How to Calculate Percentages — Formulas and Examples
Percentages are everywhere — from discount tags at the store to interest rates on loans. Despite being one of the most common math concepts, percentage calculations still trip people up. This guide covers the three core percentage formulas you'll encounter in everyday life and explains when to use each one, with clear examples.
1. Finding X% of a Number
This is the most common percentage calculation. You use it whenever you need to find a portion of a whole number based on a percentage. The formula is straightforward:
Result = (Percentage / 100) × Number
For example, to find 15% of 200, you divide 15 by 100 to get 0.15, then multiply by 200. The answer is 30. You'll use this formula when calculating sales tax, tips at restaurants, discounts during a sale, or the amount of a down payment on a large purchase. If a $250 jacket is 20% off, you compute (20 / 100) × 250 = 50, so the discount is $50 and you pay $200.
2. Finding What Percent X Is of Y
This calculation answers the question "what fraction of the whole does this part represent, expressed as a percentage?" The formula is:
Percentage = (Part / Whole) × 100
Say you scored 42 out of 50 on a test. To find your percentage score, divide 42 by 50 to get 0.84, then multiply by 100 to get 84%. This mode is useful for calculating test scores, savings rates (how much of your income did you save?), task completion rates, or comparing proportions. If a company earned $1.2 million in revenue and spent $300,000 on marketing, then marketing was (300,000 / 1,200,000) × 100 = 25% of total revenue.
3. Calculating Percentage Change
Percentage change tells you how much a value has increased or decreased relative to its original amount. The formula is:
% Change = ((New Value − Old Value) / |Old Value|) × 100
If your monthly rent went from $1,500 to $1,650, the percentage change is ((1650 − 1500) / 1500) × 100 = 10%. A positive result means an increase; a negative result means a decrease. This formula is essential for tracking price changes, stock performance, weight loss or gain, population growth, and year-over-year business metrics. If a stock dropped from $80 to $68, the change is ((68 − 80) / 80) × 100 = −15%, indicating a 15% decline.
Common Use Cases for Percentage Calculations
Percentages appear in nearly every field. In personal finance, you use them to compare interest rates, figure out how much to tip, or see how your investments performed. In business, percentages measure profit margins, conversion rates, and market share. In academics, grades are almost always expressed as percentages. In health and fitness, you track body fat percentage, calorie macro splits, and workout improvement over time.
Tips for Quick Mental Math
To find 10% of any number, just move the decimal one place left — 10% of 350 is 35. To get 5%, halve the 10% result — 5% of 350 is 17.5. For 1%, move the decimal two places left — 1% of 350 is 3.5. You can combine these: 15% of 350 is 35 + 17.5 = 52.5. These shortcuts make tipping and quick estimations much faster without reaching for a calculator.
Frequently Asked Questions
What is the difference between percentage and percentile?
A percentage is a fraction of 100 (e.g., 85%). A percentile is a ranking — being in the 85th percentile means you scored higher than 85% of participants. They are related concepts but measure different things.
Can a percentage be greater than 100%?
Yes. A percentage over 100% simply means the value exceeds the reference. If your investment doubled, the return is 200% of your original amount, or a 100% increase.
How do I convert a fraction to a percentage?
Divide the numerator by the denominator, then multiply by 100. For example, 3/8 = 0.375 × 100 = 37.5%.
Is this calculator free to use?
Yes. This percentage calculator runs entirely in your browser with no ads, no signup, and no data collection. Enter your numbers and get instant results — your data never leaves your device.
Related reading: ROI Explained: How to Calculate Return on Investment