Many cookbooks suggest the following for boiling eggs: 3-6 min for a soft yolk, 6-8 min for a medium soft yolk and 8-10 min for a hard yolk. If you are satisfied with this, there is no need for you to continue reading. But if you’ve ever wondered whether the size of an egg has any impact on the cooking time you should read on. And if you search the ultimate soft boiled egg we share a common goal! From a scientific view point, a cooking time of approximately 3-8 minutes to obtain a soft yolk is not very precise. A number of important parameters remain unanswered: What size are the eggs? Are they taken from the fridge or are they room tempered? Are they put into cold or boiling water? And if using cold water – when should the timer be started? When the heat is turned on or when the water boils? And would the size of the pan, the amount of water and the power of the stove top matter?

A formula for boiling eggs?
I still remember the very first time I heard about a formula to calculate the cooking time for eggs. I was in high school and as a recipe for the ultimate nerd the egg formula gave me a good laugh. Now – many years later – I count myself to this group of nerds And thanks to the internet, google and Peter Barham’s book “The Science of Cooking” – I have been able to find out much more. I haven’t been able to track down the formula I heard mentioned, but the best documented formula nowadays is derived by Dr. Charles D. H. Williams, a lecturer in physics at University of Exeter. He has set up a nice page on the science of boiling eggs and there’s even a pdf with the full derivation of the formula. Given the starting temperature of the egg T_egg, the temperature of the water T_water and the desired temperature T_yolk (all in °C) at the yolk-white boundry, the cooking time t (in minutes) of an egg with mass M (in grams) is given by:

Whenever possible one should use weight measurements in the kitchen, but some times an accurate balance is not available and in those cases we can turn to the Peter Barham’s formula which is published in “The science of cooking”. The circumference of an egg is easily measured around the thick end using a piece of string and a ruler. I used to have a piece of string with three knots at 13, 14 and 15 cm respectively to make it even simpler. The cooking time t (in minutes) for an egg with a circumference c (in centimeters) is given by:

Former colleagues of mine at the University of Oslo have made a nice flash animation to do calculations with Barham’s formula if you’re not too keen to dig out your calculator. Barham states that his formula gives the time for the centre of the yolk to reach the temperature T_yolk whereas Williams mention in the derivation of the formula that it calculates the time for the yolk-white boundry to reach T_yolk. I’m not able to tell whether the formulas actually differ in this respect or not (comments are welcome on this issue!). A comparison of the two formulas for a set of 50 eggs which I weighed and measured shows that for T_yolk = 63 °C and T_water = 100 °C they are quite similar, except for the larger spread of the circumference measurements (see plot below). For higher T_yolk or lower T_water Williams’ formula consistently gives longer cooking times than Barham’s formula. It remains to be seen which of the formulas will be closer to the truth.

The graph shows the cooking time for 50 eggs (sorted by increasing mass) calculated from the mass and circumference using the two formulas shown above with T_yolk = 63 °C, T_water = 100 °C and T_egg = 4 °C. For the given conditions the two formulas give similar results. The most striking lesson learnt is that measuring the circumference is in fact not very accurate, hence the larger spread of these points.

The doneness of the egg depends on the temperature of the white and the yolk. Egg white starts to coagulate in the range 62-65 °C. At these temperatures it is the most heat sensitive protein, the ovotransferrin, which constitutes 12% of the egg white, which coagulates. The major protein of egg white, ovalbumin, makes up 54% of the white and doesn’t coagulate until the temperature reaches 80 °C. The yolk begins to thicken around 65 °C and sets around 70 °C. Further heating to around 80-90 °C produces the crumbly texture typical of hard boiled eggs. Many of these changes are nicely illustrated in the picture of sous vide cooked eggs below, but the changes are also summed up in the following table:

At sea level, the temperature of boiling water is 100 °C. At higher altitudes, the boiling is lowered. As a rule of thumb, the boiling temperature of water is lowered 0.3 °C for each additional 100 m above sea level. For an accurate calculation, check out his calculator. As we shall see later, the formula can of course also be used prepare eggs at sea level, using water kept at temperatures less than 100 °C. Lastly we must know the starting temperature of the egg which will typically be 4 or 20 °C.

Based on T_water = 100 °C, T_egg = 4 °C and T_yolk = 63-67 °C I’ve prepared plots for the range of 50 eggs used in the previous graph. If the circumference or mass of an egg is known, the boiling time in minutes can easily be determined from the graphs. I’ve also prepared downloadable pdfs with the circumference and mass plots.

Cooking time for eggs with given circumference or mass to reach to reach 63, 65 and 67 °C respectively at the yolk-white boundry with T_water = 100 °C and T_egg = 4 °C (click for larger image or download pdfs with circumference and mass plots)

But is this the perfect egg?
No actually not… keep reading! The problem with using boiling water is that while you do heat the yolk to the desired temperature, you have virtually no control with the temperature of the white. If your water holds 95-100 °C, so will the white (or at least the outer most part of the white). This gives it a firm, rubbery texture. So the problem is, to put it differently, that we want to heat the yolk to somewhere above 65 °C, but we do not want to heat the white above 80 °C. The solution to this problem is to “boil” the egg at a temperature lower than 100 °C, which means not to boil it at all but rather sous vide it! Eggs are perfect for sous vide because you can just drop them into the water bath as they are. No plastic bags or vacuum packaging are required. Douglas Baldwin has cooked eggs sous vide for 75 min at different temperatures ranging from 57.8 to 66.7 °C as shown below. Notice how the egg whites and egg yolks change at the different temperatures.

Composite image of eggs cooked sous vide for 75 min at the indicated temperatures (Photo: Douglas Baldwin. Picture used with permission.)

The surprising thing with some of the sous vide eggs is that they are inverted (or opposite boiled). The white is still runny while the yolk is set. If you would like to try this but don’t have a thermostated water bath for sous vide you can improvise a little. The thermostat most people do have in their kitchen is the baking oven (at least those with electric stoves). Preheat your oven to 70 °C. Then heat 1 L of water to 65-70 °C, put the eggs in, cover with a lid and leave the pan in the oven for one hour. The tricky thing here is that oven thermometers are notoriously wrong so use a separate handheld thermometer to check your oven. With some trial and error you should be able to obtain an inverted egg with a runny white and a yolk that has set.

Although scientifically amusing the inverted egg isn’t really desirable form a culinary viewpoint – the white is a little to runny. Regrettably the formulas presented above aren’t of much help either. They fail because they only take time and not temperature into account. The perfect soft boiled egg in my opinion would have an egg white which is heated to around 70-80 °C and a yolk with temperatures ranging from 64 °C at the yolk-white boundry to about 60 °C in the center. I guess it would be possible to prepare such eggs in a sous vide water bath held at 75-80 °C in less than an hour. A further complication of cooking eggs in real life is that they continue to cook when removed from the hot water. Normally this is alleviated by shocking the eggs in cold water, but if cooked at a lower temperature this could possibly be omitted. I will start experimenting to find a perfect mass-time-temperature combination with a time window that’s as large as possible, and I’ll report the results in a future blog post. And these experiments will also include a test of the recipe for eggs cocotte by Joël Robuchon, found via Chubby Hubby’s post on slow-cooking an egg.

Exotic soft boiled eggs
In his book “Off on a comet”, science fiction author Jules Verne shows that he was actually aware of the possibility of “boiling” eggs at a temperature lower than 100 °C. He has correctly observed that water boils at lower temperature in high altitudes, and that on a fictional comet of appropriate mass, water will boil at 66 °C. The temperature is wisely chosen, because by keeping eggs at 66 °C, you really can’t do anything wrong. From the last paragraph of the excerpt it seems that the eggs were not fully cooked after “a good quarter of an hour”. Of course, there is also no mention about the size of the eggs, so any further speculations end here. But I’ll rather leave it to you to read the excerpt from the Gutenberg e-text version – it’s quite amusing:

The skillet was duly set upon the stove, and Ben Zoof was prepared to wait awhile for the water to boil. Taking up the eggs, he was surprised to notice that they hardly weighed more than they would if they had been mere shells; but he was still more surprised when he saw that before the water had been two minutes over the fire it was at full boil.

“By jingo!” he exclaimed, “a precious hot fire!”

Servadac reflected. “It cannot be that the fire is hotter,” he said, “the peculiarity must be in the water.” And taking down a centigrade thermometer, which hung upon the wall, he plunged it into the skillet. Instead of 100 degrees, the instrument registered only 66 degrees.

“Take my advice, Ben Zoof,” he said; “leave your eggs in the saucepan a good quarter of an hour.”

“Boil them hard! That will never do,” objected the orderly.

“You will not find them hard, my good fellow. Trust me, we shall be able to dip our sippets into the yolks easily enough.”

The captain was quite right in his conjecture, that this new phenomenon was caused by a diminution in the pressure of the atmosphere. Water boiling at a temperature of 66 degrees was itself an evidence that the column of air above the earth’s surface had become reduced by one-third of its altitude. The identical phenomenon would have occurred at the summit of a mountain 35,000 feet high; and had Servadac been in possession of a barometer, he would have immediately discovered the fact that only now for the first time,
as the result of experiment, revealed itself to him–a fact, moreover, which accounted for the compression of the blood-vessels which both he and Ben Zoof had experienced, as well as for the attenuation of their voices and their accelerated breathing. “And yet,” he argued with himself, “if our encampment has been projected to so great an elevation, how is it that the sea remains at its proper level?”

Once again Hector Servadac, though capable of tracing consequences, felt himself totally at a loss to comprehend their cause; hence his agitation and bewilderment!

After their prolonged immersion in the boiling water, the eggs were found to be only just sufficiently cooked; the couscous was very much in the same condition; and Ben Zoof came to the conclusion that in future he must be careful to commence his culinary operations an hour earlier. He was rejoiced at last to help his master, who, in spite of his perplexed preoccupation, seemed to have a very fair appetite for breakfast.

There is in fact no need to head off to other planents to find examples of low temperature prepared eggs. If you go to Japan you’ll find onsen tamago which litteraly translates to “hot spring eggs”. Originally baskets of eggs were lowered into hot springs, but the temperature of hot springs vary so I imagine that there were several types of onsen tamago available (does anyone happen to know the exact temperature of the hot springs used?). After cooking the egg is typically cracked into a bowl of dashi soup with mirin and soy sauce. The challenge of preparing onsen tamago eggs at home is accurate temperature control (just as with sous vide in general). One tip I found was to place the egg on top of rice that has just cooked in a rice cooker. Leave the eggs to “cook” for about one hour while the “keep warm” function of the rice cooker is turned on.

Eggs boiled in onsen (japanese: hotspring), Nagano, Japan (Photo: Miya.m. Permission: GFDL, cc-by-sa-2.1-jp).

I’ve been told that in Finland some saunas are equipped with egg racks. Depending on where the rack is placed one could probably chose between hard boiled and soft boiled eggs. But the sauna would have to be kept warm for a long time due to the slow heat transfer from the hot air. And talking about eggs and saunas: If the eggs are placed directly on the hot stones they will not only be hard boiled, but actually turn completely brown and aquire a nutty flavor. In Korea such sauna eggs are known as Maekbanseok gyeran.

Other aspects to consider when boiling eggs
An egg has somewhere between 7000 and 17000 pores, meaning that water slowly evaporates (the density decreases from 1.086 g/cm³ by 0.0017 g/cm³ daily). This is also why eggs age faster at room temperature than in the fridge. Beacause of the pores, eggs should not be stored next to foods with a strong smell such as onions (unless of course, you want onion flavored eggs). When boiling eggs it is not uncommon that they crack. The most obvious reason is that they are dropped into the water and hit the bottom of the pot. Another reason for cracking is the expansion of trapped air at the blunt end of the egg. This air cannot escape fast enough through the small pores. Conventional wisdom has it that piercing a small hole in the blunt end will let expanding air escape to avoid cracking. It turns out someone has actually scientifically tested this (with 1000 eggs) and their finding was that there was little cracking for fresh eggs, regardless if they were pierced or not. Piercing reduced the cracking of 5-day old eggs and totally eliminated cracking of 28-day old eggs. The authors theorize that the air pocket grows due to evaporation (meaning there is more air to expand) and that the egg shell of fresh eggs is porous but that the pores gradually become clogged upon storage. Curiously the abstract concludes with the following sentence (this was written in 1973, but it’s still quite unusual for a scientific journal):

Housewives should pierce eggs before boiling them, since if they are fresh it will do no harm and if they are stale it will prevent splitting.

We can safely assume that the advise holds true for men as well! Apart from piercing holes to avoid cracking it is possible to reduce the potential damage from cracking by addition of salt or vinegar to the water. This will help the egg white coagulate faster and thus plug any crack formed.

Picture of egg shell pore (Photo: Jim Ekstrom. Permission: Freeware for non-commercial use).