I find the following explanation a little more succinct and clear. I realize this is just a restate of what's already been posted, but perhaps in more clear, laymen's terms. I can't remember where I found this, but i've been using it for about 5 years and works for me, unless you make a dramatic change to the photo's aspect ratio
The exposure needed to make a print is proportional to the picture’s surface area. Thus, if you change print size, you can eliminate the need for new test strips by calculating the change in area mathematically. A pocket calculator facilitates this.
1. Divide the new print size by the old one to get the change in width.
2. Multiply this answer by itself—square it—to get the change in area.
3. Finally, multiply the original exposure time by the change in area to get the new exposure time.
For example, if you were adjusting from a 4x5 to a 16x20 print size:
Old print width = 5 inches
Old exposure time = 4 seconds
New print width = 20 inches
New width / old width = 20 / 5 = 4.0 (change in width)
4.0 * 4.0 = 16.0 (change in area)
Change in area x original exposure = 16.0 x 4 = 64
New exposure time = 64 seconds