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Physics Calculators ▶ Scale Factor Calculator

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**Table of Content**

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!

**“The ratio of the two corresponding lengths or measurements is known as the 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.

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

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.

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

**Scale Factor = Scaled Size/Real Size**

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

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:

**Scale factor of length = Scaled Length/Real Length**

**Scale Length = (d1/d2) * Real Length**

**Real Length = (d1/d2) * Scale Length**

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

**Scale Area = (d1/d2) * Real Area**

**Real Area = (d1/d2) * Scale Area**

**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.

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 |

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**

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

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.

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.

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

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

**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**

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.

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.