An egg cooks by heat moving in from wherever it touches something hot, and the shape of that problem changes with the method. Boiled and poached eggs are heated all around, a textbook heat-conduction problem for a sphere that physicist Charles D. H. Williams (University of Exeter) solved in closed form — poaching reuses that same solution without the shell, at a gentler simmer rather than a full boil. Fried eggs are heated from one side only, closer to heat moving into a thin slab than a sphere, so this tool switches to the matching one-sided diffusion solution. Scrambled eggs are different again — constant stirring keeps the mixture at one temperature throughout, so the right model is the same exponential approach to a target temperature used for the site's tea and drink-cooling calculators, not a diffusion equation at all.
A fridge-cold (4°C) large chicken egg (57g) dropped into sea-level boiling water reaches a classic soft-boiled yolk (63°C at the yolk-white boundary) in 4 minutes 32 seconds — matching Williams' own published example almost exactly. The same egg at 1500m altitude, where water boils at only 94.9°C, needs closer to 5 minutes 10 seconds.
Heat has to diffuse all the way to the centre, and that distance scales with the cube root of volume while the formula's mass term scales as mass^⅔ — so a jumbo egg takes meaningfully longer than a small one, but nowhere near "jumbo mass ÷ small mass" longer.
Boiling water at altitude is genuinely cooler — the boiling point drops as atmospheric pressure drops, exactly like the pressure-cooking relationship in reverse. Cooler water means a smaller temperature gap driving heat into the egg, so it takes longer to reach the same target, even though the water is "boiling" just as hard.
A poached egg isn't a compact sphere any more — cracked into water, it spreads out flat, which gives it far more surface area relative to its volume than a shelled egg has. That extra surface lets heat in faster, so this tool applies a calibrated adjustment to the same formula rather than pretending the shape hasn't changed.
A fried egg is heated from underneath only, by a pan, not surrounded by hot liquid — that's a one-sided diffusion problem into a thin layer, not heat converging toward the centre of a sphere. Both are real, standard heat-transfer solutions; they just apply to different shapes of the same underlying physics.
Diffusion physics assumes heat is spreading through a still object. Stirring breaks that assumption on purpose — it keeps the whole mixture at close to one temperature, which is exactly the condition an exponential-approach (lumped-capacitance) model describes well, and diffusion describes badly.
That's Williams' original derivation — it's the point that determines whether the yolk has started to set, which is what "soft" vs "hard" actually describes. A separate, more complex model (Barham's) targets the yolk centre instead; the two agree reasonably well in practice.
Above roughly 77°C, hydrogen sulphide from the white reacts with iron in the yolk to form a harmless but unappetising grey-green ring. This tool won't offer a doneness target above that, on purpose.