Interactive formula for boiling eggs

A boiled egg is pure physics: heat has to travel from the boiling water through the shell and the white into the yolk, and how far it gets decides whether you end up with a runny, jammy or firm yolk. The calculator above works it out for your egg – from its size, how warm it is when it goes into the pan, and how far above sea level the pan is. Poaching without the shell? There's a matching formula for poached eggs.

How to use it

1. Bring water to the boil in a pan big enough that the eggs don't knock against each other.
2. Set the egg's weight. It's on the carton (medium eggs are 53–63 g, typically 56 g), or weigh the egg – that's the most accurate. If you only know the size, tap S, M, L or XL.
3. Prick a small hole in the blunt end with a needle or an egg pricker. That's where the air cell sits, and the hole lets the air escape so the shell doesn't crack.
4. Lower the egg into the boiling water with a spoon and press Start timer. The Keep the screen on button above stops your phone from dozing off in the meantime.
5. When the timer rings: straight into cold water for half a minute. Otherwise the egg carries on cooking on its own heat, and a jammy yolk turns into a firm one.

What happens inside the egg

White and yolk don't set at the same temperature. Egg white starts to set at around 62 °C and is firm at 65 °C. The yolk thickens from about 65 °C, is jammy at 67–68 °C, spreadable at just over 70 °C and fully firm at 80 °C. That is why a "soft-boiled" egg is a balancing act: the white has to set just enough while the yolk stays below 65 °C.

The grey-green ring you see around the yolk of an overcooked egg is iron sulphide, formed when sulphur from the white meets iron in the yolk at high temperatures for a long time. It's harmless but tastes faintly of sulphur – and you avoid it by stopping the cooking in time and cooling the egg straight away.

The formula

The calculator is based on a model by the physicist Charles D. H. Williams at the University of Exeter. He treats the egg as a sphere with uniform thermal properties and asks how long it takes for a point at the edge of the yolk to reach a given temperature:

• t is the boiling time in minutes.
• M is the egg's weight in grams. Time grows with M^⅔, i.e. more slowly than weight – an egg twice as heavy needs about 1.6 times as long.
• T_egg is the egg's temperature when it goes into the water. An egg from the fridge (5 °C) needs about a minute longer than one from the worktop (20 °C).
• T_water is the water temperature – the boiling point, which depends on altitude.
• T_yolk is the temperature you want at the edge of the yolk. 63 °C gives a runny yolk, 67 °C jammy, 72 °C firm and 80 °C hard-boiled.

The constant 0.451 comes from the egg's physical properties: density 1.038 g/cm³, heat capacity 3.7 J/(g·K) and thermal conductivity 5.4 mW/(cm·K). The factor 0.76 is a geometric term for the yolk sitting in the centre.

The egg's weight

Weight is the only property of the egg the formula uses, and it's on the carton: the EU classes are pure weight classes. If you have kitchen scales, weigh the egg – that makes the calculator as accurate as the model allows. With neither carton nor scales, the circumference at the widest point works as an estimate: the egg is treated as a spheroid 1.3 times as long as it is wide, and the weight becomes M ≈ 0.71 · (C / π)³ grams with the circumference C in cm.

Altitude

Water boils when its vapour pressure reaches the air pressure, and air pressure falls with height. Roughly speaking the boiling point drops about 1 °C for every 300 metres: 97 °C at 1,000 metres, 93 °C at 2,000 metres and only 83 °C at 5,000 metres. The closer the boiling point gets to the temperature the yolk has to reach, the longer it takes – and high in the Alps a hard-boiled egg can need twice as long as at sea level. In Denmark altitude makes no practical difference, but the slider is there for anyone taking their eggs into the mountains.

How accurate is it?

The model has its simplifications: an egg isn't a sphere, white and yolk conduct heat differently, and coagulation happens gradually over a few degrees rather than at a single temperature. Williams' own measurements show that the model does well at sea level and slightly underestimates the time at high altitude. Allow ±30 seconds – and adjust to taste next time. Very fresh eggs (under a week) need a little longer than older ones, because the proteins in the white coagulate at a slightly higher temperature.

A few other things that matter more than you'd think: put the eggs into boiling water, not cold water brought to the boil – otherwise you don't know when the clock starts. Don't add so many eggs at once that the water stops boiling. And eggs dropped straight into boiling water are easier to peel than eggs heated up slowly.

Sources

• Charles D. H. Williams, The Science of Boiling an Egg, University of Exeter – the original model with derivation and measurements (short version on the university's page).
• Harold McGee, On Food and Cooking (Scribner, 2004) – on protein coagulation in white and yolk.
• Martin Lersch, Towards the perfect soft boiled egg, khymos.org – on temperatures and texture.