Percentage Calculator: Formula, Examples & Conversion Table
Whether you're figuring out a tip at dinner, comparing investment returns, or checking your exam score, percentages are part of almost every decision you make. Our free percentage calculator handles all six common percentage operations in one place: find a basic percentage of any number, determine what share one value is of another, compute the percentage change between two figures, increase or decrease a value by a given rate, apply a shopping discount, and convert a raw test score into a letter grade.
Each calculation updates instantly as you type, so you can explore “what-if” scenarios without pressing a button. The step-by-step formula breakdowns shown alongside every result make the math transparent, turning this tool into both a time-saver and a learning aid.
Below the calculator you'll find a complete guide to percentage formulas, a fraction-to-decimal-to-percent conversion table, a real-world worked example, and mental-math shortcuts that let you estimate percentages on the fly. Bookmark this page and never second-guess a percentage again.
Choose a tab above to get started: Basic for everyday percentage questions, Change for growth and decline rates, Discount for sale-price math, or Grade for academic scoring. All results are calculated client-side, so your numbers stay private and the tool works offline once loaded.
What is X% of Y?
X is what % of Y?
Quick Examples
Basic Percentage Results
How It Works
Basic Percentage
Formula: (Percentage ÷ 100) × Value
Example: 25% of 200 = (25 ÷ 100) × 200 = 50
Percentage of Total
Formula: (Part ÷ Total) × 100
Example: 25 of 100 = (25 ÷ 100) × 100 = 25%
What Is a Percentage?
The word percentage comes from the Latin phrase per centum, meaning “by the hundred.” A percentage expresses a number as a fraction of 100, giving us a universal scale to compare values that would otherwise be difficult to relate. When you see “45 %,” you are really looking at 45 parts out of every 100 — or the decimal 0.45, or the fraction 45/100.
Percentages are essential in daily life because they standardize comparisons. A store advertising “25 % off” instantly tells every shopper the relative size of the discount, regardless of the item's original price. Banks quote interest rates as percentages so borrowers can compare loans of different sizes. Teachers convert raw scores to percentages so a test with 40 questions and one with 100 questions can be graded on the same scale.
You encounter percentages in shopping discounts and coupon codes, tax calculations at checkout, investment returns in your brokerage account, academic grading on report cards, sports statistics like a basketball player's free-throw rate, and health metrics such as body-fat percentage or blood-oxygen saturation. Mastering percentage arithmetic is one of the highest-leverage math skills you can develop, and the formulas below will show you exactly how each calculation works.
Percentage Formulas
Every percentage problem you will ever face falls into one of the six patterns below. Learn these formulas once and you can solve any percentage question by hand or verify the results from this calculator.
1. Basic Percentage
(Percentage ÷ 100) × Value = Result
Find a specific percentage of any number.
2. Percentage of Total
(Part ÷ Total) × 100 = Percentage
Determine what share one value is of another.
3. Percentage Change
((New − Old) ÷ Old) × 100 = Change%
Measure how much a value grew or shrank.
4. Percentage Increase
Value × (1 + Rate/100) = New Value
Add a percentage on top of an existing value.
5. Percentage Decrease
Value × (1 − Rate/100) = New Value
Subtract a percentage from an existing value.
6. Reverse Percentage
Total = Part ÷ (Percentage/100)
Find the original whole when you know a part and its percentage.
Worked Example: Meet Sarah
Sarah is shopping during a holiday sale. She spots a jacket originally priced at $120 with a bright 35 % off tag. Here's how she figures out exactly what she'll pay at the register.
Step 1 — Calculate the discount amount
Multiply the original price by the discount rate:
$120 × 35% = $120 × 0.35 = $42
Step 2 — Subtract from the original price
$120 − $42 = $78 (sale price)
Step 3 — Add 8.25 % sales tax
$78 × 1.0825 = $84.44 (total due)
Step 4 — What percentage of her $100 bill did she spend?
($84.44 ÷ $100) × 100 = 84.44 %
In four quick steps Sarah used three different percentage formulas — basic percentage, percentage increase, and percentage of total. Try plugging these numbers into the calculator above to see the results update live.
Common Percentages Conversion Table
Keep this reference handy for quick conversions between fractions, decimals, and percentages.
| Fraction | Decimal | Percentage |
|---|---|---|
| 1/100 | 0.01 | 1% |
| 1/20 | 0.05 | 5% |
| 1/10 | 0.1 | 10% |
| 1/8 | 0.125 | 12.5% |
| 1/6 | 0.167 | 16.67% |
| 1/5 | 0.2 | 20% |
| 1/4 | 0.25 | 25% |
| 1/3 | 0.333 | 33.33% |
| 1/2 | 0.5 | 50% |
| 2/3 | 0.667 | 66.67% |
| 3/4 | 0.75 | 75% |
| 4/5 | 0.8 | 80% |
Quick Mental Math Tricks
You do not always need a calculator. These four shortcuts let you estimate common percentages in your head within seconds.
Finding 10 %
Move the decimal point one place to the left.
10% of $85 = $8.50
Finding a 15 % Tip
Find 10 %, then add half of that amount.
10% of $60 = $6, half = $3 → tip = $9
Finding 25 %
Divide the number by 4.
25% of $200 = $200 ÷ 4 = $50
Finding Any %
Break it into easy parts and add them up.
17.5% = 10% + 5% + 2.5% → sum the parts
Advanced Percentage Applications
Compound Interest and Annual Percentage Yield (APY)
Simple interest applies a percentage once: $10,000 at 5% annual interest earns $500 per year ($10,000 × 0.05). But compound interest applies the percentage to a growing base. If that 5% compounds annually, after year 1 you have $10,500. Year 2 calculates 5% of $10,500 = $525 in interest, giving you $11,025 total. The formula is: Final = Principal × (1 + rate)^years. For $10,000 at 5% over 10 years: $10,000 × (1.05)^10 = $16,289—not $15,000 from simple interest. The difference ($1,289) is "interest on interest."
When interest compounds more frequently, your returns increase. A 5% APR compounded monthly doesn't earn exactly 5% per year—it earns slightly more because interest accrues each month. The effective annual yield (APY) is: (1 + r/n)^n - 1, where r = 0.05 and n = 12 months. Result: (1 + 0.05/12)^12 - 1 = 1.05116 - 1 = 0.05116 or 5.116% APY. On $10,000, that extra 0.116% yields $11.60 more per year than simple 5% interest. Over 30 years, monthly compounding turns $10,000 into $44,677 vs. $43,219 with annual compounding—a $1,458 difference from compounding frequency alone.
Tax Brackets and Marginal vs. Effective Tax Rates
The U.S. federal tax system uses marginal brackets. In 2026, a single filer earning $60,000 does not pay 22% on the entire amount. Instead: the first $11,600 is taxed at 10% ($1,160), income from $11,601 to $47,150 is taxed at 12% ($4,266), and income from $47,151 to $60,000 is taxed at 22% ($2,827). Total tax = $1,160 + $4,266 + $2,827 = $8,253. The effective tax rate is $8,253 / $60,000 = 13.76%—much lower than the 22% marginal rate. Understanding this prevents the myth that "earning more pushes you into a higher bracket and reduces your take-home pay." Only the additional income above each threshold is taxed at the higher rate.
Percentage Points vs. Percentages
This distinction causes widespread confusion. If unemployment rises from 5% to 8%, that's an increase of 3 percentage points, but a 60% relative increase (since 3/5 = 0.6). News headlines saying "unemployment increased 60%" would be misleading; the correct phrasing is "increased by 3 percentage points" or "rose 60% in relative terms." Similarly, if a savings account interest rate drops from 2% to 1.5%, that's a 0.5 percentage-point decrease but a 25% relative decrease (0.5/2 = 0.25). Always clarify: are we talking about absolute percentage-point changes or relative percentage changes?
Percent Change vs. Percent Difference
Percent change measures how one value changed to another over time: ((New - Old) / Old) × 100. If a stock price goes from $50 to $60, that's ((60 - 50) / 50) × 100 = 20% increase. Percent difference compares two values without a time sequence: |Value1 - Value2| / [(Value1 + Value2) / 2] × 100. If Product A costs $50 and Product B costs $60, the percent difference is |50 - 60| / [(50 + 60)/2] × 100 = 10 / 55 × 100 ≈ 18.18%. Use percent change when tracking growth/decline; use percent difference when comparing two independent measurements.
Successive Percentage Changes Don't Add
A common error: if a price increases 10% then decreases 10%, people assume it returns to the original. Wrong. Start with $100. After a 10% increase: $100 × 1.10 = $110. After a 10% decrease: $110 × 0.90 = $99—you've lost $1. The correct formula for successive changes: multiply the factors. A 20% increase followed by a 15% decrease gives: 1.20 × 0.85 = 1.02, a net 2% increase. Or: +25% then -20% gives 1.25 × 0.80 = 1.00, exactly breaking even. To reverse a percentage increase, the required decrease is different: a 50% increase (factor 1.50) requires a 33.33% decrease (factor 0.6667) to return to the original, since 1.50 × 0.6667 ≈ 1.00.
Common Percentage Mistakes and How to Avoid Them
❌ Mistake #1: Confusing Percentage Of vs. Percentage More/Less
Question: "A laptop costs $800. The store offers 20% off. Final price?"
Wrong approach: $800 × 0.20 = $160 (thinking this is the final price)
Right approach: $800 × 0.20 = $160 discount, so final = $800 - $160 = $640
Or use the shortcut: $800 × (1 - 0.20) = $800 × 0.80 = $640. The phrase "20% off" means you pay 80% of the original, not 20%.
❌ Mistake #2: Averaging Percentages Incorrectly
Scenario: Your portfolio has three stocks: Stock A up 10%, Stock B up 20%, Stock C up 30%. Average return?
Wrong: (10 + 20 + 30) / 3 = 20% (only correct if you invested equal dollar amounts)
Right: If you invested $5,000 in A, $10,000 in B, and $15,000 in C, weight each return: [$5k × 10% + $10k × 20% + $15k × 30%] / $30k total = [$500 + $2,000 + $4,500] / $30,000 = 23.33% weighted average. Percentages must be weighted by their base values to avoid distortion.
❌ Mistake #3: Percentage Increase/Decrease Asymmetry
Question: A stock drops 50% from $100 to $50. What percentage gain is needed to recover?
Wrong answer: 50% (thinking it's symmetric)
Right answer: You need a 100% gain. From $50, a 100% increase gives $50 × 2 = $100. The formula: if you lose X%, you need a [(1 / (1 - X)) - 1] × 100% gain to recover. Lose 50%? Need (1 / 0.5) - 1 = 1.0 = 100% gain. Lose 75%? Need (1 / 0.25) - 1 = 3.0 = 300% gain. This asymmetry is why avoiding large losses matters more than chasing gains in investing.
❌ Mistake #4: Misinterpreting "Up To" Discounts
Ad claim: "Save up to 70% off!"
Reality: The phrase "up to" is a maximum, not a guarantee. Only a handful of items may be 70% off; most might be 10-20% off. The average discount across all sale items could be 25%. Retailers use this tactic to draw traffic with the headline number while applying smaller discounts to most inventory. Always check the actual discount on the specific item you want, not the advertised maximum.
❌ Mistake #5: Percentage of What Base?
Statement: "Women earn 82% of what men earn for the same work."
Ambiguity: Does this mean women earn 82% (so 18% less), or that the gap is 82 percentage points? The correct interpretation: if men earn $100, women earn $82, an 18% pay gap calculated as (100 - 82) / 100 = 18%. But some might mistakenly calculate (100 - 82) / 82 = 22% gap using women's earnings as the base. Always clarify the base—percentage of men's wages, percentage of women's wages, or percentage-point difference. The denominator changes the result.
Industry-Specific Percentage Uses
Retail: Markup, Margin, and Break-Even
Markup vs. Margin confuses even business owners. A retailer buys a product for $60 and sells it for $100. The markup is based on cost: ($100 - $60) / $60 = 66.67%. The margin is based on selling price: ($100 - $60) / $100 = 40%. Both describe the same $40 profit, but the percentage differs because the denominator differs. Markup is always higher than margin for the same transaction. If your target margin is 40%, the required markup is: 0.40 / (1 - 0.40) = 0.667 or 66.67%.
Break-even analysis: If your fixed costs are $50,000 per month and you sell a product with a 40% margin, how much revenue do you need? Fixed costs / Margin = $50,000 / 0.40 = $125,000 in sales. Each dollar of sales contributes $0.40 toward fixed costs, so you need $125k to cover the $50k overhead. If you sell items at $100 each (40% margin = $40 profit per unit), you need $50,000 / $40 = 1,250 units sold per month to break even.
Statistics: Confidence Intervals and Error Margins
Political polls report results like "52% ± 3% margin of error." This means the true value likely falls between 49% and 55% with 95% confidence (typically). The margin of error is inversely proportional to the square root of sample size: doubling your sample doesn't halve the error—it only reduces it by 1/√2 ≈ 71%. To cut the margin in half, you need four times the sample size. A poll of 1,000 people has roughly ±3% error; getting to ±1.5% requires 4,000 people. This is why national polls rarely exceed 2,000-3,000 respondents—diminishing returns on accuracy.
Economics: Inflation, Real vs. Nominal Returns
If your investment earns 7% nominal return but inflation runs at 3%, your real return is approximately 4% (using the simple formula: nominal - inflation). The precise formula is: [(1 + nominal) / (1 + inflation)] - 1 = [(1.07) / (1.03)] - 1 = 1.0388 - 1 = 3.88%. Over 30 years, $10,000 at 7% nominal grows to $76,123. But if inflation averaged 3%, the purchasing power in today's dollars is $76,123 / (1.03)^30 = $76,123 / 2.427 = $31,367—equivalent to a 3.88% real annualized return. Ignoring inflation overstates wealth accumulation.
Health and Fitness: Body Fat Percentage, Heart Rate Zones
Body fat percentage measures fat mass as a share of total weight. A 180-pound person with 20% body fat has 36 pounds of fat (180 × 0.20) and 144 pounds of lean mass. If they lose 10 pounds of pure fat, they weigh 170 pounds with 26 pounds of fat, which is 26/170 = 15.3% body fat—a 4.7 percentage-point drop. But losing 10 pounds of mixed fat and muscle (say, 7 pounds fat and 3 pounds muscle) gives: 173 pounds total, 29 pounds fat = 16.8% body fat, only a 3.2-point drop. This shows why preserving muscle during weight loss matters—it improves body composition beyond just scale weight.
Heart rate training zones use percentages of max heart rate. A 40-year-old has an estimated max HR of 220 - 40 = 180 bpm. The "fat-burning zone" (60-70% max) is 108-126 bpm. The "cardio zone" (70-85% max) is 126-153 bpm. Calculate these by multiplying: 180 × 0.60 = 108, 180 × 0.85 = 153. Wearable fitness trackers automate this, but the formula lets you set custom zones for interval training or recovery days.
Environmental Science: Percentage Reduction Targets
Climate agreements often target percentage emission reductions from a baseline year. If a country emitted 500 million tons CO₂ in 2000 and commits to a 40% reduction by 2030, the target is 500 × (1 - 0.40) = 300 million tons. If 2025 emissions are 420 million tons, the remaining reduction needed is (420 - 300) / 420 = 28.6% below current levels, or 120 million tons in absolute terms. Percent reduction from baseline vs. percent reduction from current levels are different metrics—always clarify the reference point.
Advanced Mental Math Strategies for Percentages
The Commutative Property Shortcut
Percentages are commutative: 8% of 50 = 50% of 8. Both equal 4, but 50% of 8 is easier to calculate mentally (half of 8). Use this to simplify: 4% of 75 = 75% of 4 = 3. Or 12% of 25 = 25% of 12 = 3. The formula: (A% of B) = (B% of A). When one number is a nice percentage like 25%, 50%, or 75%, flip the calculation. Example: What's 68% of 25? Flip to 25% of 68 = 68 / 4 = 17. Faster than calculating 0.68 × 25.
Doubling and Halving for Awkward Percentages
To find 35% of 80, recognize that 35% = 10% + 25%. Calculate 10% of 80 = 8, and 25% of 80 = 20, then sum: 8 + 20 = 28. Or use doubling: 35% is half of 70%, so find 70% of 80 = 56, then halve it = 28. For 17.5%, note it's half of 35%: find 35% then divide by 2. For 87.5%, recognize it's 100% - 12.5%, so subtract 12.5% from the whole.
Successive Discounts Mental Trick
A store advertises "30% off, then take an additional 20% off the sale price." What's the final price on a $100 item? It's NOT 50% off. After the first discount: $100 × 0.70 = $70. After the second: $70 × 0.80 = $56. You saved $44, which is 44% off the original, not 50%. The combined discount formula: 1 - [(1 - 0.30) × (1 - 0.20)] = 1 - (0.70 × 0.80) = 1 - 0.56 = 44%. Mental shortcut: multiply the complements (70% × 80% = 56%) and subtract from 100%.
The 1% Method for Complex Percentages
Find 1% first by moving the decimal two places left, then scale. Example: What's 7% of 350? First, 1% of 350 = 3.50. Then 7% = 7 × 3.50 = 24.50. This works well for percentages like 3%, 6%, 7%, 9%, 11%, etc. For 15% of 240: 1% = 2.40, so 15% = 15 × 2.40 = 36. You can also combine: 15% = 10% + 5%, where 5% is half of 10%. So 10% of 240 = 24, half is 12, sum is 36.
Reverse Percentage (Finding the Original Price)
You bought a jacket for $72 after a 20% discount. What was the original price? The $72 represents 80% of the original (since 100% - 20% = 80%). So: Original = $72 / 0.80 = $90. Formula: if you know the discounted price and the discount percentage, divide by (1 - discount rate). Example: a car sells for $18,000 after a 10% markdown. Original = $18,000 / 0.90 = $20,000. This "reverse percentage" technique also applies to tax: if a meal costs $54 including 8% tax, the pre-tax price is $54 / 1.08 = $50.
Real-World Percentage Scenarios: Detailed Walkthroughs
Scenario 1: Negotiating a Salary Raise
Context: You earn $75,000 and ask for a 12% raise. Your employer counters with a $7,000 increase. Should you accept?
Analysis:
- Your requested raise: $75,000 × 0.12 = $9,000 (new salary $84,000)
- Employer's offer: $75,000 + $7,000 = $82,000
- Shortfall: $9,000 - $7,000 = $2,000 less than requested
- Employer's percentage: $7,000 / $75,000 = 9.33%
Conclusion: The $7,000 offer is a 9.33% raise, falling short of your 12% request by 2.67 percentage points. Over a year, you'd earn $2,000 less than hoped. Consider whether to negotiate further or accept based on market data.
Scenario 2: Comparing Credit Card Offers
Context: Card A has 18% APR, Card B has 15.99% APR. You carry a $5,000 balance monthly. Which saves more?
Calculation:
- Card A monthly rate: 18% / 12 = 1.5% per month
- Card A monthly interest: $5,000 × 0.015 = $75/month = $900/year
- Card B monthly rate: 15.99% / 12 = 1.3325% per month
- Card B monthly interest: $5,000 × 0.013325 = $66.63/month = $799.50/year
- Annual savings with Card B: $900 - $799.50 = $100.50
Conclusion: Switching from 18% to 15.99% APR saves $100.50 per year on a $5,000 balance. The 2.01 percentage-point difference represents an 11.2% reduction in interest charges ($100.50 / $900 = 11.2%).
Scenario 3: Investment Portfolio Rebalancing
Context: Your $100,000 portfolio is 70% stocks ($70k) and 30% bonds ($30k). Stocks rise 15%, bonds gain 3%. What's your new allocation?
Step-by-step:
- New stock value: $70,000 × 1.15 = $80,500
- New bond value: $30,000 × 1.03 = $30,900
- Total portfolio: $80,500 + $30,900 = $111,400
- New stock allocation: $80,500 / $111,400 = 72.3%
- New bond allocation: $30,900 / $111,400 = 27.7%
Conclusion: Stock allocation drifted from 70% to 72.3% due to stronger returns. To rebalance back to 70/30, sell $2,562 in stocks (72.3% - 70% = 2.3% of $111,400) and buy bonds.
Why it matters: Rebalancing enforces "buy low, sell high" discipline. Stocks outperformed, so you sell some at high prices and buy underperforming bonds at relative lows, maintaining your risk target.
Scenario 4: Sales Conversion Rate Optimization
Context: Your e-commerce site gets 10,000 visitors monthly with a 2% conversion rate (200 sales). You optimize checkout flow and lift conversions to 2.4%. Annual revenue impact?
Impact analysis:
- Old monthly sales: 10,000 × 0.02 = 200
- New monthly sales: 10,000 × 0.024 = 240
- Additional sales: 240 - 200 = 40 more sales/month
- Annual additional sales: 40 × 12 = 480 sales/year
- If average order value is $150: 480 × $150 = $72,000 extra revenue
Conclusion: A 0.4 percentage-point lift (from 2% to 2.4%) represents a 20% relative increase in conversions (0.4 / 2 = 0.20) and generates $72k in incremental annual revenue.
Lesson: Small percentage improvements compound into large revenue gains at scale. This is why conversion rate optimization (CRO) is a high-leverage growth channel.