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Improve your cooking with maths! Here’s some guidance to help you cook the perfect boiled egg.

Safety: Use clean hands and equipment when handling food. This activity involves boiling water. Ask an adult to help.

You will need

• Egg
• Thermometer
• Scales
• Pen
• Paper
• Saucepan
• Water
• Slotted spoon
• Stopwatch
• Large bowl

Calculate boiling time

To boil an egg, you need to get the inside of the egg to the right temperature – around 65 °C. There are many different factors that affect the time it takes for the inside of an egg to get to that temperature.

1. You need to know how warm the egg is. Put your thermometer where the egg has been sitting, such as in the cupboard or fridge. After a minute, look at the thermometer and note the temperature.
2. You need to know how big the egg is. Weigh your egg on the scales.
3. You need to know what temperature water boils at. Find the altitude of your location on the internet. Convert your altitude from metres above sea level to kilometres above sea level. A good rule of thumb is that water will boil at 100 – (your altitude in kilometres) °C.
4. The following graph will give you a cooking time based on the weight of your egg. Look along the bottom (x axis) to find your egg’s weight and read the cooking time (on the y axis).

5. The next graph will correct the time based on the temperature of your egg. Find your egg’s temperature along the bottom (x axis) and read the extra time (on the y axis). Add this number to your cooking time.

6. The final graph will correct the time based on your water boiling temperature. Find your water boiling temperature along the bottom (x axis) and read the extra time (on the y axis). Add this number to your running total to get a final cooking time.

7. This formula is for a soft-boiled egg. For a hard-boiled egg, add 5 minutes.

Boil an egg

1. Put some water in your saucepan. You will need just enough water to cover your egg, but not too much, or it will overflow when you put your egg in.
2. Put the saucepan on the stove to boil.
3. When the water is boiling, balance the egg on your slotted spoon and carefully lower the egg into the water.
4. Start the stopwatch.
5. While the egg is boiling, half fill the large bowl with cold water.
6. When the time has elapsed, turn off the stove. Use the slotted spoon to take the egg out of the saucepan. If you are hard-boiling your egg, put it in the bowl of water to cool.
7. Crack the egg to see how successful you were. You can eat soft-boiled eggs with thin strips of ‘soldier’ toast, and hard-boiled eggs are good in a green salad!

What’s happening?

When you put an egg in boiling water, the outside of the egg heats up very quickly. It takes longer for heat to penetrate the middle of the egg. The egg needs to be heated to the point where proteins in the egg start to clump together, so the egg solidifies at around 65 °C.

British scientist Charles Williams used the ‘heat equation’ to describe the inside of a boiling egg. Charles was able to predict the temperature inside an egg, without breaking it open! He used this description to create a formula for cooking eggs. The graphs in this activity were made from Charles’s formula.

The heat equation originally comes from a book about heat flow, written by French mathematician Joseph Fourier in 1822. This important equation is still used in many areas of science, from weather prediction to plant biology.

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