How to Calculate Percentages (Fast)
To find a percent of a number, turn the percent into a decimal and multiply — 20% of $80 is 0.20 × 80 = $16. That single move handles tips, discounts, taxes, and raises. Below you'll learn the core formula, how to do percent increase and decrease, how to reverse a percentage, and a few mental-math shortcuts that make it fast in real life.
Percent of a number
"Percent" literally means "per hundred," so 20% is just 20 per 100, or 0.20. The core rule is simple:
Percent of a number = (percent ÷ 100) × the number
So 15% of 200 is 0.15 × 200 = 30. A friendly trick that makes this instant: 10% of any number is just that number with the decimal moved one place left. 10% of 250 is 25; 10% of 48 is 4.80. From there you can build almost any percentage:
- 5% is half of 10% (of 250 → 12.50).
- 20% is 10% doubled (of 250 → 50).
- 15% is 10% plus 5% (of 250 → 25 + 12.50 = 37.50).
- 1% is the decimal moved two places (1% of 250 → 2.50).
For anything awkward, the percentage calculator gives an exact answer in a second.
Percent increase and decrease
A raise, a price hike, or a markdown is a percent change. The formula compares the change to where you started:
Percent change = (new − old) ÷ old × 100
If your pay goes from $50,000 to $54,000, that's (54,000 − 50,000) ÷ 50,000 = 0.08 = an 8% raise. If a $60 jacket drops to $45, that's (45 − 60) ÷ 60 = −0.25, a 25% decrease. To apply a known change instead of measuring one, multiply: a 25%-off price is 0.75 × the original, and a 6% raise is 1.06 × your salary.
Reverse percentages
Sometimes you know the result and need the original. This trips people up because you can't just add the percentage back. If a price is $120 after a 20% discount, the $120 represents 80% of the original — so divide, don't multiply:
Original = final amount ÷ (1 − discount as a decimal)
Here, $120 ÷ 0.80 = $150 original. The same logic works upward. If a total includes a 10% add-on and comes to $110, the original is $110 ÷ 1.10 = $100. Getting reverse percentages right matters for figuring pre-tax prices, pre-tip totals, or what a pre-raise salary was.
Real-life examples
Here's how the same handful of moves cover everyday money math:
| Situation | Quick method | Result |
|---|---|---|
| 18% tip on a $60 dinner | 10% ($6) + 8% ($4.80) | $10.80 |
| 30% off a $80 coat | 0.70 × 80 | $56 |
| 7% sales tax on $45 | 0.07 × 45 | $3.15 |
| Raise from $40k to $43k | 3,000 ÷ 40,000 | 7.5% raise |
One more handy fact: percentages are reversible. "What is 8% of 50?" is the same as "what is 50% of 8?" — both equal 4. When one direction looks hard, flip it. And for tips specifically, the tip calculator does the split for you.
Mental-math shortcuts to remember
You rarely need a calculator once these become second nature:
- Find 10% (move the decimal), then scale up or down for other percentages.
- To add a percentage, multiply by 1.something (1.08 for +8%). To subtract, multiply by 0.something (0.75 for −25%).
- To reverse a percentage, divide by that same multiplier instead.
- Swap the numbers when it's easier: x% of y equals y% of x.
Master these four and the vast majority of real-world percentage problems — tips, discounts, taxes, raises — become quick head math. When a number is messy or the stakes are high, reach for the percentage calculator to confirm it.
Percentage vs percentage points
One more distinction saves you from a classic mistake: the difference between a percent change and a change in percentage points. They sound alike but mean very different things, and news headlines mix them up constantly.
Say an interest rate rises from 4% to 6%. That's a jump of 2 percentage points — but it's a 50% increase in the rate itself, because 2 is half of the starting 4. Both statements are true; they just measure different things. When someone says a savings-account rate "went up 1%," ask whether they mean one percentage point (say, 4% to 5%) or a 1% relative increase (4% to 4.04%). The gap between those two is enormous over time.
The takeaway: percentage points describe the gap between two percentages, while a percent change describes how much one number grew or shrank relative to where it started. Keep them separate and you'll read financial news far more accurately.
Turning fractions and decimals into percentages
Percentages, fractions, and decimals are three ways of writing the same thing, and switching between them makes mental math faster. To turn a decimal into a percent, move the decimal point two places right: 0.35 becomes 35%, and 0.075 becomes 7.5%. To go the other way, move it two places left.
Common fractions are worth memorizing outright because they show up everywhere in prices and discounts:
- 1/2 = 50%, 1/4 = 25%, 3/4 = 75%
- 1/5 = 20%, 1/3 ≈ 33.3%, 2/3 ≈ 66.7%
- 1/8 = 12.5%, 1/10 = 10%
Once these are automatic, a "25% off" sign instantly reads as "a quarter off," and "a third more" becomes an easy multiplication. Recognizing that 12.5% is just one-eighth, for example, lets you split a bill or estimate a discount without touching a keypad. And because a fraction like three-quarters is easier to picture than 75%, translating a percentage into its fraction is often the fastest route to the answer in your head. When exact cents matter, the discount calculator will finish the job for you.
This article is general information, not financial advice, and figures are estimates. Rules and rates change — confirm current details for your situation. See our disclaimer.