What this calculator does
A unit rate expresses a ratio with the second quantity reduced to 1. Covering 150 km in 3 hours is a unit rate of 50 km per hour. Paying 6.00 for a dozen eggs is 50 cents per egg. The arithmetic is a single division, and the value of doing it is that rates given per single unit can be compared directly, where raw ratios cannot.
The part worth care is which quantity goes where. A divided by B and B divided by A are both legitimate rates, and they answer different questions: cost per item, or items per dollar. This calculator reports both, so whichever way round the figures were entered, the one you want is on the page.
The formula
Quantity A is divided by quantity B, giving the amount of A that goes with one unit of B. The inverse, B divided by A, is shown alongside and gives the amount of B per single unit of A. Neither quantity carries units here, so labelling the answer is left to you: the arithmetic is identical whether the inputs are kilometres and hours or dollars and items.
| Term | Meaning |
|---|---|
| Unit rate | A ÷ B, the amount of the first quantity per single unit of the second. |
| Inverse rate | B ÷ A, the same relationship read the other way round. |
| Ratio | The comparison of the two quantities before either is reduced to 1. |
The inputs explained
| Field | What to enter |
|---|---|
| Quantity A (e.g. distance, cost, amount) | The quantity you want the rate to be expressed in, such as distance, cost or amount. |
| Quantity B (e.g. time, items, units) | The quantity you want the rate to be expressed per unit of, such as time, items or units. It cannot be zero. |
When to use it
Comparing package sizes in a shop
Two packs at different prices holding different quantities cannot be compared as they stand. Reducing each to a price per single item makes the cheaper one obvious, which is the same calculation a shelf unit-price label performs.
Converting a total into a speed or a pace
A distance and a time give a speed one way round and a pace the other. Both figures appear here, so there is no need to decide in advance which way the division should go.
Setting a per-unit figure for a quote or budget
A total cost divided by the number of units gives the per-unit figure a quote or a budget line is usually written in, and it scales cleanly to any other quantity afterwards.
Worked examples
Every figure in the tables below is produced by this page’s own calculator at build time, so the numbers and the tool always agree. Select any row to load that scenario.
How does the unit rate change as the second quantity grows?
The same total of 150 spread over an increasing number of units.
| Quantity B | Unit rate (A per 1 unit of B) | Inverse rate (B per 1 unit of A) |
|---|---|---|
| 1 | 150 | 0.00666667 |
| 2 | 75 | 0.01333333 |
| 3 | 50 | 0.02 |
| 5 | 30 | 0.03333333 |
| 10 | 15 | 0.06666667 |
Which pack is the better value?
A quantity of 12 held fixed, with four different totals, as four differently priced packs of the same item would give.
| Price for a dozen | Unit rate (A per 1 unit of B) | Inverse rate (B per 1 unit of A) |
|---|---|---|
| 4.80 | 0.4 | 2.5 |
| 6.00 | 0.5 | 2 |
| 7.20 | 0.6 | 1.66666667 |
| 9.60 | 0.8 | 1.25 |
Questions
What is the difference between a rate and a unit rate?
A rate compares any two quantities, such as 150 km in 3 hours. A unit rate is that same comparison with the second quantity reduced to 1, so 50 km in 1 hour. Only unit rates can be compared against each other directly.
Which quantity should I enter as A?
Whichever one you want the answer expressed in. For a price per item, price is A and the number of items is B. If you enter them the other way round, the figure you wanted is the inverse rate on the second line.
How do I use this to compare two products?
Work out the unit rate for each one separately, with price as A and quantity as B each time, then compare the two results. The smaller price per unit is the better value on price alone, setting aside any difference in quality or in how much you will actually use.
Why can quantity B not be zero?
Because the unit rate is a division by B, and dividing by zero has no result. A rate per zero units is not a meaningful quantity to ask for.
To simplify a ratio without reducing it to a per-unit figure, see the ratio calculator. For the constant linking two directly proportional quantities, see the constant of proportionality calculator.