Teaching · For Teachers · Ratios

A 50-foot boxcar
is 175 millimeters
in HO.

Choose a scale and type real-world sizes in any unit. The calculator gives the model size of each in millimeters and inches, or works backward from a model to full size, and shows the ratio arithmetic behind it.

Convert sizesWhat you get

The scale conversion calculator

The worked example is made up: a boxcar, a platform, a figure and a door for an HO station scene. Nothing you type leaves this browser.

Loading the calculator. If nothing appears, turn on JavaScript.

What you get

Teaching · For TeachersFree

What you finish with
Each measurement converted to model size or full size, in millimeters and inches or feet, with the scale as a fraction and the steps. It prints as a list and downloads as a spreadsheet.
Who it is for
Model railroaders and builders, middle school students learning ratios, teachers using models to teach scale, and families building dioramas.
Format
Browser calculator for a phone, tablet or computer, by touch or keyboard. Up to 40 measurements. Prints a list; downloads a spreadsheet (.csv); export and import a file.
Access
Free. No account, no sign-in and nothing to install. Everything you type stays in this browser; nothing is sent to Caveat.
Where it lives
The For Teachers space in Caveat Teaching.
Support
Questions, a correction or a request: team@caveatacademic.com.

How to use it

  1. Name the project and choose the scale.
  2. Choose full size to model, or model to full size.
  3. Add each measurement with its unit.
  4. Read the converted sizes and the steps.
  5. Print the list or download the spreadsheet for the workbench.

Convert sizes

How the conversion works

One ratio, one unit.

The worked example: a boxcar in HOFull size50 fta 50-foot boxcarIn millimeters15,240 mm50 × 304.8Divide by the scale÷ 87.1HOModel175.0 mmabout 6.89 inThe worked example: a boxcar in HOFull size50 fta 50-foot boxcarIn millimeters15,240 mm50 × 304.8Divide by the scale÷ 87.1HOModel175.0 mmabout 6.89 in
Convert the real size to one unit, then divide by the scale number; going from a model back to full size, multiply instead.

The arithmetic

A scale of 1:N means every length on the model is one Nth of the real length, in any unit. Put the real size into millimeters first, using the exact definitions 1 inch = 25.4 mm and 1 foot = 304.8 mm, then divide by N. To go from a model to full size, multiply by N. Areas scale by N squared and volumes by N cubed, which is why a model car weighs so little.

About the scale numbers

Railroad scales are set by standards bodies: HO is 1:87.1, N is 1:160, O is 1:48 in the United States. Plastic kits use round ratios such as 1:35 and 1:72. A manufacturer may round or stretch a scale, so check the box against a real dimension before cutting.

Sources

  1. National Model Railroad Association. Standard S-1.2, General: scale ratios for HO, N, O, S and Z (nmra.org).
  2. NIST Special Publication 811, Guide for the Use of the International System of Units (2008): the inch as exactly 25.4 mm.
  3. Common Core State Standards for Mathematics, Grade 7, 7.G.A.1: scale drawings and computing actual lengths from a scale.
  4. National Council of Teachers of Mathematics. Illuminations lessons on scale and proportion (nctm.org).

The worked example is made up. Your measurements stay in this browser. Support: team@caveatacademic.com.