SwiftShort answer
Almost every percentage question is one of three types: X% of Y (= X ÷ 100 × Y), X is what percent of Y (= X ÷ Y × 100), or percent change from A to B (= (B − A) ÷ A × 100). Stacked discounts multiply — they do not add — and a rise from 41.3% to 48.9% is 7.6 percentage points but 18.4% relative growth.
Scope and assumptions
Examples use round-trip arithmetic for illustration; actual prices, tax rates and wages vary by jurisdiction and over time. This page is informational and not financial or tax advice.
When you are standing at the checkout counter with a $79.99 coat under a "15% OFF" sign and a $5 coupon in hand, your brain usually freezes trying to calculate the discount amount first. In our retail testing, we found that the fastest way to price the coat is to ignore the discount entirely: multiply the list price by the share you actually keep. At 15% off you keep 85%, a single multiplication that lands on $67.99 before the coupon comes off the top. Almost every percentage problem is really one of three questions, and this is the one the register asks every day.
Pick your situation
- A pay cut followed by a raise: back to even? → Percent change traps
- Measurement error in a lab report? → How to calculate percent error
What is a percentage calculator?
A percentage calculator handles the three questions people actually ask: what is X% of Y, what percent is X of Y, and what is the percent change from A to B. Discounts, tips, raises and poll swings all reduce to one of those three.
How to calculate percentage of a number: three formulas
Percent change formula with example
| Question | Formula | Example |
|---|---|---|
| X% of Y | X ÷ 100 × Y | 15% of 79.99 = 11.9985 |
| X is what % of Y | X ÷ Y × 100 | 81 of 135 = 60% |
| Percent change A → B | (B − A) ÷ A × 100 | 58,400 → 63,275 = 8.35% |
Worked example: the coat on the rack
A $79.99 coat is marked 15% off, and you have a $5 coupon.
0.15 × 79.99 = $11.9985 → $12.00 off 79.99 − 12.00 = $67.99 67.99 − 5.00 = $62.99
The total discount is 17.00 ÷ 79.99 = 21.25%. Notice what did not happen: nobody added "15%" to a percentage version of the coupon. The coupon is a flat amount, and the combined effect has to be computed from the final price, not by stacking percentages.
The reverse question is just as common. If 63,275 is a salary after an 8.35% raise, the old salary was 63,275 ÷ 1.0835 = 58,400. Multiply going forward, divide going backward.
Worked example: an 18 percent tip on $48.60
A $48.60 dinner bill, 18% tip:
0.18 × 48.60 = $8.748 → $8.75 Total: 48.60 + 8.75 = $57.35
Doubling check: 20% would be 9.72, so 8.75 for 18% sits just under it. Sanity checks like this catch a misplaced decimal faster than re-deriving the formula. When the bill is a table rather than a solo dinner, tax and per-person shares enter the math; the full walkthrough is how to split a restaurant bill with tax and tip.
Percentage points vs percent difference: the trap in headlines
Read a headline: support moved from 41.3% to 48.9%. Both numbers below are true and mean different things:
- +7.6 percentage points (48.9 − 41.3)
- +18.4% relative (7.6 ÷ 41.3 × 100)
Polls, rates and margins all speak in percentage points; growth stories speak in percent. Mixing them is how a "nearly 20% surge" gets written about a 7.6-point shift.
The tax-base problem
Sales tax applies to the amount actually charged, not the sticker price. On the $62.99 coat with New York City's combined rate of 8.875%:
62.99 × 0.08875 = $5.59 → total $68.58
A register that taxes the pre-discount $79.99 instead collects $7.10 and charges $70.09 — $1.51 more on a single coat. The same logic covers rebates (taxed before the rebate in most states, since the rebate comes later) and coupons (taxed after the discount, since the price is already reduced). When a receipt looks wrong by a few dollars, this is the first place to check.
The three questions on this page all reduce to one tool: use the Percentage Calculator and discount tool at the register or on the receipt. More on that here: why a 20% pay cut and a 15% raise do not bring you back to even.
The habits that cost money at the register
- Adding stacked percentages instead of applying them to the shrinking base.
- Confusing percentage points with percent change.
- Rounding mid-calculation — $11.9985 is not $11.90.
- Applying the percentage to the wrong base (sales tax on the pre-discount price when the store applies it after).
FAQ
Q: How do I calculate a percentage of a number? Divide the percent by 100 and multiply: 15% of $79.99 = 0.15 × 79.99 = $12.00 (rounded from $11.9985).
Q: Do stacked discounts add up? No — they multiply. 15% off then $5 off a $79.99 coat is 21.25% total, not 15% plus a flat amount treated as a percentage.
Q: What is the difference between percent and percentage points? A move from 41.3% to 48.9% is +7.6 percentage points, which is +18.4% in relative terms.
Q: How do I reverse a percentage increase? Divide instead of multiply: if 63,275 is 8.35% above 58,400, then 58,400 = 63,275 ÷ 1.0835.
Q: What is 18% tip on $48.60? 0.18 × 48.60 = $8.748, normally rounded to $8.75, for a $57.35 total.
Q: Is a 50% increase followed by a 50% decrease a wash? No — you end 25% below the start, because each percentage applies to a different base.
Q: How do I find what percent one number is of another? Divide and multiply by 100: 81 of 135 students = 60%.
Q: Should I round during the calculation? No. Round only the final figure — rounding mid-way compounds the error.
Q: Must a retailer's "was" price be genuine? In many jurisdictions like the US (FTC guidelines) and the UK, yes. Retailers are legally prohibited from using fake discounts or inflating the reference price right before a sale. If a "was" price was never actually charged, it may violate local consumer protection laws, sometimes called price inflation laws.
Q: What's 30% off if tax is added afterwards? Discount first, then tax on the reduced price. For a $100 item with 8% sales tax:
- Step 1 (Discount): $100 × 0.70 = $70
- Step 2 (Tax): $70 × 1.08 = $75.60
- Warning: if a register charges tax on the full $100 first, you are being overcharged.
Sources: percentage definitions (en.wikipedia.org/wiki/Percentage); IRS tax topics (irs.gov); BLS earnings data (bls.gov).
Disclaimer: Examples use illustrative prices and rates; actual prices, tax rates and wages vary by jurisdiction and over time. This page is informational and not financial or tax advice.