# Millimeters to Inches Converter

**Conversion Rates**

A conversion rate defines the equivalent value of one unit in terms of another unit. Since millimeters are a part of the metric system, while inches are part of the imperial system, their conversion rates are not neat and will come out as decimal numbers.

For our purposes, we will be rounding the conversion rates to three significant digits.

The conversion rate between millimeters and inches can be defined either as the equivalent number of millimeters to one inch or, the other way around.

Unit | Conversion |
---|---|

millimeter | 0.0394 inches |

inch | 25.4 mm |

## Conversion Formulae

Based on our conversion rates, we can create 2 formulae that will help us with manually converting between the units.

In our formulae, we will be using IN to refer to inches, and MM to refer to millimeters.

The first formula is suitable for converting millimeters into inches. This is apparent from the fact, that the subject of the formula is the resulting (output) variable of inches. The variable we have (input) should always appear within the formula along with the constants and operations.

in = mm*0.0394

The second formula is suitable for finding the number of millimeters when we are given the inches.

mm = in*25.4

In case we do not want to remember two different constants, we can also operate with only one of them, switching between multiplication and division.

The following two alternative formulae can be created.

mm = in\div0.0394

in = mm\div25.4

### Worked-out Examples

As an example, we will be converting the sizes of some items.

*EXAMPLE 1*

An iPhone 15 is 146.7 mm long. How long is the phone in terms of inches? Round your result to 2 decimal places.

We are given millimeters and are aiming at receiving an equivalent value in inches. For these purposes, a formula with inches as the subject is suitable.

The first alternative is the following formula, into which we substitute MM = 146.7.

in = mm*0.0394 \\= 146.7*0.0394 \\= 5.78 ~inches.

The alternative formula would be used like this.

in = mm\div25.4 = 146.7\div25.4 \\= 5.78 ~inches.

Regardless of the formula, our result is the same. If we were rounding our result to more decimal places, we could see a slight difference, which is caused by the rounded nature of the constants used in the formula. This inaccuracy is insignificant in everyday situations.

*EXAMPLE 2*

A standard height of a door in the USA is defined as 80 inches. What is the standard height defined in millimeters, rounded to the nearest whole number?

We are given inches while looking for an equivalent value in millimeters. A formula with millimeters as the subject will be used. We will substitute IN = 80 into this formula.

mm = in*25.4 \\= 80*25.4 = 2,032 ~mm

Alternatively, we can use the second formula.

mm = in\div0.0394 \\= 80\div0.0394 = 2,030 ~mm

We can see a slight difference in the results, caused by rounding. If we extend the number of significant digits of each constant, we will receive more accurate values.