Rates

A rate is a special kind of ratio that compares two quantities measured in different units – kilometres per litre, pages per minute, heartbeats per second. Unlike an ordinary ratio (which compares two amounts of the same kind, like boys to girls), a rate always carries its units along with it, which is exactly what makes it so useful for describing how quickly or efficiently something happens.

One of the most familiar rates in daily life – speed, or distance per unit of time – is covered in its own dedicated page in the Measurement section of this site, with the full formula and worked examples. This page instead focuses on rates more generally: how to compute them and how to convert a rate from one time unit to another.

Computing a Rate

A rate is found the same way as a unit rate: divide one quantity by the other, keeping track of both units.

A tap fills a 45-litre tank in 9 minutes. What is the filling rate in litres per minute?

Rate = 45 litres ÷ 9 minutes = 5 litres per minute.

Converting a Rate

A machine produces 8 items per minute. What is this rate in items per hour?

There are 60 minutes in an hour: 8 × 60 = 480 items per hour.

Real-Life Application

Heart rate: beats per minute.
Pay rate: dollars earned per hour.
Data usage: megabytes downloaded per second.

Key Takeaways

A rate compares two quantities measured in different units.
Rates can be converted between time units by multiplying or dividing consistently.
Speed (distance per time) is the most common rate, covered in full in the Measurement section.

Practice: Rates

Compute the Rate