A tape reads to the sixteenth, so every number you mark has been rounded to the nearest 1/16 in. One rounding is never more than 1/32 in off, which no one will see. The trouble starts when the same rounded number is used over and over, or when the saw blade takes its own 1/8 in each time and nobody counted it. Both errors stack, and the last piece is where they land.
Example 1: seven equal pieces from one board
You need 7 equal pieces out of a 96 in board, and the blade cuts a 1/8 in kerf. Seven pieces take 6 cuts, so 3/4 in of the board turns into sawdust.
Ignore the kerf and divide the whole board: 96 in / 7 rounds to 13-11/16 in. Mark and cut six pieces at that length and the seventh comes out at 13-1/8 in, which is 9/16 in short. The rounding added almost nothing here; the 6 uncounted kerfs did the damage.
Count the kerf and divide what is left: 96 in minus 3/4 in is 95-1/4 in, and 95-1/4 in / 7 is 13.607 in, which rounds up to 13-5/8 in on the tape. Now each piece is a hair long, and seven of them plus the kerfs need 1/8 in more board than you have. The seventh piece is short again, by less, but still short.
Round down instead. At 13-9/16 in every piece is the same length and all seven fit. A seventh cut frees the last piece, leaving a 3/16 in offcut. When pieces have to match, round the repeated length down, not to the nearest, and let the leftover go to the scrap pile.
Example 2: stepping off a layout with the tape
Now lay out 7 equal spaces across a 100 in span, for balusters, shelf pins, or fence pickets. The exact space is 14.286 in, which rounds to 14-5/16 in. The quick way is to hook the tape on the last mark and measure 14-5/16 in again, 7 times. Each step carries the same small rounding forward, and by the far end the last mark lands at 100-3/16 in, 3/16 in past where it should be.
The better way is to keep the tape hooked on the start and mark each position from the exact running total, rounded once: the exact distance to mark 3 is 3 times 14.286 in, rounded to the nearest sixteenth. Every mark is then within 1/32 in of true, and the last one lands on the end.
| Mark | Stepped off at 14-5/16 in | From the start, rounded once |
|---|---|---|
| 1 | 14-5/16 in | 14-5/16 in |
| 2 | 28-5/8 in | 28-9/16 in |
| 3 | 42-15/16 in | 42-7/8 in |
| 4 | 57-1/4 in | 57-1/8 in |
| 5 | 71-9/16 in | 71-7/16 in |
| 6 | 85-7/8 in | 85-11/16 in |
| 7 | 100-3/16 in | 100 in |
The two columns agree at the first mark and drift apart one sixteenth at a time after that. On a stair rail or a fence that drift shows up as a last gap that does not match the others, which is the one everybody looks at.
The rules that fall out of this
- Subtract the kerf for every cut before you divide a board.
- When pieces must match, round the repeated length down and accept a small offcut.
- Measure every mark from one fixed start point, not from the last mark.
- Round once, at the end. Carry the exact value through the arithmetic and only round the number you are about to mark.
How CutOnce handles it
The app stores imperial lengths as whole sixty-fourths of an inch, so adding and subtracting measurements is exact, and its layout results are rounded to your fraction setting once, at the dimension it prints. Its baluster and spacing layouts work out every mark from the exact layout and round each one once, the second column above, so the marks cannot drift as they go down the rail. The examples in this post were computed the same way, from whole sixty-fourths. You can run the first one yourself in the free feet and inches calculator: subtract 3/4 in from 96 in, then divide by 7. For equal gaps between balusters, the baluster spacing calculator does the layout. How the web calculators are held to the app's answers is on the how we verify page, and the rest of the posts are on the blog.