Worked examples
25% of 200. 0.25 × 200 = 50. The remaining 75% is 150, and as a decimal 25% is 0.25.
50 is what percent of 200? 50 ÷ 200 × 100 = 25% — 50 represents one quarter of the whole.
25% of what number is 50? 50 ÷ 0.25 = 200. The multiplier is 4×, so the part times four is the whole.
500 increased by 10% is 500 × 1.10 = 550; the increase amount is 50. 500 decreased by 10% is 500 × 0.90 = 450; the decrease amount is 50.
Price changed from 80 to 100. The value increased by 25% — the absolute increase is 20, measured against the starting 80.
Percentage difference between 10 and 6. The difference is 4 and the average is 8, so the percentage difference is 50%.
20% off 1500. The discount is 300, so you pay 1200 — a 20% saving on the list price.
How to calculate percentages — and the traps to avoid
Percent means “per hundred”
A percentage is just a fraction with 100 on the bottom. “25 percent” literally means 25 per hundred, which is the fraction 25/100 and the decimal 0.25. That single idea powers every calculation on this page: to use a percentage you first turn it into a decimal by dividing by 100, and to read a decimal as a percentage you multiply by 100.
Because a percentage is a ratio, it always describes a part in relation to a whole. The whole is the 100% reference — the original price, the full mark, the starting figure — and the percentage tells you how big a slice of it you are talking about. Keeping the whole clearly in mind is the difference between a confident answer and a guess.
The three “percent of” questions are one relationship
Part, percentage, and whole are three corners of the same triangle: Part = (Percentage ÷ 100) × Whole. Know any two and you can find the third. “What is 25% of 200?” solves for the part (50). “50 is what percent of 200?” solves for the percentage (25%). “50 is 25% of what?” solves for the whole (200).
That is why the same example reads three ways. Recognising which corner is missing tells you which mode to use — and the calculator labels each one so you never have to remember the rearranged formula.
Percentage change vs percentage difference
These two sound alike and are constantly confused, but they answer different questions. Percentage change has a direction: it measures how much a value moved from a known starting point, (New − Old) ÷ Old × 100. A price rising from 80 to 100 is a 25% increase, because the 20 of growth is measured against the original 80.
Percentage difference has no starting point. It compares two values on equal footing by dividing their absolute difference by their average: |A − B| ÷ ((A + B) ÷ 2) × 100. The difference between 10 and 6 is 50%, because the gap of 4 is measured against the average of 8. Swap the two numbers and the answer is unchanged — percentage difference is symmetric, percentage change is not.
Use change when one number is clearly “before” and the other “after”. Use difference when neither value is privileged — comparing two measurements, two readings, two estimates. For the same pair of numbers they usually give different answers, so they are never interchangeable.
Why adding then removing the same percentage does not return the original
Grow 100 by 20% and you get 120. Now take 20% off 120 and you land on 96, not 100 — because the second 20% is taken from the larger 120, not the original 100. The two percentages share a name but not a base.
To reverse a 20% increase you divide by 1.20 (a 16.67% cut), and to reverse a 20% decrease you divide by 0.80 (a 25% rise). This is also why a 50% loss needs a 100% gain to recover: halving then doubling are not opposites in percentage terms. The increase/decrease mode shows the true reverse percentage for exactly this reason.
Percent vs percentage point
When the thing you are measuring is itself a percentage, language gets slippery. If an interest rate moves from 3% to 5%, that is a 2 percentage-point rise — but a 66.7% increase in the rate itself (2 ÷ 3 × 100). Headlines that blur the two can make a small change sound enormous, or the reverse.
The rule: a percentage point is the plain arithmetic gap between two percentages; a percent change is that gap measured against the starting percentage. Whenever you compare two rates, decide which one you mean before you quote a number.
Discounts, tax, tips, and commission
These are all the same arithmetic in different clothes. A discount takes a percentage off a price (Original − Original × Discount ÷ 100); tax, a tip, and a commission each add a percentage to a base (Base × Rate ÷ 100). The discount mode also lets you apply tax to the already-discounted price, which is the order most checkouts use.
A subtle point worth remembering: stacked discounts compound rather than add. A 10% discount followed by a 10% coupon is 19% off, not 20%, because the second cut applies to the already-reduced price. And tax you collect from a customer is normally money you pass on to the tax authority, not profit you keep.
Limitations
- This is a math utility, not tax, financial, or accounting advice — it does not know your local tax rules, rounding conventions, or tipping norms.
- It calculates single percentages; it does not compound interest over time or handle multi-step financial schedules.
- Percentage change can be misleading when the starting value is negative or crosses zero; interpret such results with care.
- Very large numbers may show tiny rounding in the last displayed place.
Need more than a single percentage? For sales tax and VAT/GST see the VAT calculator; for pricing from cost see the markup calculator and profit margin calculator; for before-and-after growth the dedicated percentage change calculator.
Sources & methodology
The calculator applies the standard percentage identities — Result = Percentage ÷ 100 × Whole, Percentage = Part ÷ Whole × 100, Whole = Part ÷ (Percentage ÷ 100), the increase/decrease multipliers, percentage change against the old value, and the symmetric percentage-difference formula — as published in the references below. The exported workbook reproduces the identical formulas as live, editable Excel formulas, validated cell-by-cell against this page's engine. Calculator Matters is an independent project, not affiliated with any source listed. Links open in a new tab.