Math calculators

Scale Calculator

Updated Sep 19, 2026 By Infinity Calculator
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Scale Converter

Convert a measurement from one scale ratio to another, in any of 9 length units.
Length as measured at the "From" scale.
Unit of the measurement above.
Auto-fills the ratio boxes; or pick "Custom".
From Scale (model : real)
Unit used for the converted result.
Auto-fills the target ratio boxes.
To Scale (model : real)
mm
Source: Measurement Value → Converted Result (the result field is read-only).
Working (this calculation)
Proportional Diagram

Step-by-Step Solution

Find the Scale

Know the model size and the real size? Derive the scale ratio.

Plan Resize Percentage

Work out the photocopier / plotter zoom needed to reprint a drawing at a different scale.
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Multi-Scale Comparison Table

One real-world measurement, shown as a model length across every scale you tick (2–12 scales).
Scale Selection (tick 2 to 12 scales)
6 scales selected.
Model Length at Each Scale
Scale Common Name Model Length Proportional Bar
Visual Comparison

Introduction

A scale is a ratio that links a model to the real thing. A 1:48 model plane is 48 times smaller than the real plane. This Scale Calculator converts lengths between scales, works out a scale ratio from two sizes, and shows the print zoom percent for a plan.

You can do four things with it:

  • Convert between scales. Type a length, pick a starting scale and a target scale, and get the new size. It works with 9 units, from millimeters to miles.
  • Find the scale. Enter the model size and the real size, and the tool gives you the ratio, like 1:48.
  • Resize a plan. Get the exact zoom percent to reprint a drawing at a new scale.
  • Compare many scales at once. See one real measurement shown as a model length in up to 12 scales, with a table and a chart.

Common scales are built in, so you can just pick one. Model train scales like HO, N, O, and Z are there. So are diecast car scales, hobby kit scales, and map and building scales. You can also type your own ratio.

Every answer comes with step-by-step math and a simple bar diagram, so you can see how the result was found. That is useful for model builders, architects, students, map readers, and anyone who needs to shrink or grow a size the right way.

How to use our Scale Calculator

Type in your measurement, pick your units, and choose the scale ratios you are working with. The calculator gives you the converted length, the scale ratio, the print resize percent, and a table that compares many scales at once.

Measurement Value: Enter the length you already have at the "From" scale. You can also tap the microphone button and say the number out loud.

From Unit: Pick the unit of that measurement, such as mm, cm, m, inches, or feet.

From Scale Preset: Choose a ready-made scale like 1:48, 1:87 (HO), or 1:100. Pick "Custom" if you want to type your own.

From Scale (model : real): Type the two numbers of your starting ratio. The left box is the model side, the right box is the real-world side.

To Unit: Pick the unit you want the answer shown in.

To Scale Preset: Choose the scale you want to convert to, or pick "Custom".

To Scale (model : real): Type the two numbers of your target ratio if you are not using a preset.

Converted Result: This box shows your answer. Use the copy button to save it, or press "Switch source field" to type the answer and work backwards.

Model / Scale Length: In the Find the Scale box, enter how long the model or drawing is.

Model Length Unit: Pick the unit for that model length.

Real-World / Actual Length: Enter how long the real object is. The tool then shows the scale ratio, like 1:48.

Real Length Unit: Pick the unit for the real-world length.

Original Scale Denominator: In the Plan Resize box, enter the bottom number of the drawing's current scale, such as 100 for 1:100.

Original Scale Preset: Or pick the current scale from the list to fill that number for you.

Target Scale Denominator: Enter the bottom number of the scale you want to print at, such as 50 for 1:50.

Target Scale Preset: Or pick the new scale from the list. The tool shows the zoom percent to set on your copier or plotter.

Real-World Measurement: In the comparison table, enter one real length you want to see across many scales.

Measurement Unit: Pick the unit of that real-world length.

Result Display Unit: Pick the unit for the model lengths in the table and chart.

Scale Selection: Tick 2 to 12 scales to compare. Use "Clear all scales" to start over.

What Is a Scale?

A scale tells you how a model, map, or drawing compares to the real thing. It is written as a ratio, like 1:48. That means 1 unit on the model stands for 48 of the same units in real life. So 1 inch on the model equals 48 inches on the real object.

How Scale Ratios Work

The first number is the model side. The second number is the real-world side. When the second number is bigger, the model is smaller than the real object. This is called a reduction, and it is used for cars, trains, buildings, and maps. When the first number is bigger, like 2:1, the model is larger than the real object. This is an enlargement, used for tiny parts like screws or bugs.

The Two Basic Math Steps

Every scale problem uses simple multiplying and dividing:

  • Model size → real size: multiply the model length by the scale number. A 4 in part at 1:48 is 4 × 48 = 192 in (16 ft) in real life.
  • Real size → model size: divide the real length by the scale number. A 24 ft wall at 1:48 becomes 24 ÷ 48 = 0.5 ft (6 in) on the model.

To move a measurement from one scale to another, you do both steps. First go up to real size, then come back down at the new scale.

Finding an Unknown Scale

If you know both sizes, divide the real length by the model length. Make sure both are in the same unit first. A 125 mm model of a 6 m truck is 6000 mm ÷ 125 mm = 48, so the scale is 1:48.

Resizing Printed Plans

To reprint a drawing at a new scale, divide the old scale number by the new one, then multiply by 100. Going from 1:100 to 1:50 gives 100 ÷ 50 × 100 = 200%, so you print it twice as big. Going from 1:50 to 1:100 gives 50%, or half size.

Common Scales You Will See

  • Model trains: HO 1:87, N 1:160, O 1:48, Z 1:220, OO 1:76
  • Diecast cars: 1:18, 1:24, 1:43, 1:64
  • Plastic kits: 1:35 armor, 1:72 and 1:144 aircraft, 1:350 and 1:700 ships
  • Buildings and plans: 1:50, 1:100, 1:200, 1:500
  • Maps: 1:1200, 1:25000, 1:50000
  • Dollhouses: 1:12

Tips to Avoid Mistakes

Always change both numbers to the same unit before you divide. Scale changes length only, so a model at 1:10 is 10 times shorter but takes up 100 times less area and 1000 times less volume. A smaller scale number, like 1:24, means a bigger model. A larger scale number, like 1:700, means a tiny model.


Formulas used

Unit conversion to millimetres (base unit)
L_{\text{mm}} = L_{u} \times k_{u}
Scale conversion between two scale ratios
L_{\text{target}} = L_{\text{source}} \times \frac{B_{s}}{A_{s}} \times \frac{A_{t}}{B_{t}}
Real-world length from a scaled measurement
L_{\text{real}} = L_{\text{source}} \times \frac{B_{s}}{A_{s}}
Find the scale (reduction) from model and real lengths
\text{scale} = 1 : \frac{L_{\text{real,mm}}}{L_{\text{model,mm}}}
Find the scale (enlargement, when model is larger)
\text{scale} = \frac{L_{\text{model,mm}}}{L_{\text{real,mm}}} : 1
Plan resize (copier zoom) percentage
P = \frac{D_{\text{original}}}{D_{\text{target}}} \times 100\%
Model length at a given scale (comparison table)
L_{\text{model}} = L_{\text{real}} \times \frac{A}{B}

Frequently asked questions

Which is bigger, 1:24 scale or 1:48 scale?

1:24 is bigger. The smaller the second number, the larger the model.

At 1:24, a real 12 ft car becomes 6 in long. At 1:48, that same car is only 3 in long. So 1:24 models are twice the size of 1:48 models.

What scale is 1/4 inch equals 1 foot?

It is 1:48. One foot has 12 inches, and 12 ÷ 0.25 = 48.

Other common architect scales:

  • 1 in = 1 ft → 1:12
  • 1/2 in = 1 ft → 1:24
  • 1/4 in = 1 ft → 1:48
  • 1/8 in = 1 ft → 1:96
  • 1/16 in = 1 ft → 1:192

How do I find real distance on a 1:25,000 map?

Measure the map distance, then multiply by 25,000.

On a 1:25,000 map, 1 cm equals 25,000 cm, which is 250 m. So 4 cm equals 1 km. In inches, 1 in equals about 0.39 miles.

What scale are Hot Wheels and Matchbox cars?

Most are about 1:64. A real car near 16 ft long comes out about 3 in long.

They are not exact. Makers often stretch or shrink a model so every car fits the same package size, so one car may be closer to 1:55 and another closer to 1:70.

How big is 1:12 dollhouse furniture?

At 1:12, one inch stands for one foot. Divide the real size in inches by 12.

  • A 30 in tall table → 2.5 in
  • A 6 ft (72 in) door → 6 in
  • A 5 ft (60 in) sofa → 5 in

What is the difference between scale factor and scale ratio?

They say the same thing in two ways. The ratio 1:48 is written with a colon. The scale factor is the single number you multiply or divide by, which is 48.

Divide by the factor to shrink a real size to model size. Multiply by it to grow a model size to real size.

How do I convert a 1:72 model measurement to 1:48?

Multiply by 72 ÷ 48, which is 1.5.

A 100 mm wing at 1:72 becomes 150 mm at 1:48. The rule works both ways: to go from 1:48 back to 1:72, multiply by 48 ÷ 72, or about 0.667.

How tall is a 6 foot person in HO scale?

About 21 mm, or a bit over 3/4 of an inch.

HO scale is 1:87. A 6 ft person is 1,828.8 mm tall, and 1,828.8 ÷ 87 = 21 mm. In N scale (1:160) the same person is only 11.4 mm tall.

What is the difference between N scale and HO scale?

HO is 1:87 and N is 1:160, so N trains are about half the size of HO trains.

HO is easier to handle and has more detail. N lets you fit more track and scenery in the same space.

Does printing a plan at 50% change its scale?

Yes. Printing at 50% makes every line half as long, so the scale number doubles.

A 1:50 drawing printed at 50% becomes 1:100. A 1:100 drawing printed at 200% becomes 1:50. Any printed scale bar on the sheet stays correct, but the written scale note does not.

What does 28mm scale mean in wargaming?

It means a human figure stands about 28 mm tall, measured from the feet to the eyes or head.

That works out to roughly 1:56 for a 6 ft person. Many "heroic" 28 mm figures are chunkier and sit closer to 1:48, so brands do not always match.

What does a 1:1 scale mean?

It means full size. One unit on the drawing equals one unit on the real object, so nothing is shrunk or grown.

Shop drawings and templates often use 1:1 so you can lay the part right on the paper and check the fit.

Why does my scale model look too small when the math says it is right?

Because scale only changes length, not area or volume.

A model at 1:10 is 10 times shorter, but it covers 100 times less surface and holds 1,000 times less volume. That is why a halved model looks far smaller than half.