Quick facts
- •X% of Y is Y × X ÷ 100. So 20% of 80 is 80 × 20 ÷ 100 = 16.
- •Percentage change is (new − old) ÷ old × 100. Going from 80 to 100 is a 25% increase. Going from 100 back to 80 is a 20% decrease.
- •Two discounts do not add up. 30% off and then another 30% off is 51% off, not 60%, because the second discount applies to the lower price.
- •A 10% rise followed by a 10% fall leaves you 1% lower, since the second change applies to a bigger number.
- •A 100% increase doubles a number and a 200% increase triples it. A 50% fall needs a 100% rise to get back.
Quick reference
| Percentage | Fraction | Decimal | Common use |
|---|---|---|---|
| 5% | 1/20 | 0.05 | Small fees and interest |
| 10% | 1/10 | 0.10 | Tips and small discounts |
| 20% | 1/5 | 0.20 | Sales and service charges |
| 25% | 1/4 | 0.25 | Quarter off |
| 50% | 1/2 | 0.50 | Half price |
| 75% | 3/4 | 0.75 | Three-quarters |
Worked examples
A $50 shirt is 30% off. What do I pay?
$35
30% of $50 is $15, and $50 − $15 = $35. You could also multiply by 0.70.
The same shirt gets another 30% off at the till. What now?
$24.50, a total discount of 51%
The second 30% applies to $35, not $50, so it takes off $10.50. The total saving is $25.50 on $50, which is 51%.
My investment fell 50% and then rose 50%. Am I back to even?
No. You are down 25%
$1,000 falls to $500. A 50% gain on $500 is $250, which gets you to $750. To get back to $1,000 you would need a 100% gain.
Prices rose from 80 to 100. What is the percentage increase?
25%
(100 − 80) ÷ 80 × 100 = 25. The same change in reverse, from 100 to 80, is a 20% decrease, because the starting value is different.
Adding percentages that should be multiplied
The mistake
Treating 30% off plus another 30% off as 60% off.
Do this instead
Multiply what is left. 30% off leaves 70%. Another 30% off leaves 70% of that, which is 49%. The total discount is 51%.
Why it matters
A shopper expecting a $100 item at $40 pays $49 instead. The gap repeats across every item in a basket.
Why a percentage calculator matters
Stacked discounts
- •"Extra 30% off" on top of 30% off sounds like 60% off. It is 51% off.
- •Each discount is taken from the price left after the last one.
- •Multiply the remaining shares: 0.70 × 0.70 = 0.49, so you pay 49%.
- •Check the final price on the screen, not the headline number.
Discounts and tax
- •A 20% discount followed by 20% tax does not cancel out.
- •$100 becomes $80 after the discount, then $96 after 20% is added.
- •The order matters because each percentage applies to a different amount.
- •Sales tax is normally added after the discount, so check how your shop does it.
Gains and losses are not symmetrical
- •Losing 50% needs a 100% gain to recover.
- •A 10% gain then a 10% loss is 1% down overall.
- •The base changes at every step, so percentages never simply cancel.
- •This is why large losses in investments are so hard to recover from.
What makes this percentage calculator useful
Three calculators in one
Find X% of Y, find what percent X is of Y, and find the percentage change between two values.
Formula shown
Every answer is shown with the formula so you can check it by hand or copy the method.
Stacked-discount walkthrough
A short explanation of why two 30% discounts make 51%, not 60%.
Recovery view
See the percentage gain needed to recover from a given percentage loss.
Professional applications
Retail
Shops use percentages for markups, margins and discounts, and need to know the difference between them.
An item that costs $20 and sells for $30 has a 50% markup but a 33.3% gross margin.
Finance
Analysts use percentages for returns, fees and portfolio weights.
A portfolio up 12% on $1,000,000 has gained $120,000.
Education
Teachers use percentages for marks and for teaching percentage change.
A score of 17 out of 20 is 85%. Missing two questions costs 10 percentage points, not 2.
Historical context
Frequently asked questions
How do I calculate a percentage of a number?+
Multiply the number by the percentage and divide by 100. For 20% of 80, calculate 80 × 20 ÷ 100 = 16. On a basic calculator you can also multiply by 0.20.
How do I find what percent one number is of another?+
Divide the first number by the second and multiply by 100. For example, 30 is 20% of 150, because 30 ÷ 150 × 100 = 20.
How do I calculate percentage increase or decrease?+
Subtract the old value from the new one, divide by the old value, then multiply by 100. A positive result is an increase and a negative one is a decrease. From 80 to 100 gives +25%.
What is the difference between percentage change and percentage points?+
Percentage points compare two percentages directly. If a rate rises from 4% to 6%, that is 2 percentage points, or a 50% increase in the rate itself. News and reports often mix these up.
What this calculator cannot do+
It cannot tell you whether a discount is a good deal. That depends on the price before the discount, tax, shipping and your needs. For loans, savings and exams it only does the percentage part, so use the Loan, Investment or Grade calculators for the rest.