Plan fractional ruler marks across a metric span, with every mark measured from the same starting point. Compare the selected endpoint and each mark with your original dimensions.
- Mm To Fraction Calculator
- Unit Converters
- Board Spacing Calculator
- Fractional Inch Tolerance Calculator
Fractional Ruler Layout Formula
First choose the nearest fractional endpoint, then distribute the intervals within that endpoint:
g = 25.4 / D
U = S / g
T = round(U)
qk = round(kT / N)
xk = qkg
ek = xk − kS / N
- S: original span, in millimeters.
- D: ruler denominator: 8, 16, 32, 64 or 128.
- g: millimeters per ruler tick.
- N: number of intervals, from 1 to 100.
- T: selected endpoint, in integer ticks.
- k: mark number, from 0 through N.
- qk: cumulative ticks from the start.
- xk: actual ruler-mark position, in millimeters.
- ek: signed deviation from the original ideal position, in millimeters.
Round to the nearest integer tick; an exact half tick rounds upward. The endpoint deviation is Tg − S. Adjacent gaps are qk − qk−1 ticks. The calculator rejects T < N because that span cannot provide N positive gaps at the selected increment.
How the Marks Are Distributed
Each interval uses either floor(T/N) or ceil(T/N) ticks. If r is the remainder of T divided by N, there are r longer gaps and N − r shorter gaps. Rounded cumulative positions determine their order; shorter and longer gaps need not alternate.
This method rounds the total endpoint before dividing it. It can produce different intermediate marks from rounding kU/N directly. The deviation column always compares with the original metric span, so rounding the endpoint does not hide the change in length. A mark’s deviation from the original ideal can exceed half a ruler tick because the endpoint is rounded first.
How to Use the Calculator
- Enter the original span in millimeters, using up to six decimal places and no more than 1,000,000 mm.
- Enter the number of equal intervals and choose your ruler increment.
- Select Calculate. Check the selected endpoint and its signed deviation before using the plan.
- Open the ruler-mark table. Measure every cumulative position from the same starting point instead of adding successive gaps.
Positive deviation places a mark beyond its original ideal position; negative deviation places it before that position. Ruler resolution alone does not establish measurement accuracy, acceptable fabrication tolerance, or fit. This plan does not account for kerf, material movement or measurement technique.
Worked Example: 100 mm in Four Intervals
For S = 100 mm, N = 4 and D = 16, one tick is 1.5875 mm. The original span is approximately 62.992126 ticks, so the selected endpoint is 63 ticks: 3 15/16 in = 100.0125 mm. Its deviation from the original span is +0.0125 mm.
| Mark | From start (in) | Position (mm) | Original ideal (mm) | Deviation (mm) |
|---|---|---|---|---|
| 0 | 0 | 0 | 0 | 0 |
| 1 | 1 | 25.4 | 25 | +0.4 |
| 2 | 2 | 50.8 | 50 | +0.8 |
| 3 | 2 15/16 | 74.6125 | 75 | −0.3875 |
| 4 | 3 15/16 | 100.0125 | 100 | +0.0125 |
The gaps are 1, 1, 15/16 and 1 inch: three longer gaps and one shorter gap. The largest deviation from an original ideal mark is 0.8 mm. Repeating the separately rounded original pitch of 1 inch four times instead reaches 4 inches, or 101.6 mm: +1.5875 mm beyond the selected endpoint and +1.6 mm beyond the original span.
Frequently Asked Questions
Does this keep the original span exactly?
Only when the original span lands on the selected ruler grid. Otherwise, the endpoint is rounded to the nearest tick. Check its deviation against your own length requirement.
Why are some gaps different?
If T is not divisible by N, identical whole-tick gaps cannot reach the selected endpoint. Distributed shorter and longer gaps reach it while keeping every cumulative position on the ruler grid.
Why does the calculator reject a short span?
When the rounded span has fewer ticks than intervals, at least one gap would be zero. Choose fewer intervals or a finer ruler increment.
Are the displayed millimeters exact?
Tick choices and fractions use exact arithmetic. Metric displays use up to 12 decimal places; the ≈ symbol marks a rounded decimal.
Source
NIST: SI Units — Length establishes the exact conversion of 1 inch to 25.4 mm. The endpoint-first distribution rule is defined above.
