Scale Conversion Calculator

Q: What scale is 1/4 inch equals 1 foot?

It is 1:48 . There are 12 inches in a foot, and 12 ÷ 0.25 = 48. So one inch on the plan stands for 48 inches of real building. Other common architectural scales: 1 in = 1 ft → 1:12 1/2 in = 1 ft → 1:24 3/8 in = 1 ft → 1:32 1/4 in = 1 ft → 1:48 3/16 in = 1 ft → 1:64 1/8 in = 1 ft → 1:96 1/16 in = 1 ft → 1:192

Q: How many millimeters is one real foot in HO scale?

About 3.5 mm . HO scale is 1:87. One foot is 304.8 mm, and 304.8 ÷ 87 = 3.5 mm. Quick HO numbers: 1 real meter = 11.5 mm, a 6 foot person = 21 mm tall, a 40 foot boxcar = 140 mm long.

Introduction

The Scale Conversion Calculator changes a real size into a drawing size, or a drawing size back into a real size. Type a number, pick your units, pick your scale, and get the answer right away.

You can go both ways. Use Real Size → Scale Drawing to find how big something should be on your plan or model. Use Scale Drawing → Real Size to measure a line on a map or blueprint and learn its true size.

It works with millimeters, centimeters, meters, inches, and feet. You can mix them too, like inches in and millimeters out. Pick from common scales such as 1:87 for HO trains, 1:72 for model planes, 1:48 for floor plans, or 1:24000 for maps. If your scale is not listed, enter your own number after the 1.

Every answer comes with the same result in all five units, clear step-by-step math, and a chart that shows the same real size drawn at nearby scales. Model builders, architects, students, map readers, and anyone working with scale drawings can use it to check their work fast.

How to use our Scale Conversion Calculator

Type in a measurement, pick your scales and units, and the calculator shows the matching size at your new scale, plus the same answer in all units and a step-by-step solution.

Conversion Direction: Choose "Real Size → Scale Drawing" to shrink a real measurement down to drawing or model size. Choose "Scale Drawing → Real Size" to blow a drawing measurement back up to real life.

Measurement: Enter the number you measured. Decimals are fine, like 12.5. It must be more than zero.

Input Unit: Pick the unit that matches the number you just typed: millimeters, centimeters, meters, inches or feet.

Source Scale: Pick the scale your measurement is already in. Use 1:1 for a true real-world size, or pick a model, drawing or map scale from the list.

Target Scale: Pick the scale you want the answer in, such as 1:87 for HO trains or 1:100 for a floor plan.

Custom Scale Denominator: If your scale is not in the list, choose "Custom" and type only the second number. Type 50 to get 1:50.

Output Unit: Pick the unit you want your answer in. It can be different from the input unit.

Swap ⇄ button: Click this to flip the source and target scales and units in one step.

Calculate and Reset: Results update as you type, but you can click Calculate to refresh. Click Reset to go back to the starting values. Use the Copy button to copy your answer.

What Is Scale Conversion?

A scale tells you how a drawing or model compares to the real thing. It is written as a ratio, like 1:72. That means 1 unit on the model equals 72 of the same units in real life. So a plane that is 72 feet long would be 1 foot long as a 1:72 model.

Scale conversion is the math that switches between real size and scaled size. You either shrink a real measurement down to fit your drawing, or blow a drawing measurement back up to find the true size.

How Scale Math Works

The rule is simple:

Real size → scale size: divide the real length by the scale number. At 1:50, a 10 m wall is 10 ÷ 50 = 0.2 m, or 200 mm, on paper.
Scale size → real size: multiply the drawing length by the scale number. At 1:50, a 35 mm line on paper is 35 × 50 = 1,750 mm, or 1.75 m, in real life.

To go from one scale to another scale, divide the first scale number by the second one, then multiply your measurement by that answer. Going from 1:24 to 1:48 means the part gets half as big.

Big Scale Number vs. Small Scale Number

A bigger second number means a smaller model. A 1:200 building model is tiny. A 1:12 doll house model is much larger. People call a small second number a "large scale" and a big second number a "small scale," which can be confusing at first. Just remember: the more you divide by, the smaller it gets.

Common Scales and Where They Are Used

1:12: doll houses and miniatures (1 inch = 1 foot)
1:24, 1:18: diecast and model cars
1:35: military tanks and figures
1:48, 1:72, 1:144: plastic aircraft kits
1:87 (HO), 1:160 (N), 1:220 (Z): model railroads
1:50, 1:100, 1:200: building plans and floor plans
1:24,000, 1:50,000: maps and land surveys

Tips for Accurate Results

Keep your units clear. Mixing inches and millimeters is the most common mistake, so pick the unit you will actually measure with and stick to it. For model work, millimeters are usually easiest because you avoid fractions. Also check the scale printed on the drawing before you measure, since plans are often printed smaller than full size and the printed scale bar may no longer match.

Why Scale Matters

Scale lets a whole house, ship, or city fit on one sheet of paper without losing the shape. Every part shrinks by the same amount, so angles stay the same and parts still fit together. Get the scale wrong and doors will not match walls, or a model part will not fit its kit.

Formulas used

Convert input measurement to meters

L_{\text{m}} = V \times f_{\text{in}}

Scale ratio between source and target scales

R = \frac{D_s}{D_t}

Scaled result in meters

L_{\text{out,m}} = L_{\text{m}} \times R

Convert result to the output unit

L_{\text{out}} = \frac{L_{\text{out,m}}}{f_{\text{out}}}

Overall conversion formula

L_{\text{out}} = \frac{V \times f_{\text{in}} \times \dfrac{D_s}{D_t}}{f_{\text{out}}}

Real-world size of the measurement

L_{\text{real,m}} = V \times f_{\text{in}} \times D_s

Size at a comparison scale (chart bars)

L_{d} = \frac{L_{\text{real,m}}}{d \times f_{\text{out}}}

Frequently asked questions

What scale is 1/4 inch equals 1 foot?

It is 1:48. There are 12 inches in a foot, and 12 ÷ 0.25 = 48. So one inch on the plan stands for 48 inches of real building.

Other common architectural scales:

1 in = 1 ft → 1:12
1/2 in = 1 ft → 1:24
3/8 in = 1 ft → 1:32
1/4 in = 1 ft → 1:48
3/16 in = 1 ft → 1:64
1/8 in = 1 ft → 1:96
1/16 in = 1 ft → 1:192

How do I find the scale of a drawing if it is not written on it?

Find one part where you know the true size, like a door or a car. Measure that same part on the drawing. Then divide:

Real size ÷ drawing size = scale number

Example: a door is really 2,000 mm tall and it is drawn 20 mm tall. 2,000 ÷ 20 = 100, so the drawing is 1:100. Use the same unit on both sides of the division.

Which is bigger, 1:48 or 1:72?

1:48 is bigger. The smaller the second number, the larger the model. At 1:48 you divide the real size by 48, but at 1:72 you divide by 72, so the 1:72 version comes out smaller.

A 36 foot plane is 9 inches long at 1:48 and only 6 inches long at 1:72.

How many millimeters is one real foot in HO scale?

About 3.5 mm. HO scale is 1:87. One foot is 304.8 mm, and 304.8 ÷ 87 = 3.5 mm.

Quick HO numbers: 1 real meter = 11.5 mm, a 6 foot person = 21 mm tall, a 40 foot boxcar = 140 mm long.

What does a 1:24,000 map scale mean?

It means 1 unit on the map equals 24,000 of the same units on the ground. So 1 inch on the map is 24,000 inches, which is 2,000 feet.

That makes 1 mile about 2.64 inches on the map. This is the scale used on classic USGS 7.5-minute topo maps.

What is a scale factor?

The scale factor is the number you multiply or divide by to change sizes. In 1:50, the scale factor is 50.

Going to the drawing: divide the real size by 50.
Going back to real life: multiply the drawing size by 50.

To switch between two scales, divide the first scale number by the second. From 1:24 to 1:48, that is 24 ÷ 48 = 0.5, so the part is half as big.

How do I convert a model from 1:35 to 1:48?

Divide 35 by 48 to get 0.729. Multiply every 1:35 measurement by 0.729 to get the 1:48 size.

Example: a 200 mm long 1:35 tank becomes 200 × 0.729 = 145.8 mm at 1:48. Use the same factor on every part so the shape stays right.

Does printing a drawing change its scale?

Yes. Printing with "fit to page" or "shrink to fit" makes the drawing smaller, so the printed scale no longer matches the scale written on it.

Always print at 100% or "actual size." If you are not sure, check the printed scale bar with a ruler before you measure anything.

What does 1:1 scale mean?

1:1 means full size. One millimeter on the drawing is one millimeter in real life. Nothing is shrunk or blown up.

It is used for shop drawings, templates, and cut patterns you can lay right on the material.

What is the difference between an architect's scale and an engineer's scale?

An architect's scale uses feet and inches, like 1/4 in = 1 ft (1:48). It is used for buildings and rooms.

An engineer's scale uses whole feet per inch, like 1 in = 20 ft (1:240) or 1 in = 50 ft (1:600). It is used for site plans, roads, and land. Reading a plan with the wrong ruler gives wrong sizes.

How do I turn a percentage like 50% into a scale ratio?

Divide 100 by the percent. 50% is 100 ÷ 50 = 2, so it is 1:2. 25% is 1:4, and 10% is 1:10.

Going the other way, divide 1 by the scale number and multiply by 100. 1:8 is 12.5%.

Why do model railroads use scales like 1:87 and 1:160?

Those odd numbers come from track width, not round math. HO track is 16.5 mm wide, which matches real 4 ft 8.5 in track at 1:87. N gauge track is 9 mm wide, which works out to 1:160.

The gauge came first, so the scale number had to fit it.

What does NTS mean on a plan?

NTS means "not to scale." The drawing shows how parts connect, but you cannot measure it with a scale ruler and trust the answer.

On an NTS drawing, always use the written numbers, called dimensions, instead of measuring the lines.

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