Scale Conversion Calculator & Scale Factor Calculator
Scale a measurement to a larger or smaller measurement, which is useful for architecture, modeling, and other projects. You can also add the real size and scaled size to find the scale factor.
Find the Scaled Size
Find the Real Size
Find the Scale Factor
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How to Scale a Measurement
Making a measurement smaller or larger, known as scale conversion, requires a common scale factor, which you can use to multiply or divide all measurements by.
To scale a measurement down to a smaller measurement, for instance, when making a blueprint, simply divide the real measurement by the scale factor. The scale factor is commonly expressed as 1:n or 1/n, where n is the factor.
For example, if the scale factor is 1:8 and the real measurement is 32, divide 32 ÷ 8 = 4 to convert.
To convert a scaled measurement up to the actual measurement, simply multiply the smaller measurement by the scale factor. For example, if the scale factor is 1:8 and the smaller length is 4, multiply 4 × 8 = 32 to convert it to the larger actual size.
A common tool used to scale a measurement from a real-world measurement is an architect’s scale rule. These are often used for scaling drawings and blueprints for buildings.
There are also engineering rules that are primarily used in civil engineering to scale measurements for roadways and land development.
How to Find the Scale Factor
A scale factor is a ratio of two corresponding measurements or lengths. You can use the factor to increase or decrease the dimensions of a geometric shape, drawing, or model to different sizes. You can find the scale factor in a few easy steps.
Step One: Use the Scale Factor Formula
Since the scale factor is a ratio, the first step to finding it is to use the following formula:
scale factor = scaled size / real size
So, the scale factor is a ratio of the scaled size to the real size.
Step Two: Simplify the Fraction
The next step is to reduce or simplify the fraction.
If you’re scaling down, then the ratio should be shown with a numerator of 1. If you’re scaling up, then the ratio should be shown with a denominator of 1.
To find the final scale factor when you’re scaling up, reduce the ratio to a fraction with a denominator 1. To do this, divide both the numerator and the denominator by the denominator.
If you’re scaling down, then reduce the fraction so that the numerator is 1. You can do this by dividing both the numerator and the denominator by the numerator.
Our fraction simplifier can help with this step if needed.
Step Three: Rewrite the Fraction as a Ratio
Finally, rewrite the fraction as a ratio by replacing the fraction bar with a colon. For instance, a scale factor of 1/10 can be rewritten as 1:10.
For example, let’s find the scale factor used on an architectural drawing where ½” on the drawing represents 12″ on the final building.
Replace the values in the formula above.
scale factor = ½” / 12″
Since the drawing is scaled down, then the scale factor should be reduced to a fraction with a denominator of 1.
Multiply both the numerator and denominator by 2 to simplify.
scale factor = ½” × 2 / 12″ × 2 = 1 / 24
And finally, rewrite the fraction as a ratio.
scale factor = 1 / 24 = 1:24
Thus the scale factor for this drawing is 1:24.
How to Reduce the Scale Factor
If you already know the scale factor, but it is not in the form of 1:n or 1/n, then some additional work is needed to reduce or simplify it. If the ratio is 2:3, for example, then you’ll need to reduce it so that the numerator is 1.
Use our ratio calculator to reduce a ratio. You can also reduce a ratio by dividing both the numerator and the denominator by the numerator.
For example: reduce 2/3 by dividing both numbers by 2, which would be 1/1.5 or 1:1.5.
2 ÷ 2 = 1
3 ÷ 2 = 1.5
scale factor = 1:1.5
You can quickly find the scale factor for an architectural scale by inverting the fraction, then multiplying it by 12 (inches/foot).
For example, to find the scale factor for 1/16″ = 1′, start by inverting the fraction 1/16 so that it becomes 16/1. Then, multiply that by 12, which is 192. So, the scale factor for 1/16″ = 1′ is 1:192.
|Drawing Scale||Scale Factor|
|1/16″ = 1′||1:192|
|3/32″ = 1′||1:128|
|1/8″ = 1′||1:96|
|3/16″ = 1′||1:64|
|1/4″ = 1′||1:48|
|3/8″ = 1′||1:32|
|1/2″ = 1′||1:24|
|3/4″ = 1′||1:16|
|1″ = 1′||1:12|
|1 1/2″ = 1′||1:8|
|3″ = 1′||1:4|
You can quickly find the scale factor for an engineering, or civic, scale by multiplying the feet portion by 12 (inches/foot).
For example, to find the scale factor for 1″ = 30′, multiply 30′ by 12, which is 360. So, the scale factor for 1″ = 30′ is 1:360.
|Drawing Scale||Scale Factor|
|1″ = 10′||1:120|
|1″ = 20′||1:240|
|1″ = 30′||1:360|
|1″ = 40′||1:480|
|1″ = 50′||1:600|
|1″ = 60′||1:720|
|1″ = 70′||1:840|
|1″ = 80′||1:960|
|1″ = 90′||1:1080|
|1″ = 100′||1:1200|
|Scale Factor||Model Type|
|1:4||steam trains, RC planes|
|1:8||steam trains, cars|
|1:12||cars, motorcycles, dollhouses|
|1:16||steam trains, cars, motorcycles, military vehicles, figures|
|1:20||formula one cars|
|1:24||cars, trucks, aircraft, dollhouses|
|1:32||1 gauge trains, cars, aircraft, figures|
|1:43||O-gauge trains, cars, trucks|
|1:48||O-gauge trains, dollhouses, Lego minifig|
|1:64||S-gauge trains, diecast cars, Hotwheels:Matchbox|
|1:72||aircraft, military vehicles, boats, cars|
|1:76||aircraft, military vehicles|
|1:87||HO-gauge trains, military vehicles|
|1:144||ships, rockets, spacecraft|
|1:160||N-gauge trains, wargaming|