Unit Rate Calculator
Enter two quantities and their units of measure to calculate the unit rate.
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How to Calculate Unit Rate
Unit rate, or just rate, is a measure of one quantity compared to another quantity. A unit rate is a ratio of a measurement in one unit to a measurement in another unit.
Most often, we use rates to represent a change in one quantity relative to a change in another quantity. For example, velocity, or speed, is a rate, which is defined as the change in distance relative to the change in time.
Another example of a rate is the rate of home construction, which is the number of homes built over a specified period of time. Rates can be found being used in many different aspects of life.
Unit Rate Formula
So, how do you calculate a rate given two different quantities? Start by using the unit rate formula:
rate = quantity 1 / quantity 2
or for changes in quantities:
rate = (change in quantity 1) / (change in quantity 2)
Thus, rate is equal to the quantity of unit one (or change in quantity of unit 1) divided by the quantity of unit 2 (or change in quantity of unit 2).
Rate is often expressed as “quantity 1 per quantity 2,” as in miles per hour or dollars per day.
For better interpretability, the rate can be simplified to a reduced fraction such that the denominator has a value of 1. For example, think of this as the number of miles per 1 hour or the number of dollars earned per 1 day.
Unit rates are often then even further simplified and expressed as just the numerator with the first quantity unit over the second. For instance, 25 miles/hour or 45 dollars/day.
Another common unit rate is that of unit price, which can also be considered as a rate of price to the quantity. Try our unit price calculator to learn more.
Rate Calculation Examples
For example, let’s find the rate of speed when you have traveled 100 miles in 4 hours.
rate = 100 miles / 4 hours
rate = 25 miles / 1 hour
rate = 25 miles/hour (mph)
For example, let’s find the rate of an engine that can turn a wheel 2500 revolutions in 10 minutes.
rate = 2500 revolutions / 10 minutes
rate = 250 revolutions / 1 minute
rate = 250 revolutions/minute (rpm)
For example, let’s find the flow rate for 75 gallons of fluid flowed over a 5-minute time period.
rate = 75 gallons / 5 minutes
rate = 15 gallons / 1 minute
rate = 15 gallons/minute (gpm)
Frequently Asked Questions
Why do we use unit rates?
We use unit rates to represent one quantity relative to another. More specifically, we often use unit rates to represent the change in one quantity relative to another quantity, such as miles traveled per number of hours, or mph.
What are some common examples of unit rate?
Some common examples of unit rates are miles per hour (mph), rotations per minute (rpm), and gallons per flush (gpf).
Is unit rate the same as the constant of proportionality?
Yes, unit rate is sometimes used as another name for the constant of proportionality.