Designing A Progression Of Drawer Heights In A Stack Of Drawers

A common cabinetmaking design task is to decide on the heights of drawers in a chest of drawers. For the purposes of this discussion, we will define "increment" as the amount each drawer height increases or decreases compared to the one below or above it. Commonly, each drawer increases by a constant amount/increment of height from top to bottom. There are usually practical constraints to the design: The overall height of the drawer stack may be fixed, the minimum height of the top drawer or the maximum height of the bottom drawer may be fixed, or some combination of these constraints.

A recommendation often discussed in books and online forums is to use one of the mathematical series (e.g., the Fibonacci sequence) for calculating the progression of drawer heights. These progressions usually lead to too rapid an increase in height, such that the top drawer is too shallow or the bottom drawer impractically deep.

A common approach among Period furniture makers was to increase each drawer height by the thickness of the drawer divider. For a top drawer of about 5" and dividers of about 7/8" this approach leads to a practical size for the bottom drawer and a practical size for the overall case height in a four- to six-drawer-high stack. Often, the top drawer opening was divided into spaces for two or three drawers, and the next, full-length drawer opening was made the same height to keep the bottom drawer from becoming inconveniently deep.

This approach can work well when there are dividers and the overall height of the piece is free to float. But, if the overall height or the number of drawers is pre-determined, and there are no dividers, the following simple techniques submitted by Keith Newton can be used to determine the drawer heights:

Assumptions for this example:

- Nine drawers

- Fixed case opening height of 45"

- Fixed top drawer height of 2 1/2"

If the drawers were all the same height, they would be 5" high. With an odd number of drawers, the middle drawer height will be the average drawer height, in this case 5" (45 ÷ 9 = 5). All the drawers below or above this center drawer will be incremented or decremented by the same amount. The task is to calculate this increment. The difference between the middle and top drawer heights is 2 1/2". If we divide this difference by the number of drawers, we arrive at an incremental difference of 5/8" (2 1/2 ÷ 4 = 5/8"). In this case, the top drawer will be 2 1/2" high and the bottom drawer will be 7 1/2" high.

Note: For sizes where fractions don't work out so conveniently, there is a lot to say for doing the calculations with metric or decimal measurements.

With an even number of drawers and no fixed top drawer height, the calculation is still simple.

Assumptions for this example:

- Eight drawers

- Fixed case opening of 40"

The "average" drawer height would be 5" (40 ÷ 8 = 5), but there are no average-height drawers in this case. To proceed, we choose a convenient increment for the drawers, say 1/2". Starting at the space between drawer #4 and #5, we increase the size of drawer #5 by half the increment, to 5 1/4" ( 5 + (1/2 x 1/2) = 5 1/4), and we decrease the height of drawer #4 by the same amount, to 4 3/4" (5 - (1/2 x 1/2) = 4 3/4), resulting in an increment of 1/2" between these two center drawers. We add or subtract the full 1/2" increment for the remaining drawers above and below. If this results in drawer #1 being too small, or drawer #8 too large, we can empirically adjust the increment to yield a better result.

Forum member Richard Jones (a.k.a. Sgian Dubh) describes a straightforward way to determine drawer heights if the top (smallest) drawer height and the total height of the drawer space is fixed, a common situation. See the following link for a more detailed and lucid description of the technique:

This technique postulates that, starting at the top drawer, each drawer is one increment (I) taller than the one above it. The sum of all the incremental increases is then zero for drawer #1, plus I for drawer #2, plus 2I for drawer #3, plus 3I for drawer #4, etc., for the total number of drawers involved. The sum of these incremental increases is equal to the total drawer opening height minus the top drawer height times the number of drawers. This value divided by the sum of the increments equals the increment value, I.

For the mathematically inclined, this increment (I) equals the height of the opening (H), minus the height of the top drawer (h) times the number of drawers (n), divided by the sum of n from 1 to n-1, or:

I = (H - nh) / Σ n

Assumptions for this example:

- Case opening of 1000 mm (H = 1000)

- Top drawer height of 170 mm (h = 170)

- Five drawers (n = 5), hence, the sum of increments = 10 (Σ n from 1 to n-1 = 1 + 2 + 3 + 4 = 10)

In this example, the incremental increase in drawer height is:

I = (H - nh)/Σ n from 1 to n-1

= (1000 - (5 x 170)) / (1+2+3+4)

= (1000 - 850) / 10

= 150/10 = 15 mm

Each drawer will be 15 mm taller than the one above it.

In most cases there will be a small space left between each drawer for clearance. This amount can be added to the divider thickness in the calculation of the increment height, or just subtracted from each drawer height after the heights are calculated by one of the means illustrated above.

These techniques for designing the drawer sizes reveal a precise way to lay out drawers in a case by using two dividers. Fix one divider at the height of the first drawer and a second divider for the increment by which each drawer increases in height. Starting at the top drawer, walk the dividers down the case to locate each drawer using combinations of the two divider settings. For example, the position of the bottom of drawer #1 is one divider span from the top of the case opening. The position of the bottom of drawer #2 is twice the span of the large divider plus one times the span of smaller divider.