Quick answer
A unit rate expresses how much per one unit. Calculate it by dividing the total quantity by the number of units. 12 items for £15.60 → £15.60 ÷ 12 = £1.30 per item.
How to use this calculator
Enter the total quantity and the number of units. Optionally enter a scale to project the rate to a different quantity (e.g. total cost for 50 items). The calculator returns the unit rate and the scaled total.
What is a unit rate?
A unit rate is a ratio where the second term (the denominator) equals 1. It answers "how much per one unit?" — per item, per hour, per kilometre, per kilogram. Unit rates standardise different-sized packages or time periods so they can be compared directly.
Common unit rates: price per 100 g (supermarket shelf labels), kilometres per hour (speed), calories per serving, earnings per hour, kilometres per litre (fuel efficiency).
Unit rate formula
$$\text{Unit rate} = \frac{\text{Quantity}}{\text{Number of units}}$$
$$\frac{\$15.60}{12 \text{ items}} = \$1.30 \text{ per item}$$
$$\frac{450 \text{ km}}{4.5 \text{ hours}} = 100 \text{ km/h}$$
To project the rate to any number of units n:
$$\text{Total for } n \text{ units} = \text{unit rate} \times n$$
Worked examples
Example 1: price per item
A bag of 12 oranges costs £2.76. Unit rate: £2.76 ÷ 12 = £0.23 per orange. Cost of 7 oranges: 7 × £0.23 = £1.61.
Example 2: speed
A car travels 390 km in 4.5 hours. Speed: 390 ÷ 4.5 = 86.67 km/h.
Example 3: fuel efficiency
A car uses 55 litres to travel 825 km. Efficiency: 825 ÷ 55 = 15 km/litre. For a 300 km journey: 300 ÷ 15 = 20 litres needed.
Example 4: earnings
£480 for 32 hours. Unit rate: £480 ÷ 32 = £15/hour. For 40 hours: 40 × 15 = £600.
Comparing unit rates for value
Unit rates are the standard method for finding the best-value option across different pack sizes:
$$\text{Best value: lowest unit rate}$$
| Pack size | Price | Unit rate (per 100 g) | Best value? |
|---|---|---|---|
| 250 g | £1.20 | £0.48/100 g | |
| 500 g | £2.10 | £0.42/100 g | |
| 1 kg | £3.80 | £0.38/100 g | ✓ Best value |
Common applications
| Domain | Quantity | Units | Unit rate |
|---|---|---|---|
| Supermarket | Price | Weight (g) | £/100 g |
| Transport | Distance (km) | Time (h) | km/h |
| Fuel | Distance (km) | Volume (L) | km/L or L/100 km |
| Employment | Earnings (£) | Hours | £/hour |
| Nutrition | Calories (kcal) | Serving (g) | kcal/100 g |
| Finance | Return (£) | Time (year) | £/year |
Common mistakes
Dividing in the wrong direction
The unit rate is always (quantity ÷ units), not (units ÷ quantity). Price per item = price ÷ items, not items ÷ price.
Not matching units when comparing
Comparing £/100 g with £/kg is not direct. Convert both to the same unit first: 1 kg = 1000 g, so £5/kg = £0.50/100 g.
Frequently asked questions
What is a unit rate?
A rate expressed per one unit — per item, per hour, per kilometre. Calculated by dividing the total by the number of units.
How do you calculate unit rate?
Divide the total quantity by the number of units. Example: 12 items for £15.60 → £15.60 ÷ 12 = £1.30/item.
How do you use unit rate to find best value?
Calculate the unit rate for each option (e.g. price per 100 g) and choose the lowest.