Mutation Frequency Calculator
Frequency is what you counted; rate is what happens per division — Luria and Delbrück settled the difference.
The formula
frequency = mutants / total ; usually quoted per million
Frequency is not rate
Mutation frequency counts the mutants present in a population at a moment. Mutation RATE is the chance of a new mutation arising per cell division. They are different quantities and the difference matters: a mutation that arose early in a culture is carried by all its descendants, so a single early event can produce a high frequency from a low rate.
Luria and Delbruck
That distinction was settled experimentally in 1943. If mutations arose in response to selection, parallel cultures would show similar numbers of mutants; if they arose spontaneously beforehand, the numbers would vary enormously depending on when the mutation happened. The observed variance was enormous — the "jackpot" cultures — which established that mutations are spontaneous. It is one of the cleanest experiments in biology.
Ratios are expectations, not promises
Every genetic ratio on these pages is a probability distribution, not a guarantee. A 3:1 cross does not produce three dominant offspring for every recessive one in a litter of four — it produces each offspring independently with a three-quarters chance. Small families depart from the expected ratio routinely, and that is the reason Mendel needed thousands of pea plants rather than dozens.