Percentage Calculator
Three everyday percent problems, solved with every step shown: what is X% of Y, X is what percent of Y, and percent change from old to new.
Educational tool: this calculator teaches the arithmetic behind percentages. Results are mathematical — always double-check money, tax, or grade decisions against your own records.
The percent — e.g. 20 for 20%. May exceed 100.
The whole amount the percent is taken from.
Try: · ·
Quick percent:
The portion — e.g. correct answers, discount amount.
The total — the number after the word "of".
Try: · ·
The starting value (must not be zero).
The ending value.
Try: · ·
Need reverse solving ("was $60 after 25% off — what was the original?") or chained changes? Use our full percent-change calculator.
Educational note: results are exact arithmetic shown step by step. For money, round the final answer to 2 decimals; for grades and statistics, 1–2 decimals is plenty.
Every key percent of your number
Type a number once and see 1% through 100% at a glance - handy for tips, discounts, commissions, and markups.
Which percent calculator do you need?
Percent problems come in flavors — picking the right tool avoids the classic traps. This page solves the three everyday basics. For the specialists:
| Your question | Use this |
|---|---|
| What is X% of Y? · X is what % of Y? · simple % change | This calculator (you are here) |
| Reverse or chained changes ("$60 after 25% off — original?"; "+20% then −15%") | Percent-change calculator |
| Direction-free comparison ("10 vs 14 — how different?") | Percent-difference calculator |
| Discounts, markdowns, sale prices | Percentage-decrease calculator |
| Growth, markup, raises | Percent-increase calculator |
| Fractions and mixed numbers ↔ percents | Fraction-to-percent converter |
Worked examples
Restaurant tip
Bill $84.50, tip 15%. Mode 1: 15% of 84.50.
0.15 × 84.50 = $12.675 → tip $12.68The exact math gives three decimals; money needs two, so round at the end — never in the middle.
Test score
42 correct out of 50 questions. Mode 2: 42 is what % of 50?
(42 ÷ 50) × 100 = 84%The "whole" is always the number after the word of.
Price drop
Jacket $59 → $44. Mode 3: percent change.
(44 − 59) ÷ 59 × 100 = −25.42%Negative sign = decrease. A 25.42% discount.
Excel & Google Sheets formulas
Doing this in a spreadsheet? These are the exact formulas behind each mode:
In Google Sheets: Format → Number → Percent applies the ×100 step for you — so =A1/B1 formatted as % already shows 84%.
Percentage points vs. percent change
The single most misunderstood percent idea. If an interest rate moves from 20% to 25%:
- Percentage points: 25 − 20 = 5 percentage points (plain subtraction).
- Percent change: (25 − 20) ÷ 20 × 100 = +25% (relative to where you started).
Both are correct — they answer different questions. News headlines that say "up 5%" when they mean "up 5 points" understate the move fivefold. When in doubt, Mode 3 gives you the percent change; subtract directly for the points.
Everyday uses
Discounts
"25% off $80" → discount $20, pay $60. Mode 1, then subtract.
Tips & tax
15% tip, 8% sales tax — Mode 1 on the bill, add it on.
Grades
Correct ÷ total × 100. Mode 2 turns any score into a percent.
Commission
3% of a $240,000 sale = $7,200. Mode 1.
Body & health stats
"Lost 8 of 96 kg" → Mode 2: an 8.33% reduction.
Investment moves
Portfolio $5,000 → $6,200. Mode 3: +24%.
Mental math tricks
Three building blocks handle almost every everyday percent:
- 10% - move the decimal one place left. 10% of 240 = 24.
- 5% - half of 10%. 5% of 240 = 12.
- 1% - divide by 100. 1% of 240 = 2.4.
Combine them: 15% of 240 = 10% (24) + 5% (12) = 36. 21% of 80 = 10% (8) doubled + 1% (0.8) = 16.8.
Common percentage mistakes
- Adding discounts directly. "20% off, then 10% off" is not 30% off. Multiply what remains: 0.80 x 0.90 = 0.72, so you pay 72% of the price - a 28% total discount.
- Points vs. percent. A rate rising from 20% to 25% gains 5 percentage points but 25% in relative terms.
- Rounding in the middle. Round only the final answer. Rounding 12.675 to 12.68 early, then multiplying, compounds the error.
- Wrong base. "What percent off?" always divides by the original price, not the sale price: ($80 - $60) / $80 = 25% off.
Fraction to percent reference
| Fraction | Decimal | Percent |
|---|---|---|
| 1/2 | 0.5 | 50% |
| 1/3 | 0.333... | 33.333...% |
| 2/3 | 0.666... | 66.666...% |
| 1/4 | 0.25 | 25% |
| 3/4 | 0.75 | 75% |
| 1/5 | 0.2 | 20% |
| 1/6 | 0.166... | 16.666...% |
| 1/8 | 0.125 | 12.5% |
| 1/10 | 0.1 | 10% |
| 1/20 | 0.05 | 5% |
Frequently asked questions
What is a percentage, exactly?
A percentage is a fraction of 100. The word comes from the Latin per centum, meaning "by the hundred". So 37% literally means 37 out of every 100 — the fraction 37/100, or 0.37 as a decimal.
How do I calculate X percent of a number?
Divide the percent by 100 to get a decimal, then multiply by the number. Example: 20% of 150 = (20 ÷ 100) × 150 = 0.2 × 150 = 30. Mode 1 of the calculator above does this and shows every step.
How do I find what percent one number is of another?
Divide the part by the whole, then multiply by 100. Example: 42 correct out of 50 = (42 ÷ 50) × 100 = 84%. The "whole" is the number after the word "of". Mode 2 above shows each step.
How do I calculate percent change?
Subtract the old value from the new value, divide by the old value, and multiply by 100: (new − old) ÷ old × 100. Example: 50 to 75 is (75−50) ÷ 50 × 100 = +50%. Mode 3 covers this; for reverse solving or chained changes see our percent-change calculator.
What is the difference between percent change and percentage points?
If a rate moves from 20% to 25%, that is a 5 percentage-point increase but a 25% percent change ((25−20) ÷ 20 × 100). Percentage points are the plain subtraction; percent change is relative to the starting value. Mixing them up is one of the most common percent mistakes.
What is the difference between percent change and percent difference?
Percent change is directional: it divides by the starting value, so 50 to 75 is +50% while 75 to 50 is −33.33%. Percent difference is symmetric: it divides by the average of the two values, giving the same answer either way (10 vs 14 gives 33.33%). Use our percent-difference calculator when direction does not matter.
Can a percentage be more than 100%?
Yes. Percentages above 100% simply mean "more than the whole": 150% of 40 is 60, and 200 is 400% of 50. Negative results are possible too when a value falls relative to a positive base — 1000 down to 1 is a −99.9% change.
Why does the calculator show 33.3333% instead of 33⅓%?
Some fractions never terminate as decimals — 1/3 = 0.3333… forever. We show up to 4 decimals, tell you whenever rounding happened, and display the exact fraction (100/3%) so you always know the true value. For money, round the final result to 2 decimals.
How do I calculate a discount or sale price?
Find the discount amount with Mode 1, then subtract it from the original price. Example: 25% off $80 gives a discount of 0.25 × 80 = $20, so the sale price is $60. Our percentage-decrease calculator is built exactly for this, including reverse problems like finding the original price from a sale price.
How do I add a percent to a number (tax, tip, markup)?
Compute the percent of the number (Mode 1) and add it on. Example: 8% tax on $50 gives tax of 0.08 × 50 = $4, for a total of $54. Equivalently, multiply by 1 plus the rate: 50 × 1.08 = 54. For growth problems with reverse solving, see our percent-increase calculator.
What are the Excel / Google Sheets formulas for percentages?
X% of Y: =A1*B1 where A1 holds the decimal form (0.2 for 20%), or =20%*150 directly. What percent A is of B: =A1/B1, then format the cell as %. Percent change: =(B1-A1)/A1, then format as %. In Sheets, Format → Number → Percent applies the ×100 step for you.
How do I convert a fraction to a percent?
Divide the numerator by the denominator, then multiply by 100: 3/4 = 0.75 = 75%. Watch out for repeating decimals (1/3 = 33.333…%). Our fraction-to-percent converter handles mixed numbers and flags repeating decimals honestly.
Is a percent the same as a percentile?
No. A percent is a fraction of 100. A percentile is a ranking: scoring in the 90th percentile means you beat 90% of the group — it says nothing about your raw score as a percent. Confusing the two is a classic statistics mistake.
Is this percentage calculator free? Does it store my numbers?
Yes — free forever, no signup. It runs 100% in your browser: the numbers you type never leave your device. There are no accounts, no tracking of your inputs, and it works offline once the page has loaded.
How can I do percentages in my head?
Learn three building blocks: 10% (move the decimal one place left), 5% (half of 10%), and 1% (divide by 100). Combine them: 15% of 240 = 10% (24) + 5% (12) = 36. With practice, tips and discounts become instant.
How do I find the original price before a discount?
Divide the sale price by 1 minus the discount rate: original = sale / (1 - rate). Example: $60 after 25% off gives 60 / 0.75 = $80. For full reverse solving with steps, use our percent-change calculator.
What is 20% of 50%?
Convert both to decimals and multiply: 0.20 x 0.50 = 0.10 = 10%. A percent of a percent is always smaller than either one - you are taking a slice of a slice.
What does "20% more than 50" mean?
Multiply by 1 plus the rate: 50 x 1.20 = 60. "X% more than Y" is Y x (1 + X/100); "X% less than Y" is Y x (1 - X/100). So 30% less than 200 is 200 x 0.70 = 140.
How do I convert a decimal to a percentage?
Multiply by 100 and add the % sign: 0.375 x 100 = 37.5%. Going the other way, divide by 100: 37.5% / 100 = 0.375.
What is a standard tip percentage?
15-20% is standard in the US: 15% for adequate service, 18-20% for good service, 25%+ for exceptional. On $84.50, a 20% tip is 0.20 x 84.50 = $16.90.
How do a discount and sales tax combine?
Multiply the factors - never add the percentages. Example: 20% off $100, then 8% tax: sale price $80, tax 0.08 x 80 = $6.40, total $86.40. The combined factor is 0.80 x 1.08 = 0.864, so you effectively pay 86.4% of the original.
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