Enter the factor at which you want to scale your unit, and the number/unit you wish to scale in order to calculate the scaled unit.

## Scale Formula

The following formula is used to convert a number to a new number using a scale.

a = b * sf

- Where a is the new number to be calculated
- b is the original number
- sf is the scale factor

The scale factor is a ratio or magnitude of increase that you wish to apply to an original number.

## Scale Definition

Usually, the scale is referred to as a magnitude or order change of a number. For example, take the number 1 and apply an order of magnitude of 10 to this and you get 10 as the number. The scale would be defined as a 1:10 scale.

## How to calculate a scale

A scale, or scale factor, is a ratio between two numbers. The first number is the number you wish to scale, and the second number is some factor of that number. This is typically used in science to “scale” projects from small scale to large scale. In other words, experiments are performed on a small scale and the results are recorded. Then, instead of running an actual experiment on a larger scale, the results of the first experiment are scaled using math.

Let’s review an example problem of how this might be used.

Let’s say we are trying to find out how many ping pong balls would fit in a pool, but obviously don’t have the funds to fill a full pool with ping pong balls. Instead, we design an experiment where we fill a miniature pool with ping pong balls.

The small pool lets say is 1 cubic meter. After filling it with ping pong balls, we find it holds 1000 balls.

Now we need to find out the scale factor to multiply our result by. To do this we need to divide the total volume of the large pool by the volume of the small one. Let’s assume the large pool is 10 cubic meters. Now dividing 10/1= 10. So our scale factor is 10.

Finally, we need to multiply the first result by the scale factor. So, 1000 * 10 = 10,000 ping pong balls.

## FAQ

**What is scale?**

Usually, the scale is referred to as a magnitude or order change of a number. For example, take the number 1 and apply an order of magnitude of 10 to this and you get 10 as the number. The scale would be defined as a 1:10 scale.

For more math related calculators, click here.