Math
Unit Rate Calculator
Enter a quantity and what it is measured against, such as 120 miles in 3 hours or $4.50 for 12 ounces, and get the rate per single unit both ways (miles per hour and hours per mile).
Switch to compare mode to check two options and see which has the better unit rate, with the difference and percent gap.
The amount, such as 120 miles or 4.50 dollars.
Word only; used for labels.
What the amount is measured against, such as 3 hours or 12 ounces.
Word only; used for labels. Plural is fine (hours, ounces).
Try an example
Result
Unit rate
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- Exact rate (fraction)
- —
- Reverse unit rate
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- Per 10
- —
- Per 100
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Student quick launch
Grade planning, algebra checks, and formulas students reach for most.
Study path
Use this calculator with
Follow these when you want the formula behind the answer, a short lesson, or nearby tools in the same topic.
What a unit rate is
A rate compares two quantities with different units: 120 miles in 3 hours. A unit rate rewrites it so the second quantity is exactly 1: 40 miles per 1 hour. Divide the first quantity by the second. Every rate has two unit rates; the other one here is 3 ÷ 120 = 0.025 hours per mile (1.5 minutes per mile).
| Rate | Unit rate | Reverse unit rate |
|---|---|---|
| 120 miles in 3 hours | 40 miles per hour | 0.025 hours per mile |
| $4.50 for 12 ounces | $0.375 per ounce | 2.667 ounces per dollar |
| 250 words in 5 minutes | 50 words per minute | 0.02 minutes per word |
| 3 cups flour for 2 cups sugar | 1.5 cups flour per cup sugar | 2/3 cup sugar per cup flour |
Comparing prices with unit rates
Unit price is a unit rate with money on top: dollars per ounce, cents per sheet. To find the better deal, compute the unit price of each option and pick the lower one (for prices) or the higher one (for things like miles per gallon or points per game). The calculator shows the difference and the percent gap so you can judge whether it matters.
How to use it
- Enter the first quantity and its unit, then the second quantity and its unit (for example 120 miles and 3 hours).
- Read the unit rate per 1 of the second unit, the reverse unit rate, and the exact fraction when the rate is not a clean decimal.
- For the best deal, choose Compare two options, enter option B in the same units, and say whether a lower or higher rate is better.
- Use the per-10 and per-100 lines to scale the rate to a convenient size.
How to read the answer
The unit rate tells how much of the first quantity goes with exactly one of the second. In compare mode the verdict names the better option; the difference and percent gap show how much better. A percent gap under a few percent is usually a wash once other factors count.
Common mistakes and edge cases
- Divide in the right direction: miles ÷ hours gives miles per hour; hours ÷ miles gives hours per mile.
- Units must match before comparing two options: ounces with ounces, hours with hours.
- A second quantity of 0 makes the rate undefined.
- Lower is better for prices, but higher is better for efficiency rates like miles per gallon.
- Rounded unit prices can hide small differences; the exact fraction is shown for that reason.
Worked examples
Speed
120 miles in 3 hours
Unit rate
40 miles per hour
Unit price
$4.50 for 12 ounces
Unit rate
0.375 dollars per ounce
Fraction rate
2 cups for 3 servings
Unit rate
0.6667 cups per serving
Best deal, lower wins
$4.50/12 oz vs $6.40/20 oz
Unit rate
Option B is the better deal.
Best rate, higher wins
300 miles/10 gal vs 350 miles/12.5 gal
Unit rate
Option A is the better rate.
Tie
Same rate both ways
Unit rate
Both options have the same unit rate.
Zero amount
0 miles in 2 hours
Unit rate
0 miles per hour
Undefined
Per 0 hours
Unit rate
Error
Frequently asked questions
What is a unit rate?+
A rate whose second quantity is 1: 40 miles per 1 hour, $0.375 per 1 ounce. Divide the first quantity by the second to find it.
How do you find the unit rate from a word problem?+
Identify the two quantities and the word 'per' or 'for'. Put the quantity you want to measure first and divide by the other: 120 miles for 3 hours is 120 ÷ 3 = 40 miles per hour.
What is the difference between a rate and a unit rate?+
A rate compares any two amounts (120 miles per 3 hours). A unit rate scales it so the second amount is exactly 1 (40 miles per hour).
How do I know which option is the better deal?+
Compute the unit price of each. The lower price per unit is the better deal, as long as both are in the same units.
Why are there two unit rates?+
Either quantity can be the 'per 1' one. Miles per hour answers how far in one hour; hours per mile answers how long for one mile. Both describe the same trip.
Can a unit rate be a fraction?+
Yes. 2 cups for 3 servings is 2/3 cup per serving. The calculator shows the exact fraction next to the decimal.
About this calculator
- Written by
- mathcheck editorial team
- Last reviewed
- September 4, 2026
Method
- Uses the values entered by the user and stable formulas documented on the page.
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Last updated: September 4, 2026