What is a percentage?
A percentage describes part of something as a number out of 100. “Per cent” literally means “per hundred”, so 25% means 25 out of every 100, or one quarter. Percentages make it easy to compare things of different sizes: a 20% discount means the same thing on a $10 shirt as on a $1,000 laptop.
How to calculate a percentage
Most percentage questions come back to one simple relationship:
Percentage = Part ÷ Whole × 100
Here is how each calculator above uses it, with a worked example:
- What is X% of Y? Multiply Y by X, then divide by 100. 15% of 200 = 200 × 15 ÷ 100 = 30.
- X is what percent of Y? Divide X by Y, then multiply by 100. 30 ÷ 200 × 100 = 15%.
- Percentage change. Subtract the old value from the new one, divide by the old value and multiply by 100. From 200 to 250: (250 − 200) ÷ 200 × 100 = a 25% increase.
- Increase or decrease by X%. Multiply by 1 plus or minus the percentage as a decimal. 80 increased by 25% is 80 × 1.25 = 100. Decreased by 25%, it is 80 × 0.75 = 60.
- Percentage difference. Divide the gap between two numbers by their average. For 30 and 50: 20 ÷ 40 × 100 = 50%.
- Marks percentage. Divide marks obtained by total marks and multiply by 100. See the example below.
Percentage change vs percentage difference
These sound alike but answer different questions. Percentage change has a direction: there is a starting value and an ending value, and the change is measured against the start. Use it for prices, salaries, test scores or anything that moves over time.
Percentage difference has no direction. It compares two values on equal terms, measured against their average. Use it when neither number is the “original”, such as the price of the same item in two different shops.
You can see the difference clearly with 200 and 250:
- 200 → 250 is a 25% increase.
- 250 → 200 is a 20% decrease.
- The percentage difference between 200 and 250 is 50 ÷ 225 × 100 ≈ 22.2222%, whichever order you enter them.
Same two numbers, three different answers, so it is worth choosing the one that matches your question.
How to calculate percentage of marks
Divide the marks you scored by the total marks available, then multiply by 100. If you scored 420 out of 500, that is 420 ÷ 500 × 100 = 84%.
For several subjects, add up all the marks obtained and all the total marks first, then divide. Scores of 72/100, 45/50 and 130/150 give 247 out of 300, or 82.3333%. Averaging the three separate percentages (72%, 90% and 86.67%) gives a slightly different 82.89%, because the subjects have different totals. Check which method your school uses.
Quick mental math tricks
- 10%: move the decimal point one place left. 10% of 360 is 36.
- 5%: halve the 10% figure. 5% of 360 is 18.
- 1%: move the decimal point two places left. 1% of 360 is 3.6.
- Build the rest: 15% = 10% + 5%, so 15% of 360 is 36 + 18 = 54. 20% is simply 10% doubled.
- Swap the numbers: X% of Y is always the same as Y% of X. 8% of 50 sounds hard, but 50% of 8 is easy: 4.
Frequently asked questions
How do I work out a percentage on a normal calculator?
Divide the part by the whole, then multiply by 100. To find what percent 18 is of 72, type 18 ÷ 72 × 100 = 25%. To find 18% of 72, type 72 × 18 ÷ 100 = 12.96.
Why doesn't a 50% increase followed by a 50% decrease get me back to where I started?
Because each percentage is measured from a different starting point. 100 increased by 50% is 150, but 50% of 150 is 75, so you end at 75. To undo a 50% increase you need a decrease of about 33.33%.
How do I find the original price before a discount?
Divide the sale price by 1 minus the discount written as a decimal. If an item costs $68 after 15% off, the original price was 68 ÷ 0.85 = $80.
Can a percentage be more than 100%?
Yes, when something grows beyond its starting size. Going from 50 to 150 is a 200% increase, and 150 is 300% of 50. Percentages that describe part of a fixed total, such as exam marks, are the exception and can't go above 100%.
What is the difference between percent and percentage points?
Percentage points measure the simple gap between two percentages. If an interest rate rises from 4% to 5%, it has gone up by 1 percentage point, but that is a 25% increase in the rate itself.