Unit Rate Calculator

What this calculator does

A unit rate tells you how much of one thing there is for a single unit of another: the price per item, the miles per hour, the cost per gram. It is the number that makes different-sized things easy to compare. This works it out.

Enter two quantities and it returns the rate for one unit. It runs right here in the browser.

Using the calculator

1. Enter quantity 1, the total amount (like the total price, or the distance).
2. Enter quantity 2, the number of units it is spread across (like the number of items, or the hours).
3. Press Calculate.

It returns quantity 1 for each single unit of quantity 2, rounded to two decimal places. Reset clears both boxes.

What a unit rate is

A rate compares two quantities of different kinds, like money and items, or distance and time. A unit rate is a rate where the second quantity has been boiled down to just one: not "12 dollars for 3 notebooks" but "4 dollars per notebook". That word "per" is the giveaway, and it nearly always means a unit rate.

Boiling a rate down to a single unit is what makes it useful, because once everything is expressed per one, you can line up options and compare them directly instead of juggling different quantities in your head.

The formula

Working out a unit rate is just a division:

unit rate = quantity 1 ÷ quantity 2

Quantity 1 is the total you are measuring, and quantity 2 is how many units you are dividing it across. Divide the first by the second and you have the amount for one unit.

Worked examples

Price per item. A pack of 3 notebooks costs 12. The unit rate is 12 ÷ 3 = 4, so each notebook works out at 4.

Speed. A car covers 150 miles in 3 hours. The unit rate is 150 ÷ 3 = 50, so its speed is 50 miles per hour. Speed is one of the most familiar unit rates there is, distance per single hour.

The everyday use: comparing value

The place a unit rate really earns its keep is the supermarket. Shops love to sell the same thing in different sizes at different prices, which makes it genuinely hard to tell which is the better deal. Unit rate cuts through it. Work out the price per gram, or per litre, or per sheet, for each option, and the cheaper one is simply the smaller number. A 500 gram jar at 6 is 0.012 per gram, while a 750 gram jar at 8.50 is about 0.011 per gram, so the bigger jar is very slightly better value, which you would never have guessed from the sticker prices. This same trick, often printed on shelf labels as the "unit price", works for anything sold by amount.

Mind which way round you divide

One thing to keep straight: a rate depends on which quantity you divide by, and the two directions mean different things. Dividing price by items gives "cost per item", but dividing items by price gives "items per unit of money", which is the upside-down version. They are both valid, but they answer different questions. The rule of thumb is to put whatever you want "per one of" as quantity 2, the thing you are dividing by.

Questions people ask

What is a unit rate?

A rate expressed for a single unit of the second quantity, like price per item or distance per hour. The word "per" usually signals one.

How do you calculate a unit rate?

Divide the first quantity by the second. For 12 spent on 3 items, the unit rate is 12 ÷ 3 = 4 per item.

How does it help with shopping?

Work out the price per unit for each size option, and the better value is the one with the lower unit price, regardless of the total prices.

Does the order of the two quantities matter?

Yes. Dividing one way gives cost per item, the other way gives items per unit of cost. Put the thing you want "per one of" as the second quantity.

What are some common unit rates?

Speed (miles per hour), price per item, cost per gram or litre, wage per hour, and fuel economy (miles per gallon).

References

A note on the idea. A unit rate is a ratio comparing a quantity to a single unit of another, found by division, and it is a core tool of proportional reasoning and everyday comparison. For further reading, see Rate (mathematics).

1. The unit rate, a rate reduced to a denominator of one, obtained by dividing the first quantity by the second.