Magnification formula: magnification = image size ÷ real size

The magnification formula is magnification = image size ÷ real size. Image size is how big the object looks in a drawing or photo. Real size is the true size of the object. Both sizes must be in the same unit before you divide. Magnification has no unit, so you write it as a number such as ×200. AQA prints this formula in its specification.

Three ways to use one formula

You can make any of the three quantities the subject:

magnification = image size ÷ real size
image size = magnification × real size
real size = image size ÷ magnification

A quick check helps. The image is bigger than the real object, so the image size should be the larger number once the units match. If your magnification comes out smaller than 1, you probably divided the wrong way.

Pick what you want to find in the calculator, type the two values you know and choose their units. It shows each step of the working.

Getting the units to match

Cells are tiny, so their sizes use small units. Each step down is a thousand times smaller:

1 millimetre (mm) = 1000 micrometres (µm)
1 micrometre (µm) = 1000 nanometres (nm)
1 mm = 0.001 m, 1 µm = 0.000001 m and 1 nm = 0.000000001 m

Edexcel lists these prefixes as powers of ten: milli is 10⁻³, micro is 10⁻⁶ and nano is 10⁻⁹. It adds pico, 10⁻¹², too. AQA asks you to use centi, milli, micro and nano.

Image sizes are usually measured with a ruler in millimetres. Real sizes of cells are often given in micrometres. Change one to match the other before you divide.

Using a scale bar

Many micrographs, which are photos taken through a microscope, carry a scale bar. The bar is labelled with the real length it stands for, such as 10 µm.

Measure the bar with a ruler. That is its image size. Divide by the real length written on it to get the magnification. Then divide the measured length of the cell by that magnification to find its real size.

What each board asks

AQA (8461 and 8464) prints the formula and says you should give answers in standard form where that fits. Edexcel (1BI0 and 1SC0) sets magnification calculations in a core practical but prints no formula. For Edexcel, calculating with numbers in standard form is Higher tier only. OCR Gateway (J247) lists calculating magnification as part of using a light microscope, again with no formula printed.

Magnification is GCSE work. The KS3 curriculum does not include it. An electron microscope gives much higher magnification than a light microscope. AQA says it has let biologists see many more of the parts inside cells. You can explore those parts on the animal cell diagram and the bacterial cell diagram.

Worked examples

Magnification

Change the image size to micrometres: 4 mm = 4000 µm
magnification = image size ÷ real size
magnification = 4000 ÷ 20
magnification = 200, written ×200

200

Real size

real size = image size ÷ magnification
real size = 15 mm ÷ 1500 = 0.01 mm
Change to micrometres: 0.01 mm × 1000 = 10 µm
In metres: 0.00001 m, or 1 × 10⁻⁵ m in standard form

0.0000100 m

Image size

image size = magnification × real size
image size = 2500 × 2 µm = 5000 µm
Change to millimetres: 5000 µm ÷ 1000 = 5 mm
In metres: 0.005 m, or 5 × 10⁻³ m in standard form

0.00500 m

Common mistakes

Dividing real size by image size. That gives a number smaller than 1. Put the image size on top.
Dividing millimetres by micrometres. Convert both sizes to the same unit first, or the answer is out by a factor of 1000.
Multiplying by 100 instead of 1000 when changing mm to µm.
Measuring the whole photo, or the scale bar, when the question asks for the size of the cell.
Writing a unit after the magnification. It is a ratio of two lengths, so it has none.

Practise all three rearrangements, unit changes and scale bars in Magnification Challenge. The biology hub lists the cell diagrams and the other pages in this set.

Questions people ask

Is there a magnification triangle?

Yes, you can draw one with image size on top and magnification and real size underneath. Cover the quantity you want, and the other two show how to work it out. The three rearranged formulas above give the same result.

When should I give the answer in standard form?

AQA says to use standard form where it is appropriate. That usually means a real size in metres, such as 0.00001 m, which is easier to read as 1 × 10⁻⁵ m.

What is the difference between magnification and resolution?

Magnification is how many times bigger the image is. Resolution is how much fine detail you can pick out. AQA says an electron microscope has much higher magnification and resolving power than a light microscope.