how-to · 5 min read
Punnett squares, GC content and magnification basics
Three calculations come up again and again in introductory genetics, molecular biology and microscopy: the predicted ratios from a single-gene cross, the GC content of a nucleotide sequence, and the relationship between magnification and field of view. Each has a short formula and a set of assumptions that decide whether the answer means what you think it means.
This guide walks through the reasoning behind each one, with the arithmetic shown so you can follow it by hand. The tools linked here do the same calculations in the browser, but the assumptions are the part worth understanding: a ratio or percentage is only as good as the model behind it.
What a Punnett square actually shows
A Punnett square starts by listing the gametes each parent can produce. For a single gene with two alleles, a parent with two different alleles (a heterozygote, written Aa) can pass on either the dominant A or the recessive a, while a parent with two identical alleles (AA or aa) can pass on only one kind. Write one parent's gametes across the top of a grid and the other parent's gametes down the side, then fill each cell with the combination that meets there.
For an Aa × Aa cross the result is four cells: AA, Aa, Aa and aa. Each cell represents one equally likely genotype for a single offspring, not a guarantee about a family. The square compresses the model into something countable, which is why it is still taught: it makes the link between the alleles a parent carries and the genotypes their children could inherit visible at a glance.
Genotype ratios versus phenotype ratios
The four cells of an Aa × Aa cross contain one AA, two Aa and one aa. That genotype ratio is 1 : 2 : 1. Under complete dominance, one copy of the dominant allele is enough to produce the dominant trait, so AA and Aa look the same and are grouped together. The phenotype ratio is therefore 3 dominant : 1 recessive.
That grouping depends entirely on the dominance relationship. With incomplete dominance the heterozygote shows an intermediate appearance, so all three genotypes are distinguishable and the phenotype ratio stays 1 : 2 : 1. With codominance the heterozygote shows both traits at once. Before quoting a ratio, ask which model the trait actually follows: the arithmetic of the square is the same, but the way genotypes collapse into phenotypes is not.
Assumptions behind the ratios
The clean ratios hold when a specific set of conditions is met. Each parent must produce the two gamete types in equal numbers, fertilisation must be random, and every genotype must survive equally well. The model also assumes a single gene with two alleles, no mutation, and no linkage to other genes that could bias inheritance.
Real biology breaks these assumptions in useful ways. Some alleles are lethal when homozygous, some combinations affect fertility, and many traits are influenced by several genes or by the environment. Even when the model is right, chance matters: a family of four children can easily contain one affected child rather than the expected one in four. Treat the ratio as a probability for each child, not a prediction for a family, and use larger samples when checking a pattern.
Calculating GC content from a sequence
GC content is the proportion of a nucleotide sequence made up of guanine and cytosine. The calculation is (G + C) divided by the number of unambiguous bases (A + T + U + G + C), multiplied by 100. The denominator matters: if a sequence contains ambiguity codes such as N, those positions do not identify a base, so including them as if they were non-GC would artificially lower the percentage.
Take the short sequence ATGCGCNN. Removing the two Ns leaves six unambiguous bases: one A, one T, two Gs and two Cs. The GC share is (2 + 2) / 6 = 66.7 percent. A calculator should show that denominator rather than only the final number, because a high percentage over four known bases is far less reliable than the same percentage over thousands. Cleaning the input matters too: FASTA headers, line breaks, digits and punctuation are not bases and must be removed before counting.
Magnification and field of view
Total magnification on a compound microscope is the objective power multiplied by the eyepiece power. A 40× objective with a 10× eyepiece produces a total of 400×. When the rest of the optical path stays the same, the field of view shrinks in inverse proportion to magnification: FOV₂ = FOV₁ × M₁ / M₂. If 4.5 mm is visible at 100×, then at 400× the visible diameter becomes 4.5 × 100 / 400 = 1.125 mm, or 1125 µm.
The formula assumes the eyepiece, tube lens and every other element between the sample and the eye stay unchanged, and it treats the field diameter as a linear distance. Camera adapters add their own magnification, stereo microscopes often change the optical path as you zoom, and the number printed on an eyepiece (its field number) is a useful cross-check rather than an exact promise. For measurements that matter, calibrate with a stage micrometer instead of trusting the calculated value alone.
A checklist before you trust the number
Each of these calculations is easy to run and easy to misread, so a short check catches most mistakes. The list below is worth running through before a result goes into a report or a lab notebook.
- For a cross, confirm both parents use the same letter and that the dominance model matches the trait.
- For genotype ratios, count each of AA, Aa and aa separately before grouping phenotypes.
- For GC content, confirm which bases formed the denominator and how many ambiguity codes were excluded.
- For sequences, remove headers and non-letters, and check whether the molecule is DNA or RNA before comparing values.
- For magnification, confirm the same eyepiece and optical path were used for both field-of-view measurements.