an actual size in micrometres — the units have to match before you divide.

1 mm = 1000 µm

To convert millimetres to micrometres, multiply by 1000. To convert micrometres to millimetres, divide by 1000. For example, 0.08 mm × 1000 = 80 µm, and 250 µm ÷ 1000 = 0.25 mm. The physical length has not changed in either case — only the unit used to express it has.

A worked example with mixed units

An image is 42 mm long. Its actual specimen is 70 µm long. The two measurements cannot be divided until their units match, so convert the actual size to millimetres first: 70 µm ÷ 1000 = 0.07 mm. Now the magnification calculation can proceed as normal: magnification = 42 mm ÷ 0.07 mm = 600, so the answer is ×600. Converting 42 mm into 42,000 µm before dividing would work equally well — either method is valid, as long as both sizes end up in the same unit before you divide.

Had the two values been divided without converting first, the calculation would have given 42 ÷ 70 = 0.6 — an impossible result claiming the image is smaller than the actual specimen. That impossibility is itself a useful check: if a magnification calculation ever produces a number below 1 for a specimen you know has been enlarged, mismatched units are one of the first things worth checking, alongside an inverted formula.

Common conversion mistakes

Going to the smaller unit — millimetres to micrometres — makes the number bigger, so you multiply by 1000. Going to the larger unit — micrometres to millimetres — makes the number smaller, so you divide by 1000. Check your answer against that direction before moving on: a converted value that has gone the wrong way is easy to catch if you pause and ask whether the number should have grown or shrunk. It is also worth keeping mm and µm visually distinct on the page — the two symbols are one letter apart, but a factor of 1000 apart in what they actually mean.

For the conceptual relationship between actual size, image size and magnification that this formula is built on, see size of specimens.