# The Science Behind Scaling Recipes

People that love to cook often find themselves in two camps: those that like to freestyle and experiment with their own recipes and those that follow weights, measurements and instructions to the letter.

But what happens when you need to adjust a recipe that serves 4 to serve 2? Just half it? What if you need to serve a banquet of 400? Is it a case of multiplying each quantity by 100?

It turns out that scaling recipes is quite complex and involves many factors. Fortunately, a bit of science and technology can help us solve the problem.

## What’s the Science Behind Scaling Recipes?

How can recipes be scaled? Is it simple mathematics or something more complex? I turns out it is a little complex but also very interesting.

We’ll look at some tech solutions that help with this issue a little later, but given the number of tools tackling this issue, it must be a common struggle for home cooks.

But before we can answer the question of how to successfully cook a double a recipe we have to break down the factors that affect cooking: volume, surface area, temperature and time.

## The Difference Between Volume and Surface Area

As per our original question, let’s assume we want to bake some pastry – perhaps for a delicious quiche or tart. Let’s also assume we want to make double the amount as specified in a recipe book or recipe app.

After going through the rigmarole of weighing and combining ingredients, resting the pastry in the fridge, rolling it out to the desired size and gently placing it in a tin, the pastry is ready to be baked.

Imagine the pastry was refrigerated as a block in a perfect cube (unlikely but it will make the maths easier). It’s volume is calculated by multiplying its width by its height by its depth.

volume = 10 * 10 * 10 = 1000cm3

The surface area of each side of the pastry is calculated by multiplying the horizontal by vertical dimensions.

area = 10 * 10 = 100cm2

If the original recipe makes 200g of pastry, doubling the recipe will make 400g of pastry. Now instead of a cube we’d have two cubes side by side.

The height and depth will remain the same but the length will be double. The total surface area will double and so will the volume.

volume = 20 * 10 * 10 = 2000cm3
area = 20 * 10 = 200cm2

But if we double each dimension of the pastry, the volume actually increases by 8 times while the surface area only increases by 4 times.

volume = 20 * 20 * 20 = 8000cm3
area = 20 * 20 = 400cm2

This can have a bigger impact on cooking time as the ratio of volume to surface area has changed significantly. But does the cooking time double or increase 8 times?

Can we just double the temperature so the pastry cooks in the same amount of time? Well, the simple answer is neither. So what else is involved?

## Choosing The Right Sized Equipment

When cooking pastry, it’s typically rolled out quite thin and used to line a pastry case. These come in many different shapes and sizes and when increasing the quantities of a recipe, the size of the pastry case will also need to be increased to ensure the pastry isn’t too thick.

It’s common for the thickness to be about 0.3cm to 0.5cm, regardless of the diameter of the tin being used. This will keep the crust nice and crisp and crunchy and will no doubt put contented smiles on faces around the dinner table.

If the original recipe calls for an 18cm pastry case, should that be doubled to 36cm for a double recipe? The diameter of the tin doesn’t need to double, the surface area of the tin needs to double.

The area of a circular tin is calculated by the formula

π * (d/2)2

Taking an 18cm diameter tin, the area of the base is approximately 250cm2.

3.14 * (18/2)2 = 254.34

A tin with an area of 500cm2 will have a diameter of approx. 25cm.

3.14 * (d/2)2 = 500
(d/2)2 = 500 / 3.14
(d/2) = √(500/3.14) = 12.62
d = 12.62 * 2
d = 25.24

So for double the recipe, you’ll need a tin about 1.4 times the diameter, not double.

## Cooking Time Is All About Ratios

In our hypothetical example the quantity of pastry has doubled and so has the surface area. How does this affect cooking time? Well it all comes down to volume to surface area ratio as mentioned before.

When something cooks it’s surfaces are heated from all sides. It’s water content starts to evaporate and sugars begin to caramelise.

Our increased volume of pastry will have a higher moisture content. But rolling the pastry out over a large area will provide a larger area to be heated and cause evaporation to occur more quickly.

The quantity of our pastry has doubled, the surface area has doubled and the volume has doubled. But since the thickness of the pastry remains the same, the ratio of surface area to volume is also about the same.

This means that as long as the temperature is constant, the cooking time for the double quantity and the original quantity of pastry will be almost identical.

If you’re a seasoned cook then you may know this by intuition but anyone that relies on the guidance of a recipe may not have guessed this to be the case.

## Tech to Take Away the Maths

Scaling recipes – even just by doubling the quantity – is not always simple arithmetic and there can be many complicating factors to consider.

I don’t know about you, but when I cook I prefer to focus on the food rather than mathematics. Are there any tech solutions (other than a calculator) that can help here? Well, I’m glad you ask.

### Skillet’s Online Recipe Calculator

Skillet is sub-brand of Lifehacker focused on all things cooking and food. They have an online recipe scaling calculator that converts a list of ingredients from an existing recipe into the required weights and measures for a scaled up or scaled down recipe.

You can multiply, divide or even change the shape and size of a pan. The tool is easy to use and claims it “can be used to scale any recipe up or down”.

### Kitchen Calculator

Kitchen Calculator is an app that takes away the struggle of “kitchen math”. It’s available on the App Store and features a recipe scaling tool which allows ease of scaling recipes up or down for different numbers of servings.

The app also offers a tool for converting between imperial and metric measurements and gives users the ability to add and edit lists of ingredients for more precise conversions.

### Drop

Finally, Drop combines a recipe app with a smart wireless scale. The system allows recipes to be scaled by number of servings required but also by the amount of available ingredients you have. We’ve written about Drop before but it’s such a smart piece of kit, I thought I’d mention them again for good measure.

## Recipe Scaling Tips

Recipe scaling is a bit trickier than expected and even though we covered some of the maths and tech solutions to lend a helping hand, scaling recipes is certainly not an exact science. So, what can enthusiastic amateur chefs and home cooks do to mitigate against recipe calculations gone awry?

Here are a few tips:

• Use the original cooking temperature as a reference point, monitoring closely for the results you are looking for.
• Use a temperature probe to check internal temperatures and be confident food is cooked through and safe to eat.
• When cooking more than one dish in the oven at the same time, allow for more cooking time and raise the temperature by about 25 degrees.
• Use original cooking times as a guide but bear in mind that halving a baking recipe will often take ⅔ to ¾ of the time – not half. When doubling a recipe the cooking time won’t double but be closer to 1.5 times. If volume to surface area ratios remain the same, cooking time is also remain similar but check to make sure.
• When changing pan sizes, try to keep the depth the same to reduce issues with increased volume and lower surface area.
• Dividing or multiplying a recipe is not grounds for adjusting seasoning by the same factor. Season food to taste to avoid over or under seasoning.
• Recipes can’t be scaled indefinitely. Increasing by 2-4 times works well but scaling up to banquet sized quantities will not. If you need to feed tens or hundreds of people then batch cooking is the only way to get predictable results.

So there you have it: there’s more to recipe maths than first meets the eye. The science and maths behind recipe scaling can get a little mind bending which is why it’s great to have technology come to our rescue.

If you’ve got any more recipe scaling tips or anything else you’d like to comment on, shoot us a tweet to continue the conversation. And we’ll update this post with any suitable tips that you send in. Happy cooking!

Rolled pastry in tart case photo by ebarney on Flickr used under Creative Commons