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How to convert between model scales
The rule, derived as an exact fraction
A scale a:b has a factor of a/b, so 1:72 is the factor 1/72 and 1:48 is 1/48. Converting between them divides the target factor by the current one:
k = (1 ÷ 48) ÷ (1 ÷ 72) = 72 ÷ 48 = 3/2 = 1.5 = 150%
Dividing by a fraction inverts it, which is why the current denominator ends up on top and the target denominator underneath. The order is not a convention to memorise — it falls out of the division. Get it backwards and you compute the reverse conversion instead, which is a different job entirely:
1:48 → 1:72 ⇒ 48 ÷ 72 = 2/3 = 0.666… = 66⅔%
3/2 and 2/3 are reciprocals: multiply them and you get exactly 1, which is the arithmetic statement that converting and converting back returns the original size. Note that 150% and 66⅔% are not symmetric numbers — the correction for a 50% increase is a 33⅓% decrease, and subtracting 50% instead would leave you at 75% of where you started. Kept as 3/2 and 2/3 the round trip is exact; kept as 1.5 and 0.667 it is not.
If the target denominator is smaller, the model gets bigger and k is above 1. The general form k = target factor ÷ current factor also covers enlargement scales such as 2:1 and 5:1, where assuming a 1 on the left would give the wrong answer.
Worked example
You have a 1:35 armour kit part measuring 62 mm and want it at 1:48. k = 35/48 = 0.7292…, so 72.92%. The part becomes 62 × 35/48 = 45.21 mm. Volume drops to k³ ≈ 38.8% of the original — worth knowing before you print it. Verify the direction by sanity check: 1:48 is a smaller model than 1:35, so k must be below 1, and it is.
Finding the scale you have
If the scale is unmarked, measure one dimension you can find a real-world value for and divide: a 47 mm model of a 4.1 m car is 47 ÷ 4100 = 1/87.2, so about 1:87. Measure the longest feature available, because error is proportional: 1 mm out on a 20 mm part moves the scale by 5%, the whole difference between 1:72 and 1:76.
Calculated scale is not documented convention
That 1/87.2 is a calculated scale: an exact consequence of the two numbers you supplied. HO's documented convention is 1:87.1 — 3.5 mm to the foot, recorded in NMRA S-3.2. These are two different kinds of claim, and this site never silently converts one into the other.
- Calculated scale. Whatever your measurement divides to, reported as an exact fraction. It carries the error of your measurement and nothing else.
- Documented convention. A value recorded in a published standard or, where no standard exists, a widely used commercial practice — shown with its status, source and a last-verified date.
So when the model scale calculator computes 1:76.4 from your measurement, it reports 1:76.4 and separately lists the closest documented conventions, with the arithmetic distance to each. It does not overwrite your result with 1:76.2 and it does not present 1:76 as a standard, because 1:76 is a rounded shorthand rather than a separately documented value. Deciding that your model “is” OO is your judgement about a physical object; the calculator supplies the two numbers you need to make it. The common scales reference shows each entry's status — documented standard, documented practice, or common practice — so you can see which kind of claim you are relying on.
Near-miss denominators, measured on one length
Four visually similar scales, applied to the same 18 m prototype length, give four different model lengths:
| Scale | Model length | vs 1:72 | Status in the reference data |
|---|---|---|---|
| 1:72 | 250.00 mm | — | Common practiceMost common aircraft kit scale; no single issuing standards body. |
| 1:76 | 236.84 mm | -13.16 mm | Not a separate entryUsually written as shorthand for the documented 1:76.2 (OO). Rounded, not standardised. |
| 1:76.2 | 236.22 mm | -13.78 mm | Documented standardOO, 4 mm to the foot, on 16.5 mm gauge track (NMRA S-3.2). |
| 1:87.1 | 206.66 mm | -43.34 mm | Documented standardHO, 3.5 mm to the foot, on 16.5 mm gauge track (NMRA S-3.2). |
The denominators look almost identical; the physical consequence is not. 1:72 and 1:76.2 differ by about 14 mm on this length — more than the width of a coach door. 1:76.2 and 1:87.1 differ by about 30 mm, and no amount of care in assembly hides that when two models stand side by side.
This table is a dimensional comparison, not a compatibility verdict. It does not say these scales are interchangeable, and it does not say they are not: that depends on what you are building, how close the parts sit, and which standard the components were made to. HO (1:87.1) and OO (1:76.2) both run on 16.5 mm gauge track, which is a good reminder that “same gauge” and “same scale” are separate claims.
Exact arithmetic does not make your measurement exact
Every ratio on this site is computed as an exact fraction, so no error is introduced by the calculation. That is a claim about the arithmetic, not about the input. A scale derived from a physical measurement inherits the measurement's uncertainty in full:
- A caliper reading good to ±0.1 mm on a 20 mm part is ±0.5% — enough to move a calculated 1:76 to anywhere between about 1:75.6 and 1:76.4.
- Paint thickness, mould flash, warp and rounded edges all sit inside the number you measured.
- The prototype dimension is often itself approximate, quoted differently by different sources, or varies between production batches of the real thing.
So treat a calculated scale as “consistent with” a convention rather than proof of it, and measure the longest available dimension to push proportional error down. Exactness protects you from arithmetic drift through a chain of conversions; it cannot tighten a ruler.
What conversion does not give you
Geometry converts; ecosystems do not. Track gauge, couplers, wheel standards, wire gauges, fasteners, decals and figure proportions are defined by their own standards, and the correct percentage does not make a part available in the new scale. Moulded and printed detail sized for one scale usually reads wrong at another — too coarse when enlarged, illegible when reduced. Always check the standard for the field, not just the ratio.