A real cook is never one temperature. The vessel comes up, holds, and cools, and every minute of that history kills something — just at wildly different rates. The F-value is the bookkeeping that lets those unlike minutes be added together.

$F = t \times 10^{\,(T - T_{\mathrm{ref}})/z}$ — F equals t times ten to the T minus T-ref over z. The letters: $t$ is the real time spent at temperature $T$, in minutes; $T$ is the process temperature in °C, measured at the cold spot; $T_{\mathrm{ref}}$ is the reference temperature the answer will be expressed at; $z$ is the z-value in C°; and $F$ is the equivalent time at that reference, in minutes. The exponential term on the right is the lethal rate: how many equivalent minutes one real minute is worth.

$F_0$ — F-nought — is the specific convention: reference $121.1\ ^\circ\mathrm{C}$, $z = 10\ \mathrm{C^\circ}$, the standard for spore-forming bacteria in low-acid thermal processing. And the stray decimal in 121.1 is not a rounding artefact — 121.1 °C is exactly 250 °F, and 250 °F is the number the North American canning industry built the convention on. Every metric F₀ in the world still carries that Fahrenheit fingerprint.

Read the multiplier before you touch the arithmetic, because with $z = 10$ it is always a power of ten. Ten degrees above the reference and every real minute is worth ten. Ten below and it is worth a tenth. Twenty below — a boiling-water bath at about 101 °C — and it is worth a hundredth, which is why an open bath accumulates F₀ so slowly that low-acid packs are not processed in one.

Once you have an F and a D at the same reference, the logs fall out: $\mathrm{LR} = \dfrac{F}{D}$. Both must be quoted at the SAME reference temperature — that is the whole condition under which they may be divided.

Three cautions, all of them the difference between arithmetic and a real schedule. An F quoted bare is useless: it means nothing without its reference and its z stated beside it. A real process is a sum: the honest F integrates the lethal rate over the whole recorded temperature history, and this page gives you one segment at one temperature. And measure at the cold spot, the slowest-heating point of the load — not in the free steam, which reaches temperature long before the centre of the can does.