Unit Rate Calculator
Enter a total value and a quantity, with optional units, to find the rate for exactly one unit.
Updated
Unit Rate Calculator
Our Unit Rate Calculator divides a total by a quantity to find the rate for exactly one unit: the price per pound, miles per hour, pay per hour or anything per anything. Add your own units, such as $ and lb, and the answer reads naturally, like $2.50 per lb. It also shows the working, the exact fraction, the inverse rate and the rate for 100 units, and it accepts decimals and fractions such as 3/4.
Quick answer
A unit rate is a rate with 1 in the denominator. To find it, divide the total by the quantity. For example, $10 for 4 lb is $10 ÷ 4 = $2.50 per lb, and 150 miles in 3 hours is 150 ÷ 3 = 50 miles per hour.
- Formula: unit rate = total value ÷ quantity
- Unit price: price ÷ number of units, used to compare deals
- Fractions: 1/2 mile in 1/4 hour = (1/2) ÷ (1/4) = 2 miles per hour
- Lowest unit price is the better buy
What Is a Unit Rate?
A rate compares two quantities measured in different units, such as 150 miles in 3 hours. A unit rate is the same rate written so the second quantity is 1:
= 50 miles / 1 hour
= 50 miles per hour
The word "per" means "for each one", so a unit rate answers questions like how much for one pound, how far in one hour or how much pay for one hour of work.
How to Find a Unit Rate
- Write the rate as a fraction with the thing you want "per" on the bottom.
- Divide the top by the bottom.
- Attach the units: top unit "per" one bottom unit.
$84 / 6 hours
= $84 ÷ 6
= $14 per hour
Unit Rate Examples
| Situation | Unit rate |
|---|---|
| $10 for 4 lb | $2.50 per lb |
| 150 miles in 3 h | 50 mph |
| $84 for 6 h work | $14 per hour |
| 360 mi on 12 gal | 30 mpg |
| 24 cans for $11.76 | $0.49 per can |
| $10 for 3 items | $3.33 per item |
$10 ÷ 3 is 3.333…, a repeating decimal. The calculator shows it as $3.3333 and as the exact fraction 10/3, and says that it is about $3.33 to the cent.
Unit Rates With Fractions
When either quantity is a fraction, divide the fractions (keep, change, flip). Walking 1/2 mile in 1/4 hour:
= 2 miles per hour
A recipe using 2/3 cup of sugar for 1/6 of a batch needs (2/3) ÷ (1/6) = 4 cups per batch. Type 2/3 and 1/6 straight into the calculator; it works with the exact fractions.
Comparing Unit Prices
The unit price tells you which pack is cheaper for the same amount. A 12 oz box for $3.99 or an 18 oz box for $5.49?
$5.49 ÷ 18 = $0.305 per oz
The 18 oz box costs less per ounce, so it is the better deal, provided you will use it all. Compare in the same unit: convert grams to kilograms or ounces to pounds first.
Using a Unit Rate to Scale Up
Once you know the rate for one, multiply to get any amount:
50 mph × 4.5 h = 225 miles
Dividing by the rate goes the other way: at 30 mpg, 240 miles needs 240 ÷ 30 = 8 gallons. The "For 100" row in the calculator gives the rate for 100 units, which is how many shops label prices (per 100 g or per 100 ml).
Common Unit Rates
- Speed
- Miles per hour or kilometers per hour.
- Unit price
- Price per pound, per ounce, per liter or per item.
- Wage
- Pay per hour.
- Fuel economy
- Miles per gallon or kilometers per liter.
- Heart rate
- Beats per minute.
- Density
- People per square mile, grams per cubic centimeter.
Common Mistakes
- Dividing the wrong way. 4 lb ÷ $10 = 0.4 lb per dollar, not a price per pound. Put the "per" quantity on the bottom.
- Mixing units. 30 miles in 45 minutes is 30 ÷ 0.75 = 40 miles per hour, not 30 ÷ 45.
- Rounding too early. Keep full precision until the end, then round money to the cent.
- Comparing different units. A price per ounce cannot be compared with a price per gram.
- Dividing by zero. A quantity of 0 has no unit rate.
Key Terms
- Rate
- A comparison of two quantities in different units.
- Unit rate
- A rate whose second quantity is 1.
- Unit price
- A unit rate giving the cost of one unit.
- Per
- For each one; written as / in units such as mi/h.
- Inverse rate
- The rate the other way round, such as lb per dollar.
How to Use the Unit Rate Calculator
- Enter the total value. Type the total on the top line, such as the price paid, the distance or the pay, and optionally its unit, such as $, miles or dollars. Decimals, commas and fractions such as 3/4 all work.
- Enter the quantity. Type the quantity on the bottom line, such as the weight, the time or the number of items, and optionally its unit, such as lb, hours or cans. It cannot be 0.
- Read and copy the unit rate. The rate per one unit appears as you type, such as $2.50 per lb. The table shows the working, the exact fraction, the inverse rate and the rate for 100 units. Press Copy to copy it, or Clear or Esc to start again.
Example: enter 10 with unit $ on top and 4 with unit lb below. The unit rate is $2.50 per lb, with the working 10 ÷ 4 = 2.50, the inverse 0.4 lb per $1 and $250.00 for 100 lb.
Who Can Use This Calculator?
Frequently Asked Questions (FAQs)
What is a unit rate?
A unit rate is a rate whose second quantity is 1, such as 50 miles per hour or $2.50 per pound. It tells you how much of the first quantity goes with exactly one of the second.
How do you find the unit rate?
Divide the total by the quantity. $10 for 4 lb is $10 ÷ 4 = $2.50 per lb, and 150 miles in 3 hours is 150 ÷ 3 = 50 miles per hour.
What is the unit rate formula?
Unit rate = total value ÷ quantity. The unit of the answer is the total unit per one quantity unit, for example dollars per hour.
What is the difference between a rate and a unit rate?
A rate compares any two quantities in different units, such as 150 miles in 3 hours. A unit rate is the same rate scaled so the second quantity is 1: 50 miles in 1 hour.
How do you find a unit rate with fractions?
Divide the fractions by multiplying by the reciprocal. 1/2 mile in 1/4 hour is (1/2) ÷ (1/4) = 1/2 × 4 = 2 miles per hour. You can type fractions such as 1/2 directly into the calculator.
How do you find the unit price?
Divide the price by the number of units. 24 cans for $11.76 is $11.76 ÷ 24 = $0.49 per can.
How do you use unit rates to compare prices?
Work out the price per unit for each option in the same unit, then pick the lowest. 12 oz for $3.99 is $0.3325 per oz and 18 oz for $5.49 is $0.305 per oz, so the 18 oz pack is cheaper per ounce.
Is miles per hour a unit rate?
Yes. Miles per hour is distance per one hour of time, so 60 miles per hour means 60 miles are covered in each hour. Other common unit rates are miles per gallon, dollars per hour and beats per minute.
Can a unit rate be a decimal or a fraction?
Yes. $10 for 3 items is 10/3 = $3.33 per item when rounded to the cent, and 3 cups for 4 servings is 3/4 cup per serving.
Is the Unit Rate Calculator free?
Yes. It is completely free, needs no sign-up, and can be used as many times as you like.
Try our Unit Rate Calculator to find the rate per one unit, with your own units and the working shown.