Percentage Calculator, % of a Number, % Change & More
Percentages are simple until money is involved, then everyone second guesses the maths. This free percentage increase calculator between two numbers answers the most common questions people actually ask: how much something rose or fell between two numbers, what percentage one number is of another, and, with the reverse percentage calculator, how to recover the original price before an increase or discount. Pick the mode, enter two numbers, done.
Last updated: October 22, 2026
Your result
A negative percentage change means a decrease.
The formula
X% of Y = (X ÷ 100) × YA is what % of B = (A ÷ B) × 100Percentage change from A to B = ((B − A) ÷ A) × 100
A worked example
20% of 150 is 30. Separately, 30 is 20% of 150. And going from 150 to 180 is a 20% increase, while going from 150 to 120 is a 20% decrease, the same numbers, three different questions.
More about the Percentage Calculator
What a percentage actually is
A percentage is simply a number expressed as a fraction of 100, “per cent” literally means “per hundred”. 45% is 45 out of every 100, or 0.45 as a decimal; 100% is the whole thing. That is the entire concept, and every percentage question is just a rearrangement of it.
The master formula behind all three modes above is: percentage = (part ÷ whole) × 100. To find X% of a number instead, convert the percentage to a decimal and multiply, 20% of 150 is 0.20 × 150 = 30. Percentage change between two numbers is (new − old) ÷ old × 100: a positive answer means growth, a negative one means a drop.
The three percentage questions
The three modes, one set of numbers. Start with 150. Mode one, 20% of 150: 30. Mode two, 30 is what percent of 150: 20%. Mode three, from 150 to 180 is a 20% increase; from 150 to 120 is a 20% decrease. Same numbers, three different questions, three different answers, which is exactly why a dedicated mode for each beats one generic formula box.
Where percentages actually bite: discounts (20% off $75 is $15 off. You pay $60), pay rises (£30,000 to £32,000 is 6.7%, and with recent inflation anything under ~3% was effectively a cut), investment returns, exam scores (27 out of 32 is 84.4%), and tax (your effective rate, total tax over total income, is always lower than your top marginal rate). The calculator's change mode is the workhorse; most real questions are "how much did it move."
Reverse percentages and mental shortcuts
Two mental models worth keeping. First, the 10% trick above. It makes you faster than reaching for your phone for anything ending in 5 or 0. Second, always sanity check the base: "50% more" and "50% off" are not opposites ($100 → $150 → $75). If a result looks surprising, you probably divided by the wrong number, the single most common percentage error there is.
Limits are few because the maths is exact: what you enter is what it computes, to full precision. The judgment calls are yours, which two numbers to compare, and whether a percentage or percentage points is the honest framing. For chained changes (discounts on discounts, multi year growth), run each step separately rather than adding percentages together; added percentages lie.
Percentage points vs percent change
A related trap is mixing up percent change with percentage points. If a bank raises its savings rate from 2% to 3%, that is a one percentage point increase, but a 50% relative increase. News headlines exploit this confusion constantly: "crime up 200%" sounds terrifying until you learn it went from 1 incident to 3. Whenever a percentage describes a change to another percentage, ask which of the two meanings is being used; the honest version states both.
Percentages also stack in ways that surprise people. A shop raises prices 10% then offers 10% off: you don't end up back at the original price, $100 becomes $110, then 10% off $110 is $99. That is because the second percentage acts on the new base, just as two successive 10% discounts combine to a 19% discount, not 20%. This is the same math behind compound interest and repeated discounts, and it is why "50% off, plus an extra 20% off" is 60% off total, not 70%.
Successive percentage changes do not cancel out
A $100 jacket rises 10 percent to $110. It then falls 10 percent in a sale, but the fall is 10 percent of $110, which is $11, landing at $99 rather than back at $100. Equal and opposite percentages never quite cancel, because the second one always acts on a different base than the first. The bigger the swing, the wider the gap: a 50 percent rise followed by a 50 percent fall leaves you at 75 percent of where you started.
The same compounding hides in pay rises. A salary of $4,200 a month with a 6.5 percent raise gains $273, reaching $4,473. A second identical 6.5 percent raise a year later applies to $4,473, adding about $291 and reaching roughly $4,764. Simply doubling the rate to 13 percent of the original salary would predict $4,746, about $18 a month short, because each rise also earns the percentage on all the rises before it.
Undoing a change: recovering the starting number
After that 6.5 percent raise, how do you recover the original $4,200 from the new $4,473? Divide by the growth factor: $4,473 ÷ 1.065 = $4,200 exactly. The tempting shortcut, subtracting 6.5 percent of the new salary, takes away $290.75 and lands at $4,182.25, understating the original by nearly $18. Percentages are anchored to the number they were taken from, so reversing one always means dividing by one plus the rate, never subtracting the rate from the new total.
The pattern generalises to any direction of change. To undo an increase of r percent, divide the result by (1 + r ÷ 100). To undo a decrease, divide by (1 − r ÷ 100), a price of $80 after a 20 percent markdown came from $80 ÷ 0.80 = $100, not from $80 plus a fifth. Run the division in the calculator whenever a bill, grade, or tax-inclusive total needs its before figure pulled back out of it.
The stacking trap almost everyone falls into
Two 20% discounts do not make 40% off. They make 36%. The second discount applies to the already reduced price, so $100 becomes $80, then $64. Stores know this; shoppers routinely do not. This calculator applies stacked discounts sequentially, which is the only correct way.
Take the worked example above: a $120 jacket at 30% off drops to $84. Stack an extra 10% coupon and it falls to $75.60. Add 8% sales tax and the final price is $81.65. You paid tax on a smaller amount, so against the full price with tax the real saving is $47.95, about 37%.
Checking whether a 'was/now' deal is genuine
Sale signs sometimes inflate the 'was' price. The reverse calculation exposes it: divide the sale price by (1 − discount ÷ 100). A $60 sale after a claimed 25% off implies a $60 ÷ 0.75 = $80 original, if the tag said $100, the 'discount' is fiction.
This is also handy for loyalty pricing and outlet stores, where the reference price is doing a lot of quiet work. Two minutes with the numbers beats trusting the red sticker.
Tax goes on last, usually
In almost every jurisdiction, sales tax or VAT is calculated on the discounted price, not the original. That $120 jacket is taxed on $75.60, not $120, a small mercy that genuinely lowers the bill.
The exceptions are rare but real, and where shelf prices already include tax (much of Europe), leave the tax field at 0. When in doubt, the receipt is the truth: compare the calculator's pre tax figure with the store's subtotal line.
The mental shortcuts worth memorizing
For 10% off, move the decimal point one place left: $84 → $8.40 off. For 20%, double that. For 25%, halve the price then halve again ($80 → $40 → $20 off). These three cover most sale signs you will ever see.
For anything else, the 'multiply by what's left' rule works: 30% off means you pay 70%, so multiply by 0.7. $120 × 0.7 = $84. One multiplication, no subtraction step, and it works for every percentage.
When the calculator says no
A discount is only a saving if you would have bought the item anyway. '70% off' on something you did not need is not a $70 saving. It is a $30 expense wearing a disguise. The calculator tells you the price; only you can tell it whether the purchase was real.
Watch for the anchoring trick too: an inflated 'was' price makes 30% off feel generous even when the sale price matches the everyday price elsewhere. Run the reverse calculation above, then check one competitor before celebrating.
Teaching the skill to kids
The discount aisle is a brilliant classroom: hand a child the calculator (or the mental shortcuts above) and let them work out which cereal box is actually cheaper. '30% off $6' is arithmetic with a purpose, and purpose is what makes math stick.
Start with the 10% trick, move the decimal point, then build to 20% and 25%. Within a week they will be doing sale math faster than most adults, and they will never again believe a red sticker without checking.
Discount stacking: when stores allow it
Some stores let you stack discounts, a 20% sale plus a 10% coupon, for example. The math is multiplicative, not additive: 20% then 10% off is not 30% off, it is 28% off ($100 → $80 → $72). The calculator handles sequential discounts if you run it twice.
Stacking rules vary wildly: coupons often exclude sale items, and 'extra 10% off clearance' usually applies to the already reduced price. Read the fine print, then verify with the two step calculation above, the register is not always right.
Loyalty programs and cashback (credit card rewards, shopping portals) are a second layer of stacking most people ignore. A 5% cashback on a 20%-off purchase is effectively a 24% discount, free money for clicking through the right link.
The psychology of 'was' pricing
'Was $200, now $120' feels like a $80 win, but if the item never actually sold at $200, the anchor is fiction. Some retailers inflate 'was' prices precisely to make discounts look dramatic.
Protect yourself with the reverse calculation (what was the pre discount price?) plus a 30 second competitor check. Genuine deals survive scrutiny; manufactured ones do not.
The best defense is knowing your prices: track what things normally cost before you need them. A shopper who knows the everyday price cannot be fooled by a theatrical 'was' price.
Worked example: two coupons, then the tax
Suppose a pair of shoes is priced at $85 with 25 percent off, and you hold an extra 15 percent coupon. The first discount takes the price to $63.75. The coupon then removes 15 percent of $63.75, not of the original $85, leaving $54.19. Your combined saving is 36.25 percent of the ticket price, real money, but not the 40 percent your brain wanted to add together at the shelf.
Tax is charged on what is left. At 6 percent sales tax, $54.19 grows to a final $57.44 at the till. Compare that with paying full price: $85 plus the same tax comes to $90.10. So the two stacked coupons saved you $32.66 overall, and because the discounts shrank the taxable amount first, a small slice of that saving came from paying less tax rather than less for the shoes.
Percent off or money off: which coupon wins
Percentage and fixed amount coupons trade places depending on the size of the basket. Ten dollars off a $40 item is a 25 percent saving, which beats a 20 percent coupon on the same item. But 20 percent off a $300 purchase is $60, dwarfing the same $10 voucher. The crossover is easy to find: divide the fixed amount by the percentage. A $10 coupon against a 20 percent coupon ties at exactly $50, below that ticket size the money off coupon wins, above it the percentage wins.
How to use the Percentage Calculator
- Choose the question you're answering: a percentage of a number, what percent one number is of another, or the change between two numbers.
- Enter the two numbers the mode asks for.
- Press Calculate. The change mode shows a negative for a decrease and a positive for an increase.
Discount questions
How do I work out 20% off in my head?
Multiply the price by 0.8. A $50 item at 20% off is $50 × 0.8 = $40. For 25% off multiply by 0.75; for 10% off multiply by 0.9. The calculator does it instantly and folds in tax when you need it.
Do two 20% discounts really not equal 40% off?
Right, they make 36% off, not 40%. The second 20% comes off the already reduced price ($100 → $80 → $64), not the original. Any store adding the percentages is either mistaken or hoping you won't check.
Is the tax calculated before or after the discount?
After, in almost every jurisdiction: tax applies to the discounted price. A $100 item at 20% off is taxed on $80. If your local rules differ, the receipt's subtotal line settles it, match the calculator to that.
Which is better: 40% off or buy one get one 50% off?
40% off wins. “Buy one, get one 50% off” averages out to only 25% off the pair, one item full price, one half price, while 40% off applies to every item. On two $100 items, the BOGO deal costs $150 and the 40%-off deal costs $120. Stores count on the BOGO sounding bigger; run both through the calculator above and the real answer takes seconds.
How do I find the original price if I only know the sale price and the percent off?
Work backwards by dividing, not by adding the percentage back. If you paid $63 after a 30 percent discount, the sale price is 70 percent of the original, so divide $63 by 0.70 to get $90. Adding 30 percent of $63 would give you only $81.90, which is wrong, because the discount was taken from the larger original amount while the percentage you add back is calculated on the smaller sale price.
Is the discount applied before or after shipping and handling fees?
Usually the percentage comes off the merchandise subtotal only, and shipping is added afterwards at its full rate, which is why a headline 40 percent off can feel smaller on the final bill. Some retailers discount the whole order including delivery, but that is the exception and is normally spelled out in the offer terms. When comparing two shops, compare the final totals including shipping and tax, not the discount percentages, which ignore those extras entirely.
Why does my receipt show a different discount amount than I expected?
Rounding and order of operations are the usual culprits. Many tills round the discounted price of each item to the nearest cent before adding them up, so three items at 33 percent off can differ by a cent or two from one calculation on the combined total. Coupons may also be applied before or after a store card discount depending on the retailer’s rules. A discrepancy of a few cents is arithmetic; a discrepancy of dollars means a coupon did not apply at all.
What does “up to 70 percent off” actually mean for the item I want?
It means 70 percent is the deepest discount somewhere in the sale, not the discount on everything. Typically a small slice of stock, end of line sizes, unpopular colours, display pieces, carries the headline rate, while most items sit at 20 to 40 percent off. The honest way to judge the offer is to check the actual item, size, and colour you intend to buy and run its real price through the calculator rather than trusting the banner.
How do I work out a discount with GST, HST or VAT?
Take the discount off the pre tax price first, then add tax to the reduced price. Enter the tax rate in the tax field, for example 13% HST in Ontario, 10% GST in Australia or 20% VAT in the UK. Where shelf prices already include tax, leave the tax field at zero.
How do you calculate a discount plus tax?
Take the discount off the shelf price first, then apply the tax rate to the reduced price, tax is charged on what you actually pay. The calculator above does both steps in the correct order.
Frequently asked questions
How do I calculate a percentage increase without messing it up?
Subtract the old number from the new, divide by the old number, multiply by 100. The classic slip is dividing by the new number instead, always divide by where you started. The change mode above does it for you, and labels increases and decreases clearly. (For a decrease the maths returns a negative; drop the minus sign when you say 'fell twelve percent', the word already carries the direction.)
What is the fastest mental trick for percentages?
Find 10% first, slide the decimal one place left, then scale. Twenty percent of $75: 10% is $7.50, double it, $15. Fifteen percent tip on $60: 10% is $6, half of that $3, total $9. This single trick handles most real world percentages in seconds.
What percentage did I save on a sale?
Original minus sale, divided by the original, times 100. An $80 jacket down to $60: (80 − 60) ÷ 80 × 100 = 25% saved. The calculator does it instantly, useful for checking whether that 'big discount' is actually big.
How do I calculate percentage of total sales?
Divide the part by the total, times 100. $4,500 of $30,000 is 4,500 ÷ 30,000 × 100 = 15%. Same maths as market share, conversion rates and commission splits.
How do I find the tax rate from a total price?
Divide the total by the pre-tax price, subtract 1, times 100. A $107 total on a $100 item means (107 ÷ 100 − 1) × 100 = 7%. It's adding tax in reverse, handy when the receipt shows only the final figure.
How do I calculate X percent of a number?
Convert the percent to a decimal and multiply: 15% of 200 = 200 × 0.15 = 30. Move the decimal two places left on the percent (15% becomes 0.15), then multiply. Everything else, tips, discounts, tax, interest, builds on this one.
How do I find the original price before a discount?
Divide the sale price by (1 − discount as a decimal): $60 after 25% off was 60 ÷ 0.75 = $80. The tempting mistake is adding 25% onto $60 to get $75, wrong, because the discount came off the bigger original number, not the sale price.
Is percent change the same as percent difference?
They are close cousins but not identical. Percent change measures movement from an old number to a new one, so the starting value is the base. Percent difference compares two numbers with no before and after. It uses the average of the two as the base. For small gaps they look nearly the same, but for big ones the numbers diverge, so the calculator above sticks to percent change whenever there is a clear starting point.
How do I find what percent X is of Y?
Divide X by Y and multiply by 100: (X ÷ Y) × 100. For example, 30 is what percent of 150? (30 ÷ 150) × 100 = 20%.
How do I calculate percent error?
Subtract the accepted value from your measured value, divide by the accepted value, and multiply by 100: |measured − accepted| ÷ accepted × 100. If you measured aluminum's density as 2.63 g/mL and the accepted value is 2.70 g/mL, the percent error is about 2.59%. In school chemistry labs, anything under 5% is generally considered good accuracy.