Percentage Calculator
Solve the most common percentage problems: percentage of a number, percent change, discounts, markups, reverse percentages, and percentage points — with formula and steps.
Result = Y × (X ÷ 100)- 15 ÷ 100 = 0.15
- 200 × 0.15 = 30
15% of 200 is 30. That leaves 170 of the original 200.
Common percentage calculations
Most everyday percentage work is one of the nine questions the calculator answers: taking a percentage of a number (tips, tax, commissions), expressing one number as a percentage of another (scores, completion rates), reversing a percentage to recover the original whole (price before discount, gross from net), measuring change between two values, adjusting a value up or down, pricing a discount, comparing two rates in percentage points, chaining several changes, and converting between markup and margin.
For quick mental checks, a few anchor values cover most situations:
Quick reference table for common percentage values applied to common base numbers. Useful for verification, tip estimation, and rough mental calculation.
| Percent | of $50 | of $100 | of $1,000 | of $10,000 |
|---|---|---|---|---|
| 1% | $0.50 | $1 | $10 | $100 |
| 5% | $2.50 | $5 | $50 | $500 |
| 10% | $5 | $10 | $100 | $1,000 |
| 15% (tip) | $7.50 | $15 | $150 | $1,500 |
| 20% (standard tip) | $10 | $20 | $200 | $2,000 |
| 25% | $12.50 | $25 | $250 | $2,500 |
| 33.3% (third) | $16.67 | $33.33 | $333.33 | $3,333.33 |
| 50% (half) | $25 | $50 | $500 | $5,000 |
| 75% | $37.50 | $75 | $750 | $7,500 |
Mental shortcuts: 10% = move decimal one place left; 5% = half of 10%; 20% = double 10%; 15% = 10% + half of 10%. These shortcuts are the basis of restaurant tip estimation and rapid mental verification of receipts.
Formula table
Every mode of this calculator, its formula, and a worked value:
| Question | Formula | Example |
|---|---|---|
| What is X% of Y? | Result = Y × (X ÷ 100) | 15% of 200 = 30 |
| X is what % of Y? | P = (X ÷ Y) × 100 | 30 ÷ 200 × 100 = 15% |
| X is P% of what? | Y = X ÷ (P ÷ 100) | 30 ÷ 0.15 = 200 |
| Percentage change from A to B | Change % = (B − A) ÷ |A| × 100 | 80 → 100 = +25% |
| Increase / decrease Y by P% | Result = Y × (1 ± P ÷ 100) | 200 + 15% = 230 |
| Discount / final price | Final = Price × (1 − D ÷ 100) | 20% off 80 = 64 |
| Percentage points / basis points | Percentage points = B − A Basis points = percentage points × 100 Relative change % = (percentage points ÷ |A|) × 100 | 5% → 5.5% = +0.5 pp = +50 bps |
| Compound percentage changes | Result = Start × Π(1 + pᵢ ÷ 100) | 100 +50% −50% = 75 |
| Markup / margin | Markup % = (Profit ÷ Cost) × 100 Margin % = (Profit ÷ Selling Price) × 100 | Cost 80, price 100: 25% / 20% |
The ± sign follows the direction: + for an increase, − for a decrease. |A| is the absolute value of the starting point, the convention that keeps the sign of a percent change meaningful when the base is negative.
Examples
The calculator’s verification set — each row is a real question, the mode that answers it, and the computed result:
| Question | Mode | Answer | Last step |
|---|---|---|---|
| 15% of 200 | What is X% of Y? | 30 | 200 × 0.15 = 30 |
| 150% of 80 | What is X% of Y? | 120 | 80 × 1.5 = 120 |
| 7.5% of 640 | What is X% of Y? | 48 | 640 × 0.075 = 48 |
| 30 is what percent of 200? | X is what percent of Y? | 15% | 0.15 × 100 = 15% |
| 30 is 15% of what? | X is P% of what? | 200 | 30 ÷ 0.15 = 200 |
| Change from 80 to 100 | Percentage change from A to B | +25% | 0.25 × 100 = +25% |
| Change from 100 to 80 | Percentage change from A to B | -20% | -0.2 × 100 = -20% |
| Change from 10 to 0 | Percentage change from A to B | -100% | -1 × 100 = -100% |
| Change from 0 to 10 | Percentage change from A to B | Undefined | 10 ÷ 0 → division by zero |
| Increase 200 by 15% | Increase or decrease a value by X% | 230 | 200 + 30 = 230 |
| Decrease 200 by 15% | Increase or decrease a value by X% | 170 | 200 − 30 = 170 |
| 20% off 80 | Discount and final price | 64 | 80 − 16 = 64 |
| 5% to 5.5% (rates) | Percentage points and basis points | +0.5 pp | 0.5 ÷ 5 × 100 = +10% relative change |
| +50%, then −50% from 100 | Apply several % changes in a row | 75 | Net effect: -25% |
| −50%, then +100% from 100 | Apply several % changes in a row | 100 | Net effect: 0% |
| Cost 80, price 100 (markup / margin) | Markup and margin from cost and price | 25% | 20 ÷ 100 × 100 = 20% margin |
Every figure above is produced by the same engine that powers the calculator — including the deliberately undefined case (percent change from a base of zero), which fails closed instead of showing a number.
Percentage mistakes
The arithmetic of percentages is easy; the mistakes are conceptual, and the same few appear everywhere:
- Adding sequential changes. +50% followed by −50% is not 0% — it is −25%, because changes multiply. The compound-changes mode above shows the running value at every step.
- Confusing percentage points with percent. A rate moving 5% → 5.5% is +0.5 percentage points but a +10% relative change. Headlines mix these constantly; the points mode reports both, labelled.
- Reversing a discount with the same percentage. After a 20% discount, adding 20% back does not restore the price — you need +25%. Undoing an X% decrease always takes a larger percentage increase.
- Dividing by the wrong base. Percent change is measured against the starting value: 80 → 100 is +25%, but 100 → 80 is −20%. Same gap, different base, different percentage.
- Treating markup and margin as the same number. They divide by different bases (cost vs price): a 25% markup is only a 20% margin. Pricing a product for a 25% margin using the markup formula under-prices it.
- Taking a percentage of a zero base. “What percent of 0 is 30” and “percent change from 0” have no answer. The calculator says so explicitly rather than inventing a number.
Percentage points vs percent change
When the Federal Reserve raises interest rates from 5% to 5.5%, that is a 0.5 percentage point increase — but it is a 10% increase in the rate (0.5/5 = 10%). Conflating the two is the most common percentage-reporting error in financial media. The convention: 'percentage points' (or basis points = 1/100 of a percentage point) refers to absolute change in a percentage value; 'percent' refers to relative change.
Example: a tax rate going from 20% to 25% is a 5 percentage point increase OR a 25% relative increase. A bank's loan default rate moving from 2% to 3% is a 1 percentage point increase but a 50% relative increase. Investor reporting prefers basis points for interest-rate moves (a 25 basis point cut = a 0.25 percentage point cut = colloquially 'a quarter point').
The reverse problem: small percentage points often map to very large relative changes. A company moving from 2% net margin to 4% net margin doubled its margin (100% relative increase) but only saw a 2 percentage point improvement. Both numbers are correct; both are useful in different contexts. Public-company earnings releases typically report both the absolute change in basis points or percentage points AND the relative change in percent — providing complete information to readers.
Discounts, tax, tips, markups
Retail and money math is percentage math with a story attached. A discount multiplies the price by (1 − rate): 20% off 80 is 80 × 0.8 = 64. A sales tax or a tip multiplies by (1 + rate): a 15% tip on a 200 bill adds 30, for 230 total. Stacked discounts compound rather than add — “20% off, then an extra 10% off” is 28% off, not 30%.
To recover a pre-tax or pre-discount figure, use the reverse-percentage mode, not subtraction: if a receipt shows 108 including 8% tax, the base price is 108 ÷ 1.08 = 100, not 108 − 8% = 99.36.
Markup and margin describe the same profit from two sides. Markup divides the profit by the cost; margin divides it by the selling price. Buying at 80 and selling at 100 is a 25% markup but a 20% margin. The two are linked by margin = markup ÷ (1 + markup): a 100% markup is a 50% margin, and no finite markup ever reaches a 100% margin.
Investment returns and compounding
Percentages do not compose linearly. A 20% gain followed by a 20% loss does NOT return you to the original — it leaves you at 96% (1.2 × 0.8 = 0.96). A 50% gain followed by a 50% loss leaves you at 75%. This asymmetry compounds: to recover from a 50% loss requires a 100% gain, not 50%. The general rule: to recover from an X% loss requires a (X/(1-X)) × 100% gain, which exceeds X for any X > 0.
This is why investment-return reporting uses geometric (compound) mean rather than arithmetic mean. An investment that returns +50%, then −50% in two consecutive years has arithmetic mean return of 0% but geometric mean of −13.4% — the correct measure of multi-year performance. CFA Institute and Bogleheads investment-education resources are unanimous on this point; financial reporting that uses arithmetic mean across volatile years systematically overstates true compound returns.
Practical implications: in stock-market or business-result reporting, always look for CAGR (Compound Annual Growth Rate) rather than simple average annual return. In personal-finance, accept that aggressive growth strategies require commensurate drawdown recovery — a portfolio that drops 50% in a bad year requires a 100% subsequent gain to break even, which often takes 5-10 years at historical equity returns.
FAQ
How do I find a percentage of a number?
Multiply the number by the percentage, then divide by 100. For example, 15% of 200 is 200 multiplied by 15, divided by 100, which is 30. The '% of a number' mode shows both steps.
How do I work out what percent one number is of another?
Divide the part by the whole and multiply by 100: 30 divided by 200 is 0.15, so 30 is 15% of 200. If the whole is zero the question has no answer — the calculator reports it as undefined instead of showing a number.
What is a reverse percentage?
A reverse percentage recovers the original whole from a known part: if 30 is 15% of some number, divide 30 by 0.15 to get 200. It is the calculation behind 'price before the discount' and 'gross from net' questions — use the 'X is P% of what' mode.
What is the difference between percentage points and percent?
Percentage points measure the absolute gap between two rates; percent measures the relative change. A rate moving from 5% to 5.5% rises 0.5 percentage points (50 basis points) but 10% in relative terms. The points mode reports all three figures, labelled.
Why don't a 50% gain and a 50% loss cancel out?
Because sequential percentage changes multiply instead of adding. 100 increased by 50% is 150, and 150 decreased by 50% is 75 — a net −25%. Recovering from an X% loss always requires a gain larger than X%; the compound-changes mode shows the running value at every step.
Can a percentage be more than 100%?
Yes. A percentage above 100% simply means more than the whole — 150% of 80 is 120. The calculator accepts percentages well above 100 and negative percentages, and warns when a decrease beyond 100% would push a value below zero.
How do I turn a percentage into a decimal?
Divide the percentage by 100. So 15% becomes 0.15, and 7.5% becomes 0.075. Multiplying by that decimal gives the percentage of any number — every step panel on this page shows that conversion explicitly.
What is the difference between markup and margin?
Both describe the same profit, but markup divides it by the cost while margin divides it by the selling price. Buying at 80 and selling at 100 is a 25% markup but only a 20% margin. Pricing for a target margin with the markup formula under-prices the product.
When is this calculator unreliable?
It is computationally reliable, and divisions by zero are reported as undefined rather than as numbers. The pitfalls are conceptual: sequential percentage changes compound multiplicatively (a 20% increase then a 20% decrease leaves 96%, not 100%); percentage points are not percentages (a tax rate going 20% to 25% is +5 points but a +25% relative increase); and for multi-year financial data you should use CAGR (geometric mean), not the arithmetic average, which overstates compound returns when there is volatility.
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Methodology, sources, review
This calculator implements nine percentage operations, each shown on the page with its formula, numeric steps and interpretation: (1) X% of Y = Y × (X/100); (2) X is what % of Y = (X/Y) × 100; (3) X is P% of what = X ÷ (P/100), the reverse percentage behind price-before-discount and gross-from-net questions; (4) percentage change from A to B = (B − A) ÷ |A| × 100; (5) increase or decrease Y by P% = Y × (1 ± P/100); (6) discount: final price = price × (1 − D/100), with the saving reported separately; (7) percentage points = new rate − old rate, with basis points = points × 100 and the relative percent change reported alongside; (8) compound sequential changes: result = start × (1 + p₁/100) × (1 + p₂/100) × …, with the net single-change equivalent; (9) markup = (price − cost)/cost × 100 and margin = (price − cost)/price × 100. A free-text question box maps phrasings like '20% off 80' or '30 is what percent of 200' onto these modes with the same engine. Edge cases fail closed: division by zero (X is what % of 0, percent change from a zero base, 0% reverse percentage, markup on zero cost) is reported as undefined with an explanation rather than a number, and inputs may include %, currency symbols, commas and spaces. RELIABILITY: reliable as a direct arithmetic tool. Limitations are conceptual rather than computational: sequential percentage changes compound multiplicatively, not additively (a 20% increase followed by a 20% decrease leaves 96% of the original, not 100%), and percentage points are not percentages — both distinctions are computed and labelled explicitly on the page.
Reviewed according to the CalcDomain Editorial Policy & Calculator Methodology. We document formulas, edge cases, sources, update dates, and correction paths for calculator pages.
Updated
Sources
- U.S. Bureau of Labor Statistics — CPI — Consumer Price Index Detailed Reports · consulted June 1, 2026 · Authoritative U.S. percentage reporting in inflation — the canonical real-world application of percentage math
- Investopedia — Percentage — Percentage Definition and Formulas · consulted June 1, 2026 · Standard reference for percentage formulas across the three canonical forms
- Khan Academy — Percentages — Percent and percent change · consulted June 1, 2026 · Open-access reference for the conceptual foundations of percentage math