What is the unit rate?
Type the two quantities of a rate, such as 455 miles and 14 gallons, and their units. The unit rate calculator divides them to get the amount for 1 unit, 32.5 miles per gallon, and also gives the rate the other way round and the simplest whole-number ratio.
- Unit rate
- 32.5
The unit rate is 32.5 miles per gallon.
- In words
- 32.5 miles per gallon
- The other way round
- 0.03076923077
- The other way round, in words
- 0.03076923077 gallons per mile
- Simplest ratio
- 65 : 2
Unit rate: 32.5. The unit rate is 32.5 miles per gallon.
How to calculate
Turns a rate such as 455 miles on 14 gallons into a unit rate, the amount per 1 unit (32.5 miles per gallon), with the rate the other way round and the simplest ratio.
Example with the default inputs (Amount 455, Unit of the amount miles, Per 14, Unit of the second quantity gallons): The unit rate is 32.5 miles per gallon.
Method: unit rate = amount ÷ second quantity; the other way round = second quantity ÷ amount.
- Typed decimals are read exactly, so 3.99 ÷ 24 is exactly 0.16625 and a shown rate rounds half up.
- The unit names are only labels; the calculator does not convert units.
- In the words, the unit after "per" drops a final "s" unless the letter before it is s or u (gallons becomes gallon).
Worked examples
Each example is checked against the calculator on every build.
- Amount 455, Unit of the amount miles, Per 14, Unit of the second quantity gallons gives Unit rate 32.5, In words 32.5 miles per gallon, Simplest ratio 65 : 2, The other way round 0.030769.Source: OpenStax, Prealgebra 2e, §5.6 Ratios and Rate (a unit rate is a rate with denominator of 1 unit; Examples 5.64 to 5.66), https://openstax.org/books/prealgebra-2e/pages/5-6-ratios-and-rate (retrieved 2026-10-02), Example 5.65: 455 ÷ 14 = 32.5 miles per gallon
- Amount 384, Unit of the amount dollars, Per 32, Unit of the second quantity hours gives Unit rate 12, In words 12 dollars per hour, Simplest ratio 12 : 1.Source: OpenStax, Prealgebra 2e, §5.6 Ratios and Rate (a unit rate is a rate with denominator of 1 unit; Examples 5.64 to 5.66), https://openstax.org/books/prealgebra-2e/pages/5-6-ratios-and-rate (retrieved 2026-10-02), Example 5.64: $384 for 32 hours is $12 per hour
- Amount 3.99, Unit of the amount dollars, Per 24, Unit of the second quantity bottles gives Unit rate 0.16625, Simplest ratio 133 : 800, In words 0.16625 dollars per bottle.Source: OpenStax, Prealgebra 2e, §5.6 Ratios and Rate (a unit rate is a rate with denominator of 1 unit; Examples 5.64 to 5.66), https://openstax.org/books/prealgebra-2e/pages/5-6-ratios-and-rate (retrieved 2026-10-02), Example 5.66: $3.99 for 24 bottles is about $0.17 per bottle
How it works
For a rate of a (the amount) per b (the second quantity):
- unit rate = a ÷ b, the amount for 1 unit of the second quantity
- the other way round = b ÷ a, the second quantity for 1 unit of the amount (left out when a is 0)
- simplest ratio: a ÷ b written as a fraction p/q in lowest terms, shown as
p : q
Each typed number is read as the exact decimal you typed, so the division is exact: 3.99 ÷ 24 is exactly 0.16625. The shown values are rounded once from that exact result, halves rounded up.
Rules
- The amount is from 0 to 10¹⁵; the second quantity is from 10⁻¹⁵ to 10¹⁵.
- The unit names are optional labels of up to 40 characters; spaces inside are squeezed to one. An empty name reads as "units".
- In the words, the unit after "per" drops a final "s" when the letter before it is not s or u (gallons becomes gallon, glass stays glass).
Output format. The unit rate and the other way round to 10 significant figures; in words as <rate> <unit of the amount> per <unit of the second quantity>, and the other way as <inverse> <unit of the second quantity> per <unit of the amount>, both with the number to 10 significant figures and a true minus sign (−) in any exponent; the ratio as p : q.
Worked examples by hand
455 miles on 14 gallons (OpenStax Example 5.65). 455 ÷ 14 = 32.5 miles per gallon. 455/14 = 65/2, so the ratio is 65 : 2. The other way: 14 ÷ 455 = 0.03076923077 gallons per mile.
$384 for 32 hours (Example 5.64). 384 ÷ 32 = 12 dollars per hour, ratio 12 : 1.
$3.99 for 24 bottles (Example 5.66). 3.99 ÷ 24 = 0.16625 dollars per bottle (about $0.17). 3.99/24 = 399/2,400 = 133 : 800.
Other questions people ask
What is a unit rate?
A rate compares two quantities with different units, such as 120 miles in 2 hours. A unit rate is the same rate with 1 unit on the bottom: 60 miles per hour. OpenStax defines it as a rate with denominator of 1 unit.
How do I find a unit rate?
Divide the first quantity by the second. Anita earns $384 for 32 hours, so her unit rate is 384 ÷ 32 = $12 per hour. Sven drives 455 miles on 14 gallons, so his car gets 455 ÷ 14 = 32.5 miles per gallon.
What is the difference between a unit rate and a unit price?
A unit price is a unit rate where the first quantity is money: the price of one item or one ounce. A case of 24 bottles for $3.99 has a unit price of 3.99 ÷ 24 = $0.16625, about 17 cents a bottle. To compare two sizes, the lower unit price is the better buy.
Why does the calculator show the rate the other way round?
Both directions describe the same rate. 32.5 miles per gallon is also 14 ÷ 455 ≈ 0.03077 gallons per mile. One is often easier to use: miles per gallon tells you range, gallons per mile tells you fuel for a trip.
What is the simplest ratio?
It is the two quantities scaled to the smallest whole numbers with the same ratio. 455 : 14 divides by 7 to 65 : 2, and 3.99 : 24 is 399 : 2,400, which divides by 3 to 133 : 800.
Does the calculator convert units?
No. The unit names are labels for the answer. To compare rates in different units, convert them first, for example 1 gallon = 3.785411784 liters.