How do I calculate percentage increase?

Subtract the old value from the new value, divide by the old value, and multiply by 100. For example, going from 80 to 100 is ((100 − 80) ÷ 80) × 100 = 25% increase.

What is the formula for percentage of a number?

To find X% of a number Y, divide X by 100 and multiply by Y. For example, 15% of 200 is (15 ÷ 100) × 200 = 30.

How do I find the original price after a discount?

Divide the sale price by (1 − the discount as a decimal). If an item costs $60 after a 25% discount, the original was 60 ÷ 0.75 = $80.

30. Multiply 200 by 0.15, or take 10% (20) and add half of that (10).

How do I calculate a percentage increase?

Subtract the old value from the new, divide by the old value, multiply by 100. Formula: ((new − old) ÷ old) × 100.

Percentage calculator — % of, what %, % change

Three modes for the three percentage questions you actually ask. Updates as you type.

The three flavours of percentage math

Most percentage questions reduce to one of three patterns: what is X% of Y, X is what % of Y, or what's the % change from X to Y. They sound similar but they need different formulas, and confusing them is where most percentage mistakes come from. Each tab here owns one flavour so you don't have to remember which formula to use.

The formulas

% of:(a ÷ 100) × b — "15% of $80" → 12
is what %:(a ÷ b) × 100 — "12 is what % of 80" → 15%
% change:((b − a) ÷ |a|) × 100 — "from $80 to $100" → +25%

Worked examples

What is 30% of $240? → (30 ÷ 100) × 240 = $72
18 is what % of 72? → (18 ÷ 72) × 100 = 25%
Price went from $80 to $96 — what's the % increase? → ((96 − 80) ÷ 80) × 100 = 20%
Item marked down 35% from $120 — what's the sale price? → 120 × (1 − 0.35) = 120 × 0.65 = $78

Percentage cheat table

Mental math shortcuts for common percentages:

10% of any number — move the decimal one place left
5% — half of 10%
1% — move the decimal two places left
15% — add 10% and 5% together
20% — double the 10%
25% — divide by 4
33% — divide by 3 (approximately)
50% — divide by 2

Reverse percentage — finding the original

If a price after a 20% discount is $80, the original wasn't $80 + 20%. The correct method: original = discounted price ÷ (1 − discount%). So $80 ÷ 0.80 = $100. The common mistake is adding the discount percentage back onto the discounted price — that gives $96, not $100, because you're applying 20% to the wrong base.

Percentage points vs percent change

These two phrases measure different things and are often conflated in media coverage. If interest rates rise from 2% to 3%, that's an increase of 1 percentage point— the arithmetic difference between two percentages. But it's a 50% change— because 1 is 50% of 2. Percentage points describe absolute changes in rates or proportions; percent change describes the relative movement. When a headline says "rates jumped 50%" versus "rates rose 1 percentage point," they can be describing the exact same event.

The trap with percent change

A 50% loss followed by a 50% gain doesn't put you back where you started. If you start at $100, lose 50%, you're at $50. A 50% gain on $50 only takes you to $75 — you needed a 100% gain to recover. This is why percent-change figures over multiple periods are easy to misread; for compounded growth, look at multiplicative ratios instead of additive percentages.

Tipping, sales tax, and discounts

For tipping a meal, use the tip calculator — it adds the tip on top and splits the bill in one move. For a sales discount, multiply by (1 − discount%). For sales tax on top of a price, multiply by (1 + tax%). Stacked discounts (e.g. 20% off, then another 10% off the discounted price) compound multiplicatively, not additively.

Percentage calculator