Calculate magnification and actual size
Magnification relates image size to actual specimen size; both sizes must use the same units before division.
AS Level · Cambridge International Biology 9700, 2028–2030. Written practice is self-checked; supervised practical skills and human subject-teacher review remain necessary.
Before you begin
- Know that cells are the basic units of living organisms and that a light microscope uses lenses to form an enlarged image.
Work on paper. Try each question before revealing help, and explain why your method works.
Quick readiness check
Which equation defines magnification?
What you will learn
- Use magnification = image size ÷ actual size
- Calculate image magnification or specimen size from drawings, photomicrographs and electron micrographs
Use one consistent unit
Magnification = image size ÷ actual size. Rearrange to actual size = image size ÷ magnification, or image size = magnification × actual size. Magnification is a ratio and has no unit.
Convert measurements to the same unit before dividing. For example, 1 mm = 1000 µm and 1 µm = 1000 nm. A correct numerical ratio with mismatched units gives an incorrect answer.
Check scale and rounding
Measure the image as displayed or printed, not a differently resized copy. A scale bar can be used: compare the measured bar length with its stated actual length to obtain magnification. State actual specimen size with its unit and give magnification without one.
Round only at the end and keep a sensible number of significant figures for the measurements supplied. If an image is resized, the magnification printed on the original may no longer apply.
Pause and explain
Before calculating magnification, what must be true of image size and actual size?
Worked example
A cell measures 24 mm on a printed image and its actual length is 80 µm. Calculate the magnification.
Show the worked solution
- Convert 24 mm to micrometres.
- Divide image size by actual size.
Answer 24 mm = 24 000 µm. Magnification = 24 000 ÷ 80 = ×300.
Try a topic test
Choose Easy, Normal or Difficult. Save your answers and open worked review after finishing.
Test this topic →From guided practice to a new situation
Write your answer and reasoning first. Use a hint only if you are stuck. The model solution is for self-checking; your written work is not automatically marked.
An electron micrograph shows a mitochondrion 18 mm long. Its actual length is 6 µm. Calculate magnification.
Give me a hint
Convert 18 mm to micrometres, then divide.
Compare my reasoning
- 18 mm = 18 000 µm.
- 18 000 ÷ 6 = 3000.
Magnification = 18 000 µm ÷ 6 µm = ×3000.
Look for these in your work
- Units matched
- Magnification correct and unitless
A drawing has magnification ×250 and a cell is 32 mm long on the drawing. Find its actual length in micrometres.
Give me a hint
Use actual size = image size ÷ magnification.
Compare my reasoning
- 32 mm ÷ 250 = 0.128 mm.
- 0.128 mm = 128 µm.
Actual length = 32 mm ÷ 250 = 0.128 mm = 128 µm.
Look for these in your work
- Formula rearranged
- Unit conversion correct
A scale bar labelled 20 µm measures 8 mm on a printed image. Find the magnification of the printed image.
Give me a hint
Use measured image-bar length divided by actual-bar length.
Compare my reasoning
- 8 mm = 8000 µm.
- 8000 ÷ 20 = 400.
The printed image magnification is 8000 µm ÷ 20 µm = ×400.
Look for these in your work
- Scale-bar units matched
- Resized image scale interpreted
Common mistakes
- Dividing sizes expressed in different units
- Adding a length unit to magnification
- Using a magnification label after an image has been resized
What can you explain now?
Which equation defines magnification?
Compare with the explanation
Image size ÷ actual size
The image is compared with the specimen’s actual size.
After trying it yourself, choose your next review. This is your self-assessment.
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Make it stick
State the magnification equation and explain why image and actual sizes must use the same units.
If you needed the solution, close it and solve the problem again from a blank page. A correct answer is stronger when you can explain the reason for each step.