Scale Conversion Calculator
Convert real-world dimensions to model scale dimensions. Supports common model scales like HO (1:87), N (1:160), O (1:48), and more.
About this calculator
This calculator converts a real-world dimension into the equivalent size on a scale model. It first normalizes Real Dimension to inches based on Input Unit (feet are multiplied by 12, millimeters divided by 25.4, and meters multiplied by 39.3701, while inches pass through unchanged), then divides that inch value by Scale Denominator -- the "87" in a 1:87 HO-scale ratio, or "160" in N scale -- to get Model Size (inches). Model Size (mm) is the same result converted to millimeters by multiplying by 25.4, useful for calipers marked in metric.
Scale Factor is simply 1 divided by Scale Denominator, expressed as a decimal multiplier you can apply directly to any other real-world measurement in the same scale without re-running the calculator, and Model-to-Real Ratio just restates Scale Denominator as the "1:X" figure printed on most scale model packaging. Because every output is a direct division or multiplication by Scale Denominator, a larger denominator always produces a smaller model -- N scale's 1:160 shrinks a given real dimension much further than O scale's 1:48 does. Common denominators include 48 (O), 64 (S), 76 (OO), 87 (HO), and 160 (N), though the calculator accepts any denominator from 1 to 1,000 for custom or less common scales.
Convert
Results
How to Use This Calculator
- Enter Real Dimension, Scale Denominator, and Input Unit.
- Select the Input Unit — Inches, Feet, Millimeters, or Meters — to match how your real dimension is measured.
- Set Scale Denominator to your target scale (e.g., 87 for HO, 160 for N).
- Review Model Size (inches) and Model Size (mm).
- Use Scale Factor and Model-to-Real Ratio to inform your decision.
How the result changes with Scale Denominator
| Scale Denominator | Model Size (inches) | Model Size (mm) |
|---|---|---|
| 44 | 1.636 | 41.56 |
| 65 | 1.108 | 28.14 |
| 131 | 0.55 | 13.96 |
| 218 | 0.33 | 8.39 |
What each input means
- Real Dimension
- The real-world dimension to convert to model scale
- Scale Denominator
- The scale ratio denominator (e.g., 87 for 1:87 HO scale, 160 for N scale)
- Input Unit
- Unit of the real-world measurement
How this is calculated
Worked example, using the default values
- Identify Input ParametersReal Dimension = 72, Scale Denominator = 87, Input Unit = 1 = 3 input(s) provided
- Calculate Model SizeModel Size0.828 = 0.828
- Calculate Model SizeModel Size21.02 = 21.02
- Calculate Scale FactorScale Factor0.0115 = 0.0115
- Calculate Model-to-Real RatioModel-to-Real Ratio87 = 87
Engine last updated . Checked against 2 independently-derived tests — how we verify calculators. Built by Paul Gunder, a software engineer, not a licensed financial, medical, or legal professional.
Frequently Asked Questions
Why does Model Size (inches) shrink when I raise Scale Denominator?
Model Size (inches) is Real Dimension (converted to inches) divided directly by Scale Denominator. A larger denominator means each inch of the real object is divided into more parts to find the model equivalent, so the model gets smaller -- moving from HO scale's denominator of 87 to N scale's 160 shrinks the model to about 54% of its former size for the same real-world dimension (87 / 160 ≈ 0.54), not a full half, since 160 is only about 1.84x 87, not quite double.
What's the difference between Scale Factor and Model-to-Real Ratio?
Scale Factor is 1 divided by Scale Denominator, shown as a decimal (e.g., about 0.0115 for 1:87 HO scale) that you can multiply directly against any real dimension to get its model equivalent. Model-to-Real Ratio just displays Scale Denominator itself with a "1:" prefix, matching the "1:87" or "1:160" notation printed on commercial model packaging -- the two outputs describe the same ratio, just formatted for different uses.
Does the Input Unit I select change the final scale ratio?
No. Input Unit only controls how Real Dimension is converted to inches before the scale division happens -- feet, millimeters, and meters are all normalized to inches first using fixed conversion factors, then divided by Scale Denominator the same way regardless of which unit you originally entered. Scale Factor and Model-to-Real Ratio depend only on Scale Denominator, never on Input Unit.
Why do I need Model Size in both inches and millimeters?
Different hobby tools default to different units -- a caliper or ruler marked in inches works directly from Model Size (inches), while a metric caliper or a 3D printer's native units call for Model Size (mm), which is the same value multiplied by 25.4. Both are shown together so you don't have to do the unit conversion by hand after already converting for scale.
What scale denominator should I use for a common model railroad scale?
Common denominators include 160 for N scale, 87 for HO scale, 76 for OO scale (the UK equivalent of HO), 64 for S scale, and 48 for O scale -- enter whichever denominator matches your layout or kit. The calculator itself doesn't validate that a denominator corresponds to a named scale, so double-check the number against your manufacturer's packaging if you're not sure which named scale you're working in.
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