Magnification tells you how many times larger the image is than the real object. The formula is magnification = image size ÷ actual size, and it only works when both lengths are in the same unit.
This skill is used whenever a question gives you a drawing, a photomicrograph or a scale and asks how big a cell really is. It sits at the heart of cells and microscopy.
What are the units, and how do I move between them?
Cells are so small that millimetres are awkward. Biologists use the micrometre, written µm.
| Change | Rule | Example |
|---|---|---|
| mm to µm | multiply by 1000 | 0.15 mm = 150 µm |
| µm to mm | divide by 1000 | 45 µm = 0.045 mm |
| cm to mm | multiply by 10 | 4.5 cm = 45 mm |
A quick sense check helps. A micrometre is tiny, so the same length has a bigger number in µm than in mm.
How do I use the formula?
Use a formula triangle with image size in the upper box and magnification and actual size at the bottom. Cover the quantity you want, and the triangle shows the operation.
- Write down what you know, including the units.
- Convert so both lengths use the same unit.
- Substitute and calculate.
- Write the answer with × in front if it is a magnification, or with a length unit if it is a size.
Worked example
A student draws an onion epidermal cell.
The drawing is 45 mm long. The real cell is 0.15 mm long. Calculate the magnification of the drawing.
Step 1, write what you know. Image size = 45 mm. Actual size = 0.15 mm.
Step 2, check the units. Both are in mm, so no conversion is needed.
Step 3, substitute. Magnification = 45 ÷ 0.15 = 300.
Step 4, write the answer. ×300
Step 5, check by converting both to µm. 45 mm = 45 000 µm and 0.15 mm = 150 µm. Then 45 000 ÷ 150 = 300. The same answer, so it is reliable.
Now use the same idea the other way. A second drawing of a cell is 36 mm long, made at ×400. Find the actual length.
Actual size = image size ÷ magnification = 36 ÷ 400 = 0.09 mm. In µm that is 0.09 × 1000 = 90 µm.
The mistake to watch for
The usual slip is to divide two lengths that are in different units.
Mistaken answer: Image 45 mm, actual 150 µm. Magnification = 45 ÷ 150 = 0.3
The student did not notice that 45 is in mm and 150 is in µm. A drawing larger than the real cell cannot have a magnification below 1.
The correction is to convert first.
45 mm = 45 000 µm, so 45 000 ÷ 150 = 300. As a habit, write the unit next to every number before you divide, and ask whether the answer makes sense. A drawing larger than the real cell always has a magnification greater than 1.
Check yourself
Try these first, then open each answer.
1. An image of a cell is 12 mm long. The actual cell is 0.03 mm long. Calculate the magnification.
Show answer
Both lengths are in mm. 12 ÷ 0.03 = 400. Check: 12 mm = 12 000 µm and 0.03 mm = 30 µm, and 12 000 ÷ 30 = 400.
×400
2. A cell is 8 µm across. A diagram shows it at ×1500. How wide is the diagram in mm?
Show answer
Image size = magnification × actual size = 1500 × 8 µm = 12 000 µm. Divide by 1000 to convert to mm: 12 000 ÷ 1000 = 12.
12 mm
3. A photomicrograph at ×250 shows a cell 30 mm long. Find the real length of the cell in µm.
Show answer
Actual size = image size ÷ magnification = 30 ÷ 250 = 0.12 mm. Multiply by 1000 to convert to µm: 0.12 × 1000 = 120.
120 µm
Where this leads next
Next, separate the two sizes that students confuse in distinguishing image size from actual size. Before that, revisit identifying structures from a cell diagram if you want to practise choosing which structure to measure. The full topic is tested in the cells and microscopy practice set.
If you understand the formula but still lose marks on unit conversions, a one-to-one teacher can set short, fresh calculations until the routine becomes automatic, as part of online one-to-one Biology tuition.