# Sugar-to-Flour Mass Ratios in Cake Recipes

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The Hemingway we are talking about did not choose his death.

— Orson Welles, talking about Ernest Hemingway and how he suffered near the end of his life. Hemingway was not the same man at the end of his life that Welles had known earlier.

## Introduction

Figure 1: Histogram of Sugar-to-Flour Mass Ratios in 62 Cake Recipes.

I have been working at becoming a better baker. Specifically, I have been trying to understand how recipes are developed. Many baker's begin developing their recipe's based on ratios of ingredients. The classic rule ratio of thumb for cake recipes is to use equal masses of flour, sugar, butter, and eggs – with the ingredient ratios expressed as 1:1:1:1.

I recently noticed that many of the recipes that I have been using do not follow this rule of thumb. I was most curious about how the ratio of sugar-to-flour varied between recipes. I found a text database of cake recipes and decide to create a histogram that shows how the sugar-to-flour mass ratio varies.

## Background

### Flour and Sugar Densities

Recipes in the US tend to use volume measures like cups rather than mass measures. To convert these volume measures to masses, I needed to determine the densities of flour and sugar in terms of cups (Figure 2).

Figure 2: Computing the Density Ratio of Sugar-to-Flour.

### Confounding Issues

Cake recipes frequently contain ingredients that affect the amount of flour or sugar required. Example of these confounding ingredients include:

• cocoa (reduces the need for flour)
• honey (reduces the need for granulated sugar)
• applesauce
• candied fruit (e.g. cherries)

Also, the recipes sometimes call out sifted flour, which has a lower density than unsifted flour. For my analysis here, I am ignoring confounding ingredients and just looking at the ingredients labeled sugar and flour (granulated or brown) and taking their mass ratios.

## Analysis

My analysis was performed using Excel and Power Query. I have included my analysis and data here. I did not use every recipe in the text database because many recipes had obvious confounding sources of sugar. For example, some recipes had large amounts of sugar added in the form of juices and fruits. I flagged the recipes I used by prefixing their names and their flour and sugar ingredients with "@" symbols. This made it simple to extract the information that I needed.

Once I had extracted the ingredients, I then determined the volume ratios and converted the volume ratios to mass ratios using the densities of flour and sugar.

## Conclusion

The 1:1 mass ratio between flour and sugar appears to be violated frequently. In fact, the 1:1 volume ratio between flour and sugar is more common than the 1:1 mass ratio.

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