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Culture calculations

Cell biology · Cell structure · note 8 of 9

Spec 4.1.1.6
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Culture calculationsSpec 4.1.1.6

In short

To find the number of bacteria after a certain time, divide the total time by the mean division time to get the number of divisions. Then multiply the starting number by 2 to the power of the number of divisions. The cross-sectional area of a colony or clear zone is πr², where the radius is half the diameter.

Number of bacteria after a certain time

You should be able to calculate the number of bacteria in a population after a certain time if you are given the mean division time. Each division doubles the population.

  1. Work out the number of divisions: total time ÷ mean division time (use the same units).
  2. Number of bacteria = starting number × 2 to the power of the number of divisions.

Bacterial population

A single bacterium divides every 20 minutes. How many bacteria are there after 2 hours?

  1. 2 hours = 120 minutes. Number of divisions = 120 ÷ 20 = 6.
  2. Number of bacteria = 1 × 2⁶ = 64.

Answer: 64 bacteria

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Standard form

A single bacterium divides every 20 minutes. How many bacteria are there after 8 hours? Give your answer in standard form to 2 significant figures.

  1. 8 hours = 480 minutes. Number of divisions = 480 ÷ 20 = 24.
  2. Number of bacteria = 2²⁴ = 16 777 216.
  3. Move the decimal point 7 places: 1.6777216 × 10⁷. To 2 significant figures: 1.7 × 10⁷.

Answer: 1.7 × 10⁷ bacteria

Areas of colonies and clear areas

You should be able to calculate the cross-sectional area of colonies, or of clear areas around colonies, using πr². The radius is half of the diameter.

area = π × r²

Area of a clear zone

The clear zone around an antibiotic disc has a diameter of 14 mm. Calculate its cross-sectional area. Use π = 3.14.

  1. Radius = 14 ÷ 2 = 7 mm.
  2. Area = π × r² = 3.14 × 7 × 7 = 3.14 × 49 = 153.86 mm².

Answer: About 154 mm²

Common mistake:

Using the diameter as the radius is the most common error. Halve the diameter first, then square the radius.

Written and checked against the AQA GCSE Biology (8461) specification · Updated October 2026

Frequently asked questions

What is the difference between prokaryotic and eukaryotic cells?

Eukaryotic cells, such as plant and animal cells, have their genetic material enclosed in a nucleus. Prokaryotic cells, such as bacteria, are much smaller and their genetic material is not in a nucleus. It is a single DNA loop, and there may be plasmids. Both types of cell have a cell membrane and cytoplasm.

Why do plant cells have a cell wall?

Plant cells have a cell wall made of cellulose because it strengthens the cell. Animal cells do not have a cell wall. Plant cells also often have a permanent vacuole filled with cell sap, which helps keep the cell firm, and chloroplasts, which contain chlorophyll to absorb light energy for photosynthesis.

How do you calculate magnification in biology?

Magnification is calculated with magnification = size of image ÷ size of real object. Make sure both measurements are in the same units before you divide. Rearranged, real size = image size ÷ magnification. For a light microscope, the total magnification is the eyepiece lens magnification multiplied by the objective lens magnification.

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