Unit Rate Calculator (amount per one unit: per hour, per item, per kg)

Understanding the unit rate calculator — concept and principle

This calculator turns a rate such as 150 km in 2.5 hours into a unit rate (per 1 unit), gives the inverse unit rate, and scales the rate to any number of units. Use it for speed, unit prices when shopping, fuel use, wages per hour, recipe scaling and maths homework.

Divide by the 2.5 hours to get the amount for one hour, then multiply by 4 for four hours.

How it is calculated

Unit rate = first quantity ÷ second quantity (amount per 1 of the second unit).
Inverse unit rate = second quantity ÷ first quantity (amount of the second per 1 of the first).
Scaled amount = unit rate × chosen number of second units.

A unit price is the special case where the first quantity is money and the second is items, weight or volume.

The principle

A rate compares two quantities with different units. Dividing both by the second quantity keeps the same ratio but makes the denominator 1, which is what "per" means. Once rates are written per one unit, they can be compared directly (which shop is cheaper per kilogram?) and scaled by simple multiplication, because the relationship is proportional. The inverse rate answers the opposite question, such as minutes per kilometre instead of kilometres per hour.

Worked example

Default inputs: 150 km in 2.5 hours, scale to 4 hours.

Unit rate = 150 ÷ 2.5 = 60 km per 1 hour.
Inverse unit rate = 2.5 ÷ 150 ≈ 0.0166666667 hours per km, which is 1 minute per km.
Scaled: 60 × 4 = 240 km in 4 hours.

Each point is the calculator re-run with only “Second quantity (amount)” changed; the gold point is the default example. Change the inputs above and this chart follows your numbers.

Second quantity (amount)	Unit rate
0.625	240
1.25	120
1.88	80
2.5	60
3.12	48
3.75	40
5	30

How to read the result

The unit rate is the "per one" figure you can compare or multiply. When comparing prices, the lower unit price is the better deal for the same quality. When scaling, remember the result is only correct if the rate stays constant, which is often not true for speeds over long trips or for bulk discounts.

Common mistakes

Dividing the wrong way round, giving hours per km when you wanted km per hour.
Comparing unit prices in different units, such as per 100 g and per kg.
Assuming a rate stays constant when it does not, such as average speed including stops.
Forgetting to convert minutes to hours before dividing.

Keep in mind: Shop shelf labels may use different base units for similar products. Check the unit before comparing.

Frequently asked questions

What is a unit rate?

A rate with a denominator of 1 unit, such as 60 km per hour or 2,000 won per kilogram.

How do I find the unit price?

Divide the price by the number of units, for example price ÷ weight.

What is the inverse unit rate used for?

To answer the opposite question, such as time per kilometre or kilograms per dollar.

Sources: OpenStax, Prealgebra 2e (2020), §5.7 Ratios and Rate

Checked 9 Nov 2026. OpenStax, Prealgebra 2e (2020), §5.7 Ratios and Rate (a rate compares two quantities of different units; a unit rate is a rate with denominator 1 unit, found by dividing the numerator by the denominator; a unit price is a unit rate for one item) — read via the LibreTexts copy of the OpenStax text.

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