Quilometros<-->milhas

Convert Miles to Kilometers

Conversion between miles and kilometers can be messy. You need to convert between different measurement systems! Before moving on you might want to grab a calculator.

Ok, got one handy? Keep reading.

For every $\text{mile}$, there are $1.60934 \text{ kilometers}$...and for every $\text{kilometer}$, there are $0.62137 \text{ miles}$. The mile is part of the Imperial units system, and the kilometer is part of the metric system.

When we want to convert from miles to km, we can multiply by: $$1 \text{ mi}= \frac{1.60934\text{ km}}{1\text{ mi}}\quad\text{or by}\quad1 \text{ km}= \frac{1\text{ mi}}{0.62137\text{ km}}$$

If we do this, the multiplication will cause the miles to cancel out.

Convert Kilometers to Miles

When we want to convert from kilometers to miles, we can do the reverse; multiply by: $$1 \text{ km} = \frac{1\text{ mi}}{1.60934\text{ km}}\quad\text{or by}\quad 1 \text{ mi}= \frac{0.62137\text{ km}}{1\text{ mi}}$$

For example, if we want to convert $1$ mile to kilometers, we do the following: $$1\text{ mi} \times \frac{1.60934\text{ km}}{1\text{ mi}} = \frac{1\text{ mi} \times1.60934\text{ km}}{1\text{ mi}} = 1.60934\text{ km}$$

If we do this, the multiplication will cause the kilometers to cancel out.

Your Turn

Try the question below yourself.

$$500\text{ km} \times \frac{1\text{ mi}}{1.60934\text{ km}} = \frac{500\text{ km} \times 1\text{ mi}}{1.60934\text{ km}} = \frac{500\cancel{\text{ km}} \times 1\text{ mi}}{1.60934\cancel{\text{ km}}} = 310.686\text{ mi}$$

So, $500 \text{ kilometers}$ is equal to $\boxed{360.686} \text{ miles}$.

Kilometers vs. Miles

$1.609 \text{ kilometers}$ equal $1 \text{ mile}$. $\\$

The kilometer is a unit of measurement, as is the mille. However, a mile is longer than a kilometer. "Mile" is a bigger unit. These are all units used to measure distance. On the other hand, some units measure a different quantity, such as time.

Multiply to convert bigger to smaller units, divide to convert smaller to bigger units! In this case, multiply to convert from kilometers to miles. Also, divide to convert from miles to kilometers.

Why do we care??

Different countries use different units of length for measuring things. Miles and kilometers are both used a lot when traveling. For instance, if you were to drive from Nashville, Tennessee to Fayetteville, Arkansas, that's $531$ miles of driving. But maybe you want to know how far that is in kilometers.

Examples

What is $5 \text{ miles}$ in kilometers?

Since we are converting miles to kilometer, from a bigger unit to a smaller unit, we multiply.

$$5 \text{ mile} \times \frac{1.609\text{ kilometer}}{1\text{ mile}} = 5 \cancel{\text{ mile}} \times \frac{1.609\text{ kilometer}}{1\cancel{\text{ mile}}}=\boxed{8.045\text{ kilometer}}$$

Try it!

$$\begin{align} &5 \text{ kilometer} \div \frac{1.609\text{ kilometer}}{1\text{ mile}}\\ &=5 \text{ kilometer} \times \frac{1\text{ mile}}{1.609\text{ kilometer}}\\ &=\frac{5}{1.609}\text{ miles}\\ &=\boxed{3.1 \text{ miles}} \end{align}$$

(Video) Converting Miles to Kilometers

by Simon Deacon

This quick video by Simon Deacon explains how to convert miles (mi) to kilometers (km).

$\large{\text{Problem-Solving Strategy}}$

One type of problem will have a car traveling at some miles per hour over a distance of some kilometers. You need to find how long it will take to drive that distance. When we say "how long," we mean the distance traveled. In other cases we might want to know the amount of time.

Example: A car is driving at $60\text{ miles per hour}$ (mph). How long will it take the car to go $120 \text{ km}$?

To solve this, we need to know the conversion from kilometers to miles. Here it is! Ta-da! $$\boxed{1\text{ km}=0.6214\text{ mi}}$$

In words this means $1$ kilometer of length equals $0.6214$ miles. The number $0.6214$ has four digits past the decimal point. So you might want a calculator.

To make things a little easier, and if you don't need to be $100$ percent accurate (for instance in a Fermi Problem), you can use the quick conversion: $$\boxed{8\text{ km}\approx5\text{ mi}}$$

For right now though we're not in any hurry. So we'll use the

$$\boxed{1\text{ km}=0.6214\text{ mi}}$$

conversion. Let's solve this problem now. We can set up a conversion table.

$$\begin{array}{c|c} 1\text{ hr}&0.6214\text{ mi}&120\text{ km}\\ \hline 60\text{ mi}&1\text{ km} \end{array}$$ $$\begin{array}{c|c} 1\text{ hr}&0.6214\cancel{\text{ mi}}&120\cancel{\text{ km}}\\ \hline 60\cancel{\text{ mi}}&1\cancel{\text{ km}} \end{array}$$ $$=\frac{1\times0.6214\times120}{60\times1}=\boxed{1.2428\text{ hr}}$$

We can also convert between other units of distance. This includes feet and meters, and centimeters, meters, and kilometers. The meter is the base unit for distance. This means scientists like to convert between meters and other units for distance, including miles and kilometers. Nonetheless it's important to know how to do conversions in both directions.

Finally, the same strategy is used to convert between units of time, such as minutes and seconds, and also to convert between units of mass, such as grams and kilograms. The conversion tables will look very similar. It's just the exact numbers used that will be different.