# Calculating Drawer Heights

## Introduction

As you can tell from all the recent posts on construction, I am in the middle of planning some remodeling on my home. One of my projects includes designing a chest of drawers. It turns out that there are some common ways of determining pleasing drawer heights. I thought I would review them here. After a quick survey around the web, I found the following mathematical approaches to drawer sizing. They are all based on some form of numerical series.

• uniform progression
The simplest approach is to just make all the drawers the same size.
• arithmetic progression
This approach uses an arithmetic series to determine the drawer sizes. I did find an online calculator for this progression.
• geometric progression
This approach uses a geometric series to determine the drawer sizes. I also found an online calculator this one.
• Fibonacci series
This approach uses a Fibonacci series to determine the drawer sizes.
• Hambridge progression
A commonly used approach that can be drawn using a geometric construction that allows calculations to be avoided. I found an online calculator for this progression as well.

## Comparison of Drawer Appearances

To determine the approach I wanted to take, I decided to use a 6-drawer, 50" tall chest of drawers as an example. Figure 1 illustrates this example.

Figure 1: Illustration of a 6-Drawer, 50 inch set of drawers.

## Calculation Details

I am a big Mathcad fan and I coded these sequences into Mathcad, which I show in the following screen shots.

### Uniform Progression

Figure 2: Computation of the uniform progression drawer heights.

### Arithmetic Progression

Figure 3: Computation of the arithmetic progression drawer heights.

### Geometric Progression

Figure 4: Computation of the geometric progression drawer heights.

### Fibonacci Series

Figure 5: Computation of the Fibonacci series drawer heights.

### Hambridge Progression

Figure 6: Computation of the Hambridge progression drawer heights.

The Hambridge progression can be drawn using a compass in the field. This process is illustrated in Figure 7.

Figure 7: Illustration of the Hambridge progression construction.

## Other Examples

This entry was posted in Construction and tagged , , . Bookmark the permalink.

### 7 Responses to Calculating Drawer Heights

1. Excellent illustration of the different patterns that can be used in design! This idea would make a great project combining mathematics and wood shop in secondary school.

• mathscinotes says:

There are numerous mathematical rules that are used in construction. For example, I built a large bathroom cabinet a few years ago and used the arithmetic progression for the drawers heights and the golden mean for the aspect ratios of the doors. As I remodel parts of my house, I plan to document the interesting ones here. So you will see a weird blend of optics and carpentry/woodworking for awhile.

2. Joel says:

The Woodsmith Shop had a nice show on making cabinets. Unfortunately because I had seen it I just deleted that episode. Don't know when it will return. They talked about cutting the drawer fronts and sizing them. As they say in England, "Mind the gaps". You have to factor those in as well. They used a board on the inside to position the hinges, because they used full pull out hinges. This way they both sides were at the same height and parallel.

• mathscinotes says:

As always, how you define things is important. I looked at one book and one online calculator. Both computed the ratio drawers heights by ignoring the space between the drawers. So the gaps between the drawers simply add to the overall height of the cabinet. I must admit that I find something unsatisfying about that approach. It almost seems like you should gap height to the overall drawer height as well. Because the two references I saw did not do that, I decided not to do it either. However, it is an easy thing to add.

• Joel says: