Future Scientists

Revision note 1.6

Size, Scale and Magnification

Cells are too small to measure conveniently in metres. Accurate microscopy calculations depend on using the magnification equation and converting every measurement to the same unit.

CoreCalculationHigher-tier depth

What you need to know

  • Convert between millimetres, micrometres and nanometres.
  • Calculate image size, actual size or magnification.
  • Use a scale bar to estimate actual size.
  • Compare sizes using orders of magnitude.
  • Use standard form where required.

Units used in cell biology

metre (m)1 m
millimetre (mm)10−3 m
micrometre (µm)10−6 m
nanometre (nm)10−9 m
  • 1 metre = 1,000 millimetres.
  • 1 millimetre = 1,000 micrometres.
  • 1 micrometre = 1,000 nanometres.

Moving to a smaller unit multiplies the number by 1,000. Moving to a larger unit divides it by 1,000.

Unit examples

0.08 mm = 0.08 × 1,000 = 80 µm.
650 nm = 650 ÷ 1,000 = 0.65 µm.

Misconception AlertUnits do not need to match when using the magnification equation.Select to reveal the correctionSelect to hide the correction
Correct understanding

Image size and actual size must be converted into the same unit before using the magnification equation.

The magnification equation

magnification = image size ÷ actual sizeM = I ÷ A

Magnification has no unit because it is a ratio. Write it as ×400, for example. Rearranging gives:

Find image size

I = M × A

Find actual size

A = I ÷ M

Measure a printed image with a ruler in millimetres. Then convert either the image size or the actual size so both are in the same unit.

Worked examples

Example 1: calculate magnification

A cell image is 48 mm long. The cell's actual length is 120 µm.

  1. Convert 48 mm to micrometres: 48 × 1,000 = 48,000 µm.
  2. M = 48,000 ÷ 120.
  3. Magnification = ×400.
Example 2: calculate actual size

An image is 75 mm wide and has a magnification of ×2,500.

  1. A = 75 mm ÷ 2,500 = 0.03 mm.
  2. Convert to micrometres: 0.03 × 1,000.
  3. Actual width = 30 µm.
Example 3: calculate image size

A bacterium is 2 µm long and is shown at ×15,000.

  1. I = 2 µm × 15,000 = 30,000 µm.
  2. Convert to millimetres: 30,000 ÷ 1,000.
  3. Image length = 30 mm.

Using a scale bar

A scale bar shows the actual distance represented by a line on an image. Because the scale bar is enlarged by the same amount as the specimen, you can compare their measured lengths.

actual specimen size = measured specimen length ÷ measured scale-bar length × scale-bar value
Scale-bar example

A cell measures 60 mm on a page. A 15 mm scale bar represents 10 µm.

Actual size = 60 ÷ 15 × 10 = 40 µm.

If a digital image is resized, a scale bar remains valid only when it resizes with the image.

Standard form and orders of magnitude

Standard form writes a number as a × 10n, where a is at least 1 but less than 10. For example, 0.0000045 m is 4.5 × 10−6 m.

An order of magnitude is a factor of ten. A 50 µm cell is one order of magnitude larger than a 5 µm bacterium because it is ten times larger.

Extended

When comparing values, divide the larger size by the smaller. A result of 100 means the larger is two orders of magnitude greater because 100 = 102.

Quick retrieval check

1. Convert 0.25 mm to micrometres.
0.25 × 1,000 = 250 µm.
2. Convert 3,500 nm to micrometres.
3,500 ÷ 1,000 = 3.5 µm.
3. A 20 mm image represents a 50 µm cell. What is the magnification?
20 mm = 20,000 µm. M = 20,000 ÷ 50 = ×400.
4. Why does magnification have no unit?
It is a ratio between two lengths expressed in the same unit, so the units cancel.

Exam connection

Question

A micrograph shows a mitochondrion 36 mm long. Its actual length is 3.0 µm. Calculate the magnification.

Show the answer

36 mm = 36,000 µm. M = 36,000 ÷ 3.0 = ×12,000.

Final check

A microscope image should normally be larger than the object. If your calculated magnification is below ×1, recheck the unit conversion.