# What is the unit rate?

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.

- Page: https://www.acalculator.org/math/unit-rate-calculator
- JSON spec: https://www.acalculator.org/math/unit-rate-calculator.json
- Version: 6c4a16a9af20

## Default answer

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.

## Inputs

| Key | Label | Description |
| --- | --- | --- |
| a | Amount | The first quantity of the rate, such as 455 miles or $3.99. |
| au | Unit of the amount | What the amount counts, such as miles or dollars. |
| b | Per | The second quantity, such as 14 gallons or 24 bottles. It is more than 0. |
| bu | Unit of the second quantity | What the second quantity counts, such as gallons. |

## Outputs

| Key | Label | Description |
| --- | --- | --- |
| rate | Unit rate | Amount ÷ second quantity: how much for 1 unit of the second quantity. |
| sentence | In words | The unit rate with its units, to 10 significant figures. |
| inverse | The other way round | Second quantity ÷ amount: how much of the second quantity for 1 unit of the amount. |
| inverseSentence | The other way round, in words | The inverse rate with its units, to 10 significant figures. |
| ratio | Simplest ratio | Amount : second quantity as the smallest whole numbers with the same ratio. |

## Method

unit rate = amount ÷ second quantity; the other way round = second quantity ÷ amount.

## Assumptions

- 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

1. a = 455, au = miles, b = 14, bu = gallons gives rate = 32.5, sentence = 32.5 miles per gallon, ratio = 65 : 2, inverse = 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.
2. a = 384, au = dollars, b = 32, bu = hours gives rate = 12, sentence = 12 dollars per hour, 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.
3. a = 3.99, au = dollars, b = 24, bu = bottles gives rate = 0.16625, ratio = 133 : 800, sentence = 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.

## FAQ

### 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.

## Sources

- OpenStax, Prealgebra 2e, §5.6 Ratios and Rate (rates, unit rates and unit price; Examples 5.64, 5.65 and 5.66), CC BY 4.0. https://openstax.org/books/prealgebra-2e/pages/5-6-ratios-and-rate (retrieved 2026-10-02)