This calculator help us find the scale factor between two lengths, simply enter two lengths, it will automatically calculate the scale factor, supports different length units (mm, cm, m, km, in, ft, yd, mi), in addition corresponding visual graphic and formula, easy understanding the calculation process and the result.

### How to use the scale factor calcutor

- Enter the length of A and B
- Number accept decimal or fraction, eg. 6, 12, 4.7, 1/2, 5 3/8
- If the length units are different, choose the right unit
- The result(scale factor) will be calculated automatically.

### How to figure out scale factor ?

In two similar geometric figures, the scale factor is the ratio of their corresponding sides, dividing the two corresponding lengths of the sides will gives the ratio, for example

#### What is the scale factor between 4 cm and 10 cm ?

4 and 10 are divisible by 2

Length A : 4 ÷ 2 = 2

Length B : 10 ÷ 2 = 5

so the scale factor from A to B is 2:5

#### If 12 inches equals 3 inches, what is the scale factor ?

12 and 3 are divisible by 3

12 ÷ 3 = 4

3 ÷ 3 = 1

12:3 ratio simplified is 4:1

so the scale factor of 12 inches to 3 inches is 4:1

#### If 1/4 inches equals 2 feet, what is the scale factor ?

1⁄4 in = 1 ÷ 4 = 0.25 in

2 ft = 12 × 2 = 24 in

1 ÷ 0.25 = 4

24 × 4 = 96

0.25:24 ratio simplified is 1:96

so the scale factor of 1⁄4 inches to 2 feet is 1:96

If you want to know what is the length under conversion at different scales, try this scale length conversion tool, it helps us calculate the length quickly.

When enlarging a shape or image, we use a scale factor to tell us how many times bigger we want each line/side to become. For example, if we enlarged a rectangle by scale factor 2, each side would become twice as long. If we enlarged by a scale factor of 10, each side would become 10 times as long.

The same idea works with fractional scale factors. A scale factor of 1/2 would make every side 1/2 as big (this is still called an enlargement, even though we have ended up with a smaller shape).

## Watch How to use Scale Factors with Area and Volume on the DoingMaths YouTube channel

## Enlarging with a Scale Factor of 5.

## Enlarging with a Scale Factor of 5

In the diagram above, the left-hand triangle has been enlarged by a scale factor of 5 to produce the triangle on the right. As you can see, each of the three side lengths of the original triangle have been multiplied by 5 to produce the side lengths of the new triangle.

## Scale Factors with Area

But what effect does enlarging by a scale factor have on the area of a shape? Is the area also multiplied by the scale factor?

Let's look at an example.

## Enlarging an Area by a Scale Factor.

## Enlarging an area by a scale factor

In the diagram above, we have started with a rectangle of 3cm by 5cm and then enlarged this by a scale factor of 2 to get a new rectangle of 6cm by 10cm (each side has been multiplied by 2).

Look at what has happened to the areas:

Original area = 3 x 5 = 15cm 2

New area = 6 x 10 = 60cm 2

The new area is 4 times the size of the old area. By looking at the numbers we can see why this has happened.

The length and the height of the rectangle have both been multiplied by 2, hence when we find the area of the new rectangle we now have two lots of x2 in there, hence the area has been multiplied by 2 twice, the equivalent of multiplying by 4.

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More formally, we can think of it like this:

After an enlargement of scale factor n:

New area = n x original length x n x original height

= n x n x original length x original height

= n 2 x original area.

So to find the new area of an enlarged shape, you multiply the old area by the square of the scale factor.

This is true for all 2-d shapes, not just rectangles. The reasoning is the same; area is always two dimensions multiplied together. These dimensions are both being multiplied by the same scale factor, hence the area is multiplied by the scale factor squared.

## Enlarging a Volume by a Scale Factor

## Enlarging a Volume by a Scale Factor

What about if we enlarge a volume by a scale factor?

Look at the diagram above. We have enlarged the left hand cuboid by a scale factor of 3 to produce the cuboid on the right. You can see that each side has been multiplied by 3.

The volume of a cuboid is height x width x length, so:

Original volume = 2 x 3 x 6 = 36cm 3

New volume = 9 x 6 x 18 = 972cm 3

By using division we can quickly see that the new volume is actually 27 times larger than the original volume. But why is this?

When enlarging the area we needed to take into account how two multiplied sides were both being multiplied by the scale factor, hence we ended up using the square of the scale factor to find the new area.

For volume it is a very similar idea, however this time we have three dimensions to take into consideration. Again, each of these is being multiplied by the scale factor, so we need to multiply our original volume by the scale factor cubed.

More formally, we can think of it like this:

After an enlargement of scale factor n:

New volume = n x original length x n x original height x n x original width

I’m trying to scale a point from a map (Latitude, Longitude) to an image (x, y). For that i need to find the scale factor between the 2 NON-SIMILAR rectangles (i think).

I’ll clarify, let’s say:

Rectangle 1: A(40.0, 50.0) B(40.0, 56.0) C(43.0, 56.0) D(43.0, 50.0)

(Latitude Delta = 3, Longitude Delta = 6).

Rectangle 2: E(0, 0) F(500, 0) G(500, 300) H(0, 300)

(X Delta = 500, Y Delta = 300).

How can i scale a point P(41.5, 52.5) from rectangle 1 to point (x, y) on rectangle 2?

**UPDATE:**

I’m trying to display the user current location (Lat, Lon) on a custom image (not a map image, a drawing of my own) therefor i can’t use maps (MKMapKit, Google, Tom-Tom).

I have the user current location (via CoreLocation) and an image (800×460).

The area that i’m mapping is small so i don’t need to worry about the earth’s curve.

I’m trying to find a formula that’ll help me scale my user (Lat, Lon) location into my image (on my iPhone screen)

## 2 Answers 2

Well , getting the rectangle that is similar with the first one but fits in the second one is not hard. Here’s how:

I’m not sure this is what you are trying to achieve.

If you’re happy with the distortions it introduces you can just treat x ( latitude ) and y ( longitude ) coordinates separately.

If you think you’re not going to be happy with such distortions, what do you propose to do about the incommensurate scales in latitude and longitude ? 1°lat != 1°long in the latitudes in your question.

If you need help scaling from a line of one length to a line of another, update your question.

**EDIT** following comment by OP.

OK, so you want to map an interval of 3° in latitude to an interval of 300 pixels (I guess) in Y, and an interval of 6° in longitude to an interval of 500 pixels in X.

I’m still not entirely sure if you are concerned about introducing further distortions; if you’re not it’s very easy. I’ll suppose that the bottom left of your screen area is pixel (1,1) and that that is where you want to map (40°,56°) to. For every minute of longitude east of that point, move (500/360) pixels to the right. For every minute of latitude north of the corner, move (300/180) pixels up.

This rough-and-ready projection will not preserve the appearance of 2D shapes (for example a square will project to a rectangle) but there are many map projections in widespread use which do not preserve shapes.

Similar triangles are objects that have the same shape and angle size, but their side lengths are different. The corresponding sides of the triangles, however, are in the same length ratio, also called the scale factor. Multiplying the smaller triangle’s side lengths by the scale factor will give you the side lengths of the larger triangle. Similarly, dividing the larger triangle’s side lengths by the scale factor will give you the side lengths of the smaller triangle.

Set up ratios of the corresponding sides of the triangles. For example, the ratio of small to big triangle sides in two triangles is 5/10, 10/20 and 20/40.

Divide both numbers in one of the ratios by their highest common factor. This will give you the scale factor of the bigger triangle to the smaller triangle. In the example, 5 is the highest common factor in the 5/10 ratio. Dividing 5 and 10 by 5 gives you a ratio of 1/2.

Multiply the other sides in the larger triangle by the the ratio calculated in Step 2. In the example, when you multiply 20 by 1/2 and 40 by 1/2, you get 10 and 20, respectively. This confirms that the scale factor of the bigger triangle to the smaller triangle is 1/2.

Divide one of the sides in the bigger triangle by its corresponding side in the smaller triangle to determine the scale factor for the smaller triangle to the bigger triangle. In the example, if you divided 40 by 20 you would get a scale factor of 2.

Multiply the other sides in the smaller triangle by the the scale factor calculated in Step 4. In the example, when you multiply 5 by 2 and 10 by 2, you get 10 and 20, respectively. This confirms that the scale factor of the smaller triangle to the bigger triangle is 2.

When we are trying to find a scale factor, we will have two objects that are basically the same, but one is bigger than the other.

(note: these squares are not to scale)

The scale factor is simply what we could multiply one of the objects by to get the other one. For example, if we had the area of the square on the right, we could multiply the scale factor to find the area of of square on the left.

Now, your asking, *how do we find the scale factor?*

We need to find an corrosponding legnth from our squares, and make it a ratio.

So we can look at our example here, and we can see that the first square last a legnth of 1, whereas the second square has a legnth of 5. Let’s make this a ratio!

This is basically saying that the first square is 1/5 the size of the second square. And it is our scale factor.

The scale factor could also be 5/1, or just 5, and this is just saying that the second square is 5 times the size of the first square.

How we might use this scale factor is to find the height of the second square in the example picture. The height is unknown (x), but we can figure this out.

We know that the first square is 1/5 the size of the second square, or in other words, the second square is *5 times bigger than the first square*. Knowing this we could multiply the hieght of the first square(4) by 5 to find the height of the second square, so the height of the second square is 20!

Also, scale factors doesn’t have to just apply to squares, it can apply to triangles, circles, etc!

### 5 +0 Answers

When we are trying to find a scale factor, we will have two objects that are basically the same, but one is bigger than the other.

(note: these squares are not to scale)

The scale factor is simply what we could multiply one of the objects by to get the other one. For example, if we had the area of the square on the right, we could multiply the scale factor to find the area of of square on the left.

Now, your asking, *how do we find the scale factor?*

We need to find an corrosponding legnth from our squares, and make it a ratio.

So we can look at our example here, and we can see that the first square last a legnth of 1, whereas the second square has a legnth of 5. Let’s make this a ratio!

This is basically saying that the first square is 1/5 the size of the second square. And it is our scale factor.

The scale factor could also be 5/1, or just 5, and this is just saying that the second square is 5 times the size of the first square.

How we might use this scale factor is to find the height of the second square in the example picture. The height is unknown (x), but we can figure this out.

We know that the first square is 1/5 the size of the second square, or in other words, the second square is *5 times bigger than the first square*. Knowing this we could multiply the hieght of the first square(4) by 5 to find the height of the second square, so the height of the second square is 20!

Also, scale factors doesn’t have to just apply to squares, it can apply to triangles, circles, etc!

A scale factor is a number by which a quantity is multiplied, changing the magnitude of the quantity. Scale factors are often used in geometric contexts, as part of figure models, and more.

The larger penguin model above is 3 times larger than the smaller penguin; To change the larger penguin into the smaller one, we would use a scale factor of . The pentagon shown in green is enlarged by a scale factor of 2 to produce the pentagon shown in blue.

## Scaling geometric figures

The scale factor tells us what to multiply each side length of a geometric figure by to produce a scaled, similar figure.

Triangle ABC is similar to triangle DEF (△ABC

△DEF), which means that the corresponding side lengths of the triangles are proportional:

Any of the three ratios can be used to determine the scale factor.

Find the lengths of sides b and d for the triangles below given that △ABC

Since the triangles are similar, . We can find the scale factor using the ratio of a pair of corresponding sides: . This is the scale factor we multiply a side length of triangle ABC by to find its corresponding side length in DEF. We would multiply a side length of DEF by instead to find its corresponding side length in ABC.

We could also set the ratios of the corresponding sides equal to find b and d.

Recommended practice includes specification of scale factors for each plant input and output variable, which is especially important when certain variables have much larger or smaller magnitudes than others.

The scale factor should equal (or approximate) the span of the variable. *Span* is the difference between its maximum and minimum value in engineering units, that is, the unit of measure specified in the plant model. Internally, MPC divides each plant input and output signal by its scale factor to generate dimensionless signals.

The potential benefits of scaling are as follows:

Default MPC tuning weights work best when all signals are of order unity. Appropriate scale factors make the default weights a good starting point for controller tuning and refinement.

When choosing cost function weights, you can focus on the relative priority of each term rather than a combination of priority and signal scale.

Improved numerical conditioning. When values are scaled, round-off errors have less impact on calculations.

Once you have tuned the controller, changing a scale factor is likely to affect performance and the controller may need retuning. Best practice is to establish scale factors at the beginning of controller design and hold them constant thereafter.

You can define scale factors at the command line and using the **MPC Designer** app.

### Determine Scale Factors

To identify scale factors, estimate the span of each plant input and output variable in engineering units.

If the signal has known bounds, use the difference between the upper and lower limit.

If you do not know the signal bounds, consider running open-loop plant model simulations. You can vary the inputs over their likely ranges, and record output signal spans.

If you have no idea, use the default scale factor (=1).

### Specify Scale Factors at Command Line

After you create the MPC controller object using the mpc command, set the scale factor property for each plant input and output variable.

For example, the following commands create a random plant, specify the signal types, and define a scale factor for each signal.

### Specify Scale Factors Using MPC Designer

After opening **MPC Designer** and defining the initial MPC structure, on the **MPC Designer** tab, click **I/O Attributes** .

In the Input and Output Channel Specifications dialog box, specify a **Scale Factor** for each input and output signal.

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 Scale Size
- Find the Scale Factor

## Find the Scaled Size

## Find the Scale Factor

## Scaled Results:

#### Scale Factor

#### Scaled Size

## On this page:

- Scale Conversion Calculator
- How to Scale Up or Down
- How to Find the Scale Factor
- How to Reduce the Scale Factor
- Commonly Used Architectural Scales
- Commonly Used Model Scales

## How to Scale Up or Down

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.

## 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 too, 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.

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.

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 to 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.

1. Click View tab Viewports panel Scale Monitor. Find. The Scale Monitor dialog box is displayed.

2. In the drawing area, move the cursor over the scale area (or a viewport ) and check the Scale Monitor dialog box.

3. Press ENTER to exit this command.

## How do you scale in AutoCAD?

## What is the formula for scale factor?

The basic formula to find the scale factor of a figure is: Scale factor = Dimensions of the new shape ÷ Dimensions of the original shape. This can also be used to calculate the dimensions of the new figure or the original figure by simply substituting the values in the same formula.

## How do you scale proportionally in AutoCAD?

With a calculator, divide the intended length by the measured length. Enter the SCALE (Command). Select a base point, such as 0,0,0. Enter the obtained scale factor to adjust all objects in the drawing model to their correct size.2 mar. 2021

## What is the scale factor for MM to inches?

Conversion TableCurrent base unitsDesired base unitsScale factormillimetersinches.03937centimetersmillimeters10centimetersmeters.01centimetersinches.39378 autres lignes

## How do you calculate scale?

To scale an object to a smaller size, you simply divide each dimension by the required scale factor. For example, if you would like to apply a scale factor of 1:6 and the length of the item is 60 cm, you simply divide 60 / 6 = 10 cm to get the new dimension.

## What is the scale factor for 1 20?

1″ = 20′ Multiply the feet by 12. 20 x 12 = Scale Factor 240.2 fév. 2021

## What is scale factor in AutoCAD?

Scale Factor. Multiplies the dimensions of the selected objects by the specified scale. A scale factor greater than 1 enlarges the objects. A scale factor between 0 and 1 shrinks the objects. You can also drag the cursor to make the object larger or smaller.15 déc. 2015

## How do I reduce scale size in AutoCAD?

This will show you how to change scale in AutoCAD without changing the dimension. How to scale down in AutoCAD – Window select the object(s) in AutoCAD, type SCALE, and then specify a number between 0 and 1. Hit Enter. The size of the object(s) will SCALE DOWN by that factor.

## What is the scale factor of 1 5?

If the scale factor is 1/5, that means the original triangle would have dimensions 5 times larger than the current model. So if the current base is 5 units in size, the original triangle would be 5 times larger.17 nov. 2017

## What does scale factor mean in maths?

A scale factor in math is the ratio between corresponding measurements of an object and a representation of that object.27 sept. 2020

## What is a scale factor in math in 7th grade?

VOCABULARY. ● Scale Factor: The ratio of any two corresponding lengths in two similar. geometric figures. ● Corresponding Angles: Angles in matching locations of two shapes.7 avr. 2020

## How do you scale a survey in AutoCAD?

How do you scale a survey in AutoCAD? Press Ctrl + A on your keyboard to select all elements in the drawing. Type ‘scale’ in to the command bar and press enter. AutoCAD will ask ‘SCALE Specify base point:’, type ‘0,0’ (without the quotes) and press enter.

## How do you match the scale of two drawings in AutoCAD?

1. Draw a line that is at the proper length (Ex: If the dimension shows 25′, draw a line at that length).

2. Type ALIGN into the command line and press Enter. …

3. Select the image to be scaled and press Enter.

## How do you set limits in AutoCAD?

1. At the Command prompt, enter limits.

2. Enter the coordinates for a point at the lower-left corner of the grid limits.

3. Enter the coordinates for a point at the upper-right corner of the grid limits.