How to Calculate Percentages

Percentages show up everywhere: sale tags, pay rises, interest rates, exam marks, nutrition labels and news headlines. They all rest on one simple idea, and once you see it, every percentage question becomes one of a few standard patterns. This guide walks through each pattern with a worked example you can check, and points out where people most often go wrong.

What a percentage really is

“Percent” means per hundred. 25% is 25 out of every 100, which is the fraction 25/100, the decimal 0.25, or one quarter. Converting between the three forms is the first skill to master:

Fraction	Decimal	Percent
1/2	0.5	50%
1/4	0.25	25%
3/8	0.375	37.5%
1/3	0.333…	33.3%
3/2	1.5	150%

• Percent → decimal: divide by 100 (move the decimal point two places left). 7.5% = 0.075.
• Decimal → percent: multiply by 100. 0.375 = 37.5%.
• Fraction → percent: divide the top by the bottom, then multiply by 100. 18 out of 24 = 18 ÷ 24 = 0.75 = 75%.

The three core percentage questions

Almost every percentage problem has three numbers in it: the part, the whole and the percentage. You know two of them and want the third.

part = whole × percent ÷ 100
percent = part ÷ whole × 100
whole = part ÷ (percent ÷ 100)

1. What is X% of Y?

35% of 240 = 0.35 × 240 = 84. Use this for tips, commission, tax and “how much is the discount”.

2. X is what percent of Y?

18 out of 24 = 18 ÷ 24 × 100 = 75%. Use this for test scores, completion rates and market share.

3. X is Y% of what?

42 is 60% of what? 42 ÷ 0.60 = 70. This is the “reverse” question, and it is the one people most often get wrong. More on that below.

The percentage calculator has a row for each of these, so you can type two numbers and read off the third.

Percentage change: increases and decreases

To measure how much something changed, compare the difference with the starting value:

percentage change = (new − old) ÷ old × 100

Worked example: a price rise and its reverse

A monthly subscription goes from $80 to $92.

1. Difference: 92 − 80 = 12.
2. Divide by the starting value: 12 ÷ 80 = 0.15.
3. Multiply by 100: +15%.

Now suppose it later drops back from $92 to $80. The difference is the same $12, but the starting value is now 92, so the change is 12 ÷ 92 = −13.04%. Going up 15% and coming down 13% land you in exactly the same place. That asymmetry surprises a lot of people, and the percentage change calculator shows both directions at once.

Applying a change

To increase a number by a percentage, multiply by (1 + rate). To decrease it, multiply by (1 − rate):

• $120 increased by 25% = 120 × 1.25 = $150
• $150 decreased by 20% = 150 × 0.80 = $120

Reverse percentages: finding the original

When you know the amount after a percentage was added or taken off, divide by the same multiplier instead of subtracting.

• Before a discount: a jacket on sale for $68 after 15% off. Original price = 68 ÷ 0.85 = $80.
• Before tax: a receipt total of $54 including 8% sales tax. Price before tax = 54 ÷ 1.08 = $50, and the tax was $4.

The tempting shortcut, taking 8% off $54, gives $49.68. That’s wrong, because the 8% was calculated on $50, not on $54. The sales tax calculator can add or remove tax in either direction.

Stacked and successive percentages

Percentages that apply one after another multiply. They don’t add.

• Stacked discounts: 20% off, then an extra 10% at the till, is 0.80 × 0.90 = 0.72 of the price, a total of 28% off, not 30%. The discount calculator handles a second discount for you.
• Growth over several years: 5% a year for 3 years is 1.05³ = 1.1576, a total rise of 15.76%, not 15%. This is compounding, the same effect that makes savings grow faster over time.
• A fall then a rise: −10% then +10% is 0.9 × 1.1 = 0.99, a net loss of 1%.

Everyday percentage calculations

Tips and splitting the bill

A restaurant bill of $86.40 with an 18% tip: 86.40 × 0.18 = $15.552, so $15.55. The total is $101.95, and split four ways that is $25.4875, so $25.49 each. The tip calculator does the rounding and the split in one go.

Percent vs. percentage points

If a savings rate rises from 3.5% to 4.2%, it went up by 0.7 percentage points. Relative to where it started, that is a 20% increase (0.7 ÷ 3.5). Both statements are true, but they sound very different, which is why careful reporting says which one it means.

Percentage difference between two values

When neither value is the “starting” one, for example comparing two quotes of $48 and $60, use the average as the base: 12 ÷ 54 × 100 = 22.2% difference.

Weighted percentages: grades and scores

When parts of a total count for different amounts, you can’t simply average the percentages. Multiply each score by its weight, then add the results.

A course grade is 20% homework, 30% midterm and 50% final exam. A student scores 85%, 90% and 74%:

0.20 × 85 + 0.30 × 90 + 0.50 × 74 = 17 + 27 + 37 = 81%

The plain average of the three scores is 83%, which overstates the grade because the weakest result, the final, carries half the weight. The same method works for portfolio returns, survey results and any “share of the total” figure where the parts differ in size.

Mental math shortcuts

• 10%: move the decimal point one place left. 10% of 340 = 34.
• 5%: half of 10%. 20%: double 10%. 15%: 10% plus 5%.
• 1%: move the decimal point two places left, then multiply for any whole number.
• Swap trick: X% of Y equals Y% of X. 8% of 50 is the same as 50% of 8, which is 4.
• 25%, 50%, 75%: divide by 4, halve, or take three quarters.

Common mistakes to avoid

1. Dividing by the wrong base. Percentage change always divides by the old value. From 80 to 100 is +25%, but from 100 to 80 is −20%.
2. Reversing by subtraction. To undo a 15% discount, divide by 0.85. Adding 15% back gives the wrong original.
3. Adding successive percentages. Chain them by multiplying the multipliers.
4. Mixing percent and percentage points. Say which one you mean, especially with interest rates and polls.
5. Rounding too early. Keep full precision until the final answer, then round once, usually to two decimal places for money.

Percentages are simple once you identify which of the core questions you are answering. When in doubt, write down the part, the whole and the percentage, mark the one you don’t know, and use the matching formula.

Frequently asked questions

What is the easiest way to work out a percentage of a number?

Turn the percentage into a decimal by dividing it by 100, then multiply. 35% of 240 is 0.35 × 240 = 84. For quick mental estimates, find 10% by moving the decimal point one place left and build from there.

How do I find the original price before a discount?

Divide the sale price by (1 − discount as a decimal). A $68 item that was 15% off originally cost 68 ÷ 0.85 = $80. Adding 15% to $68 gives $78.20, which is wrong.

Why don't two 10% changes cancel out?

Because the second change applies to a different starting amount. A 10% fall followed by a 10% rise gives 0.9 × 1.1 = 0.99, a net loss of 1%.

What is the difference between percent and percentage points?

Percentage points are the plain difference between two percentages. A rate that moves from 3.5% to 4.2% rose by 0.7 percentage points, which is a 20% increase relative to where it started.

Can a percentage be more than 100%?

Yes. 150 is 150% of 100, and a price that goes from $40 to $100 has risen by 150%. A decrease, however, can never be more than 100%, because you can't lose more than everything.