Type two quantities, such as 150 miles in 3 hours or $4.50 for 12 ounces, and get the unit rate per 1 unit with the division shown. Switch to compare mode to see which of two or three rates is the better deal.
Last updated:
What do you want to do?
e.g. miles, dollars, words, pages
e.g. hours, ounces, minutes, gallons
Quantities
How much of the first unit for this many of the second unit?
How many of the second unit does this much of the first unit take?
Which rate is better?
Enter your values to see the result.
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How to use the Unit Rate Calculator
Choose a mode: find one unit rate or compare rates.
Name the units, for example miles and hours, so the answer reads naturally.
Enter the two quantities: the amount on top and the amount you want “per 1” of.
Add an amount to scale to (optional) to answer questions like “how far in 7 hours?”.
Press Calculate to see the unit rate, the steps and the ratio table.
Unit rate formula
A rate compares two quantities measured in different units. To turn any rate into a unit rate, divide both parts by the second quantity:
unit rate = first quantity ÷ second quantity (the answer is “per 1” of the second unit)
Once you know the unit rate, multiply it by any amount to scale up (50 mph × 7 h = 350 miles), or divide an amount by it to work backwards (350 miles ÷ 50 mph = 7 hours). Writing the rate as a fraction with the units attached helps you check that the units cancel the way you expect.
Unit rate examples
Situation
Rate
Division
Unit rate
Road trip
150 miles in 3 hours
150 ÷ 3
50 miles per hour
Grocery price
$4.50 for 12 oz
4.50 ÷ 12
$0.375 per ounce
Typing
360 words in 8 minutes
360 ÷ 8
45 words per minute
Part-time job
$96 for 6 hours
96 ÷ 6
$16 per hour
Fuel economy
324 miles on 12 gallons
324 ÷ 12
27 miles per gallon
Recipe
3/4 cup for 1/2 batch
0.75 ÷ 0.5
1.5 cups per batch
Reading
84 pages in 3.5 hours
84 ÷ 3.5
24 pages per hour
Tips for unit rate word problems
Find the word “per”. The quantity after “per” (or “each”, “for every”, “a”) goes on the bottom.
Keep units consistent. If one rate is in minutes and the other in hours, convert first, or the comparison is meaningless.
Decide which way is better. For prices and costs the lower unit rate wins; for speed, pay and output the higher one wins.
Use a ratio table to check your answer: every row should give the same unit rate when you divide.
Round only at the end. Store prices are often shown to a tenth of a cent, so keep a few decimals while comparing.
Frequently asked questions
What is a unit rate?
A unit rate is a rate in which the second quantity is 1. 150 miles in 3 hours is a rate; 50 miles per 1 hour is the unit rate. It lets you compare situations that use different amounts.
How do you find a unit rate?
Divide the first quantity by the second. For 360 words in 8 minutes, 360 ÷ 8 = 45 words per minute. Dividing the other way (8 ÷ 360) gives the inverse rate, about 0.022 minutes per word.
How do you find a unit rate with fractions?
Divide the fractions as usual: multiply the first by the reciprocal of the second. For 3/4 cup per 1/2 batch, 3/4 ÷ 1/2 = 3/4 × 2/1 = 1.5 cups per batch. You can type fractions as decimals (0.75 and 0.5).
What is the difference between a rate and a unit rate?
A rate compares two quantities with different units, like $12 for 4 pounds. A unit rate is the same rate simplified so the second quantity is exactly 1: $3 per pound.
How do I use unit rates to compare prices?
Find the price per unit for each option and pick the lowest. $5.40 for 18 oz is $0.30 per ounce and $3.20 for 10 oz is $0.32 per ounce, so the larger package is the better buy. Use the compare mode with “lower is better”.
Is unit rate the same as unit price?
Unit price is one kind of unit rate where the first quantity is money (dollars per ounce, per item). Unit rates also cover speed, pay, typing speed, fuel economy and any other “per 1” comparison.
Are all the tools on FreeToolCabin tested for quality and accuracy?
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