Percentage Calculator

What Is a Percentage?

A percentage is a way of expressing a number as a fraction of one hundred. The word comes from the Latin per centum, meaning “by the hundred,” and the symbol % simply stands in for “divided by 100.” So 25% is another way of writing 25/100, or the decimal 0.25. Percentages let you compare proportions on a common scale regardless of the underlying totals, which is why they appear everywhere from discounts and tax rates to test scores, statistics, and interest rates.

Most everyday percentage questions fall into a handful of patterns: finding a portion of a quantity, expressing one quantity as a share of another, measuring how much a value has grown or shrunk, applying an increase or decrease, and working backwards to an original value. This calculator gives each pattern its own card so you can pick the one that matches your question without rearranging formulas yourself.

How to Use This Percentage Calculator

Pick the card that matches your question and type your numbers into it — the answer appears instantly, there is no button to press. Below every answer you see the formula with your numbers filled in, so you can check the arithmetic or copy the working into a report. Click Copy to copy just the result.

• What is X% of Y? — the portion, e.g. 10% of 200 = 20.
• X is what percent of Y? — the share, e.g. 25 out of 200 = 12.5%. This is the classic 25 / 200 × 100.
• Percentage change — how much a value rose or fell, e.g. from 80 to 100 is a 25% increase.
• Add or subtract a percentage — shows both 200 + 15% and 200 − 15% at once.
• X is Y% of what? — the whole when you only know a part, e.g. 30 is 15% of 200.
• Reverse percentage — the value before a percentage was added or removed, e.g. a price of 120 that already includes 20% tax was 100 before tax.
• Percentage difference — how far apart two values are relative to their average, when neither one is the “original”.

Numbers may contain thousands separators (1,250,000), a decimal comma (7,5) or a trailing % sign. Copy link to these calculations copies a URL that reopens the page with all your current inputs, which is handy for sharing a calculation with a colleague.

Percentage Formulas

• X% of Y = (X / 100) × Y
• X is what % of Y = (X / Y) × 100
• Percentage change = ((New − Old) / |Old|) × 100
• Increase by X% = Value × (1 + X / 100)
• Decrease by X% = Value × (1 − X / 100)
• X is Y% of what = X / (Y / 100)
• Original before an increase of X% = Final / (1 + X / 100); before a decrease: Final / (1 − X / 100)
• Percentage difference = |A − B| / ((A + B) / 2) × 100

Reverse Percentages: the Most Common Mistake

Suppose a jacket costs 120 after a 20% markup and you want the original price. It is tempting to take 20% off 120, which gives 96 — but that is wrong. The 20% was calculated on the original price, not on 120. The correct approach is to divide: 120 / 1.20 = 100. You can check it: 100 + 20% = 120. The same applies to removing sales tax or VAT from a gross price, or finding the price before a discount: a sale price of 75 after 25% off was 75 / 0.75 = 100, not 75 + 25% = 93.75. The Reverse percentage card does this division for you.

Percentage Change vs. Percentage Difference

Use percentage change when there is a clear before and after — last year’s revenue and this year’s, an old price and a new one. The old value is the reference, so the direction matters: 80 → 100 is +25%, but 100 → 80 is −20%. Use percentage difference when you compare two values on equal footing, such as two measurements, two product prices or two survey results. It divides by the average of both values, so the result is the same whichever number you enter first: 40 and 60 differ by 40%.

Real-World Use Cases

• Shopping discounts — work out the saving of a “30% off” sale with the X% of Y card, or the price before the discount with the reverse card.
• Tips, tax and VAT — add a 15% tip or a tax rate to a bill, or remove tax from a gross price.
• Grades and scores — find what percentage 42 correct answers out of 50 represents.
• Tracking growth — measure the percentage change between last month’s and this month’s figures, e.g. page views, revenue or response times.
• Performance and benchmarks — compare two benchmark runs with percentage difference, or express a speed-up as a percentage change.

Tips for Working with Percentages

• To turn a percentage into a decimal, divide by 100; to go the other way, multiply by 100.
• Percentage change always uses the original value as the denominator, so a rise from 80 to 100 is a 25% increase, not 20%.
• A percentage increase followed by the same percentage decrease does not return to the start — a 20% rise then a 20% fall leaves you 4% below the original.
• Distinguish percentage change from percentage points: an interest rate moving from 3% to 5% rose by 2 percentage points, which is a 66.7% relative increase.
• X% of Y is always the same as Y% of X — 8% of 50 is the same as 50% of 8, which is easier to do in your head.

Features

• Seven calculation types — percentage of a number, percentage of a total, percentage change, increase/decrease, finding the whole, reverse percentage and percentage difference.
• Live results with working — every answer shows the formula with your numbers filled in.
• Clear error messages — for example when a calculation would divide by zero.
• Flexible input — decimals, negative numbers, thousands separators, decimal commas and % signs.
• Copy and share — copy any result, or a link that reopens all your calculations.
• 100% client-side — your numbers never leave your browser.

Frequently Asked Questions

How do I calculate a percentage of a number?

Divide the percentage by 100 and multiply by the number. For example, 15% of 200 equals (15 / 100) × 200 = 30. Use the “What is X% of Y?” card to do this automatically.

How do I find what percentage one number is of another?

Divide the part by the whole and multiply by 100. For example, 25 out of 200 is (25 / 200) × 100 = 12.5%. The “X is what percent of Y?” card performs this calculation for you.

How is percentage change calculated?

Subtract the old value from the new value, divide by the absolute value of the old value, and multiply by 100. The result is an increase if it is positive and a decrease if it is negative. A change from 0 is undefined, because you cannot divide by zero.

How do I find the original number before a percentage increase?

Divide the final value by 1 plus the percentage as a decimal. If a price is 120 after a 20% increase, the original was 120 / 1.2 = 100. For a decrease, divide by 1 minus the percentage: 75 after a 25% discount was 75 / 0.75 = 100.

How do I find the whole when I know a part and its percentage?

Divide the part by the percentage as a decimal. If 30 is 15% of a number, the number is 30 / 0.15 = 200. Use the “X is Y% of what?” card.

What is the difference between percentage change and percentage difference?

Percentage change compares a new value to an old one and divides by the old value, so its direction matters. Percentage difference compares two values on equal terms and divides by their average, so 40 vs. 60 and 60 vs. 40 both give 40%.

What is the difference between percentage change and percentage points?

Percentage change is relative, so going from 50 to 75 is a 50% increase. Percentage points are absolute, so an interest rate moving from 3% to 5% is a 2 percentage-point rise, even though that is a 66.7% relative increase.

Are my numbers sent to a server?

No. All calculators run entirely in your browser using client-side JavaScript, so the values you enter are never transmitted or stored anywhere. Only if you copy a share link are your inputs written into that link.