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Unit Rate Calculator
Divide two amounts to find the unit rate: how much for 1 unit, such as dollars per apple or miles per hour.
The total, such as 3 or 150
The word you use, such as dollars or miles
for
How many units that total covers, such as 12 or 2.5
The unit rate is the first amount for 1 of these
Enter two amounts to see how much for 1 unit.
This unit rate calculator is for the lesson on what a unit rate is and how to find it. Type two amounts and the units in your own words, such as dollars and apples or miles and hours. The page divides the first amount by the second, simplifies that fraction, and shows the amount per 1 unit, then the other direction. Money amounts are shown in cents when cents are exact. A second amount of 0 is undefined, because a unit rate cannot divide by zero.
What a unit rate is
A unit rate is a rate with 1 as the second amount. It answers how much for one: dollars for 1 apple, or miles for 1 hour. The word per means for each one. 0.25 dollars per apple means 0.25 dollars for 1 apple. 60 miles per hour means 60 miles for 1 hour. If the second amount is not 1 yet, divide so that it becomes 1.
How to find the unit rate
The unit rate formula is the first amount divided by the second amount. Put the quantity you are measuring first and the number of units second. 3 dollars for 12 apples is 3 divided by 12. Simplify the fraction before you switch to a decimal: 3/12 = 1/4 = 0.25, so the unit rate is 0.25 dollars per apple. The other direction uses the same amounts swapped. 12 divided by 3 is 4, which is 4 apples per dollar.
Speed is the same division. 150 miles in 2.5 hours is 150 divided by 2.5, which is 60. The unit rate is 60 miles per hour, or 60 miles for 1 hour. A price works the same way. 3.60 dollars for 12 ounces is 0.30 dollars per ounce.
Cents, rounding, and a zero denominator
When the unit is dollars, the rate is shown in cents if those two decimal places are the exact amount, such as 0.25 or 0.30. If rounding to the nearest cent would hide the rate, the page keeps the extra decimal places when they are exact, or it rounds to 8 significant figures and says that it did. A non-money unit uses = when the decimal is exact and ≈ with 8 significant figures when it is rounded. The note under the rate says which. The second amount has to be greater than 0. Division by zero is undefined, so there is no unit rate. A negative amount is not a rate in this lesson, because the comparison is positive.
Comparing two prices, or solving a proportion with one term missing, is the next step after a single unit rate. The proportion calculator does both.
A related lesson
Frequently Asked Questions
What is a unit rate?
A unit rate is a comparison with 1 in the second amount. It tells you how much for one unit. Dollars per apple and miles per hour are unit rates. 3 dollars for 12 apples is 0.25 dollars per apple, and 150 miles in 2.5 hours is 60 miles per hour.
How do you find the unit rate?
Divide the first amount by the second amount, then simplify. For 3 dollars and 12 apples, 3/12 = 1/4 = 0.25, so the unit rate is 0.25 dollars per apple. Check the other direction too: 12/3 = 4 apples per dollar. The second amount has to be greater than 0.
How do you find miles per hour?
Divide the miles by the hours. 150 miles in 2.5 hours is 150 divided by 2.5, which equals 60. The unit rate is 60 miles per hour, meaning 60 miles for 1 hour.
What is the unit rate for 3.60 dollars and 12 ounces?
Divide 3.60 by 12. That is 0.30, so the unit price is 0.30 dollars per ounce. The other direction is about 3.3333333 ounces per dollar, rounded to 8 significant figures, because 12/3.60 does not end.
Why is a unit rate undefined when the denominator is 0?
Finding the amount per 1 divides by the second amount. Division by zero has no result, so a second amount of 0 is undefined. A negative number is rejected too. In this lesson a rate compares two positive amounts, such as dollars and apples or miles and hours.