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Scale Factor Calculator

Scale Factor Calculator

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Conversion Type

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You Want To Calculate

You Want To Calculate

Scale Factor Form

Scaled Length

 

Real Length

 

d1

d2

Scaled Area

 

Real Area

 

Scaled Volume

 

Real volume

 

Scale Factor

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Table of Content

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With the help of this free online model scale calculator, you can swiftly determine the actual length and the scaled length with respect to the scaled ratio. Moreover, let this free scale converter do the conversions regarding model size, model factor, volume change, and area change in a glimpse of an eye. You may be astounded enough, but it really works. Let’s find how!

Scale Factor:

“The ratio of the two corresponding lengths or measurements is known as the scale factor”

scale factor

Basically, the scale factor is used to increase or decrease the size of any geometrical figure. Our best scale factor calculator allows you to estimate the scale factor most efficiently by including minimal errors.

Scaling Up:

If you are scaling up, then your fraction must be containing a numerator of 1.

Scaling Down:

Similarly, if you are scaling down, your ratio must contain 1 in its denominator.

For instance, you could make use of our free online dilation calculator to determine the scale factor more precisely.

Scale Factor Equation:

You can go for calculating the scale factor with the help of the following formula:

Scale Factor = Scaled Size/Real Size

Steps Involved In Determining The Scale Factor:

Below are the key steps that you must opt to determine the scale factor of any object:

  • Use the scale factor formula
  • Go for simplifying the fraction
  • Reconvert the fraction as the ratio

Important Formulas:

Let us have a look at some crucial formulas that are very important in finding the scaled and real measurements of length, volume, and area that you could also determine with the aid of our best scale calculator. How does it sound? Really great? Good enough! Anyways, let’s move forward:

Length:

Scale factor of length = Scaled Length/Real Length

Scale Length = (d1/d2) * Real Length

Real Length = (d1/d2) * Scale Length

Area:

Scale Factor = sqrt{(Scale Area/Real Area)}

Scale Area = (d1/d2) * Real Area

Real Area = (d1/d2) * Scale Area

Volume:

Scale Factor = ⅓ * (Scale Volume/Real Volume)

Scale Volume = (d1/d2) * Real Volume

Real Volume = (d1/d2) * Scaled Volume

All of the above expressions are also taken into consideration by the scale factor calculator while doing instant calculations.

Conversion Charts:

Here we have enlisted some scale factors of the architectural scales below:

Architectural 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

 

Moreover, you can also use a scale calculator to analyze the scale factors of any other architectural measurements.

Scale Factors For Various Models:

What about going through the scale factors of some important models as described below on the table:

Scale Factor Model Type
1:4 steam trains, RC planes
1:8 steam trains, cars
1:10 figures
1:12 cars, motorcycles, dollhouses
1:16 steam trains, cars, motorcycles, military vehicles, figures
1:18 diecast cars
1:20 formula one cars
1:22.5 G-gauge trains
1:24 cars, trucks, aircraft, dollhouses
1:25 cars, trucks
1:32 1 gauge trains, cars, aircraft, figures
1:35 military vehicles
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
1:96 ships, spacecraft
1:100 aircraft, spacecraft
1:120 TT-gauge trains
1:144 ships, rockets, spacecraft
1:160 N-gauge trains, wargaming
1:200 aircraft, ships
1:220 Z-gauge trains
1:285 wargaming
1:350 ships
1:700 ships
1:720 ships

 

How To Calculate Scale Factor?

What about resolving a couple of examples to understand together what measurements the scale factor deals with.

Example # 01:

What would be the real length of the object with a scale length of 64 cm into inches and a scale factor of 5 1 in inches?

Solution:

Here we have:

Scale factor = 5 1 in inches = 5/1 inches

Scale length = 64 cm into inches = 24.4 inches

Now performing scale conversion from the scale to real measurements as follows:

Real Length = (d1/d2) * Scale Length

Real Length = (5/1) * 24.4 inches

Real Length = (5/1) * 24.4 inches

Real Length = 122 inches

Which is the required length of the object if not scaled down that you could verify if you use our best scale calculator.

Example # 02:

What would be the scale factor when real length is 20m to feet and scale length is 5 meters in feet?

Solution:

First of all we have:

Real length = 20m = 65.6 feet

Scale length = 5m = 16.4 feet

Here we have the following formula:

Scale factor of length = Scaled Length/Real Length

Scale factor of length = 65.6 feet/16.4 feet

Scale factor of length = 4 feet

Example # 03:

What is the change in the scale factor when a certain length of 20 inches is scale on a scale of 1 to 10? Keep in mind that the measurements are supposed to be centimeters.

Solution:

First of all, converting measurements from inches to centimeters as follows:
20in to cm = 20 * 2.54

= 50.8 cm

Now we have:

Scale Length = (d1/d2) * Real Length

Scale Length = (1/10) * 50.8 cm

Scale Length = 5.08 cm

How Scale Calculator Works?

This free scale finder exactly finds the real and scaled size values of the figures as per the desired dimensions. Let us have a look at its working!

Input:

  • First of all, select which quantity you want to do calculations for
  • From the next drop down list, select whether you want to calculate real size, scale size, or scale factor
  • After you make a selection, go for entering the wanted parameters in their designated fields and select the respective units
  • At the end, tap the calculate button

Output:
The free online ratio scale conversion calculator calculates:

  • Real size of the area, volume, or length
  • Scaled size of the area, volume, or length
  • Scale factor

FAQ’s:

How does the length converter convert various units of the dimensions taken?

The free length conversion calculator asks you every time to select the units of the length, area and volume before you tap the calculate button. For a better understanding, you can read the section “How scale calculator works?” thoroughly.

What do you mean by the term scale?

A particular change in the order or magnitude of the number is termed the scale.
For example; if you take a number say 5 and apply a magnitude of 4 to it, you will get the number of the order 20.

What is the scale factor of 2?

The scale factor of 2 represents that you will get a new shape that will be twice the size of the actual figure.

What do 1 64 scale buildings maps display?

1/64 represents that the size of the building has been reduced upto 64 times and then drawn on the blueprint.

What is the value of the scale factor in inches if the length of a certain box is 230mm and real length as 4mm?

Scale length = 230mm to inches = 9.05 inches

Real length = 4mm to inches = 0.157 inches

Scale factor of length = 9.05 inches/0.157 inches

Conclusion:

So far we discussed how scale factor affects the size, area, and volume of any object. Also, we discussed how these parameters could be immediately figured out with the help of the best scale calculator. So go for using our free calculator and get a grip on the calculations even stronger than before.

References:

From the source of wikipedia: Scale factor, Dilation 

From the source of khan academy: Identify scale factor, Scale copies

From the source of lumen learning:  Simultaneity And Time Dilation, Time Dilation, The Twin Paradox.