How to Calculate Percentages: Formulas and Examples

Percent of a number, percentage change and reverse percentages, with simple formulas and worked examples.

4 min read

Percentages show up everywhere: discounts, tips, tax, pay rises, exam scores, interest rates and growth figures. The good news is that almost every percentage question is one of a handful of types, and each has a short formula. Once you know which type you are dealing with, the math takes seconds.

"Percent" simply means "per hundred". 25% is 25 out of every 100, or 0.25 as a decimal. Every formula below builds on that.

1. Percent of a number

Use this when you know the percentage and want the amount, for example 15% of a $60 bill.

result = percent ÷ 100 × number. Example: 15 ÷ 100 × 60 = 9. The tip is $9.

Shortcut: 10% is the number with the decimal point moved one place left (60 becomes 6). From there, 5% is half of that and 20% is double.

2. What percent one number is of another

Use this for scores and shares, for example 42 correct answers out of 50.

percent = part ÷ whole × 100. Example: 42 ÷ 50 × 100 = 84%.

3. Percentage change (increase or decrease)

Use this to compare an old value with a new one, for example rent going from $1,200 to $1,320.

change = (new − old) ÷ old × 100. Example: (1,320 − 1,200) ÷ 1,200 × 100 = 10%. A positive result is an increase, a negative one a decrease. Always divide by the old value, the one you started from.

4. Increase or decrease a number by a percent

Use this for price changes and discounts, for example a $80 jacket with 25% off.

increased = number × (1 + percent ÷ 100) and decreased = number × (1 − percent ÷ 100). Example: 80 × 0.75 = 60. The jacket costs $60.

5. Reverse percentage: finding the original value

Use this when you know the final amount and the percentage, and want the starting value. For example, a price is $96 after a 20% increase. What was it before?

original = final ÷ (1 + percent ÷ 100) for an increase, or final ÷ (1 − percent ÷ 100) for a decrease. Example: 96 ÷ 1.2 = 80. The tempting shortcut of taking 20% off $96 gives $76.80, which is wrong. This is the same calculation used to remove sales tax or VAT from a price, which the VAT Calculator does for you.

6. Percentage difference

Use this to compare two values when neither one is the "before", for example two shops charging $45 and $55 for the same item.

difference = |a − b| ÷ ((a + b) ÷ 2) × 100. Example: 10 ÷ 50 × 100 = 20%. It compares the gap with the average of the two values, so the result is the same whichever way round you put them.

How to calculate percentages with QodeCat

The Percentage Calculator covers the common cases on one page, and results appear as you type. There is no button to press.

Find the card that matches your question: Percent of a number, Percent ratio, Percentage change, Increase / decrease by percent or Percentage difference.
Type your two values into the fields of that card. Decimals and negative numbers are fine.
Read the result under the fields. Percentage change also tells you whether it was an increase or a decrease, and the increase/decrease card shows both results at once.
Click the copy button next to a result to paste it elsewhere.

For a reverse percentage, use the formula above, or the VAT Calculator if you are taking tax out of a price.

Common mistakes

Dividing by the wrong number in a percentage change. Always divide by the starting value.
Assuming a rise and a fall cancel out. $100 down 20% is $80, and $80 up 20% is $96, not $100.
Mixing up percent and percentage points. An interest rate going from 2% to 3% is a rise of 1 percentage point, but a 50% increase.
Adding percentages that apply one after another. Two 10% discounts are 19% off in total, not 20%.
Taking the percentage off the final price to undo an increase. Divide instead, as in the reverse percentage formula.

Frequently asked questions

How do I calculate a percentage on a phone calculator?

Turn the percent into a decimal and multiply. For 18% of 250, type 0.18 × 250 = 45. That avoids the % key, which behaves differently on different calculators.

Can a percentage be more than 100%?

Yes. A value that grows from 50 to 150 has increased by 200%. A share of a whole, like a test score, cannot go above 100% though.

How to Calculate Percentages: Formulas and Examples

Percent of a number, percentage change and reverse percentages, with simple formulas and worked examples.

4 min read

"Percent" simply means "per hundred". 25% is 25 out of every 100, or 0.25 as a decimal. Every formula below builds on that.

1. Percent of a number

Use this when you know the percentage and want the amount, for example 15% of a $60 bill.

result = percent ÷ 100 × number. Example: 15 ÷ 100 × 60 = 9. The tip is $9.

Shortcut: 10% is the number with the decimal point moved one place left (60 becomes 6). From there, 5% is half of that and 20% is double.

2. What percent one number is of another

Use this for scores and shares, for example 42 correct answers out of 50.

percent = part ÷ whole × 100. Example: 42 ÷ 50 × 100 = 84%.

3. Percentage change (increase or decrease)

Use this to compare an old value with a new one, for example rent going from $1,200 to $1,320.

4. Increase or decrease a number by a percent

Use this for price changes and discounts, for example a $80 jacket with 25% off.

increased = number × (1 + percent ÷ 100) and decreased = number × (1 − percent ÷ 100). Example: 80 × 0.75 = 60. The jacket costs $60.

5. Reverse percentage: finding the original value

Use this when you know the final amount and the percentage, and want the starting value. For example, a price is $96 after a 20% increase. What was it before?

6. Percentage difference

Use this to compare two values when neither one is the "before", for example two shops charging $45 and $55 for the same item.

difference = |a − b| ÷ ((a + b) ÷ 2) × 100. Example: 10 ÷ 50 × 100 = 20%. It compares the gap with the average of the two values, so the result is the same whichever way round you put them.

How to calculate percentages with QodeCat

The Percentage Calculator covers the common cases on one page, and results appear as you type. There is no button to press.

Find the card that matches your question: Percent of a number, Percent ratio, Percentage change, Increase / decrease by percent or Percentage difference.
Type your two values into the fields of that card. Decimals and negative numbers are fine.
Read the result under the fields. Percentage change also tells you whether it was an increase or a decrease, and the increase/decrease card shows both results at once.
Click the copy button next to a result to paste it elsewhere.

For a reverse percentage, use the formula above, or the VAT Calculator if you are taking tax out of a price.

Common mistakes

Dividing by the wrong number in a percentage change. Always divide by the starting value.
Assuming a rise and a fall cancel out. $100 down 20% is $80, and $80 up 20% is $96, not $100.
Mixing up percent and percentage points. An interest rate going from 2% to 3% is a rise of 1 percentage point, but a 50% increase.
Adding percentages that apply one after another. Two 10% discounts are 19% off in total, not 20%.
Taking the percentage off the final price to undo an increase. Divide instead, as in the reverse percentage formula.

Frequently asked questions

How do I calculate a percentage on a phone calculator?

Turn the percent into a decimal and multiply. For 18% of 250, type 0.18 × 250 = 45. That avoids the % key, which behaves differently on different calculators.

Can a percentage be more than 100%?

Yes. A value that grows from 50 to 150 has increased by 200%. A share of a whole, like a test score, cannot go above 100% though.