Percentage Calculator
Various percentage-related calculations including basic percentages, increase/decrease percentages, and finding percentages
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What is a Percentage?
A percentage expresses a number as a fraction of 100. The word literally means “per hundred” — so 25% means 25 out of every 100, or one quarter. To convert between forms: 50% = 0.5 = ½ = 50/100. They are all the same value written differently.
Percentages show up everywhere because they make comparisons easy. A $12 discount means little on its own, but a 30% discount tells you instantly how significant the sale is. Sales tax, interest rates, battery life, exam scores, and election polls are all reported as percentages for the same reason: a 0–100 scale is easy to interpret at a glance.
Values above 100% are also valid — they simply mean “more than the whole.” If a stock price grows from $50 to $125, it has risen 150%, because the gain ($75) is 1.5 times the original amount.
How to Calculate Percentages
There are four common cases:
Find X% of Y: (X × Y) ÷ 100
Percentage increase: (New − Original) ÷ Original × 100
Percentage decrease: (Original − New) ÷ Original × 100
X is what % of Y: (X ÷ Y) × 100
Worked example — a 25% discount on an $80 shirt:
Discount = 80 × 25 ÷ 100 = $20 → Final price = $80 − $20 = $60
Worked example — salary raise from $50,000 to $54,000:
Increase = (54000 − 50000) ÷ 50000 × 100 = 8%
Key tip: Always divide by the original (starting) value when computing increase or decrease — not by the new value. Dividing by the wrong base is the single most common percentage mistake.
Common Use Cases
Shopping discounts — Sale tags show “30% off,” but the final price isn’t always obvious. Multiplying the price by 0.70 (or computing 30% and subtracting) gives the checkout total before tax.
Salary and raises — A 5% raise means different dollar amounts at different pay levels. Converting an offer into a percentage makes it comparable to your current salary regardless of the currency or base amount.
Exam scores and accuracy — Getting 42 out of 50 correct is 84%. Percentages let teachers compare performance across tests of different lengths.
Investment returns — A stock that goes from $100 to $115 has returned 15%. Percentages (not dollar gains) let you compare investments of different sizes on equal footing.
Frequently Asked Questions
How do I calculate a percentage increase?
To calculate a percentage increase, subtract the original value from the new value, divide by the original value, then multiply by 100. For example, if a price rises from $40 to $50: (50 − 40) ÷ 40 × 100 = 25% increase. If you instead know the increase rate and want the new value, multiply the original by (1 + rate): 40 × 1.25 = 50.
What's the difference between a percentage increase and a percentage decrease?
A percentage increase adds a share of the original value back onto it (original × 1.20 for +20%), while a percentage decrease removes that share (original × 0.80 for −20%). The formulas are symmetric, but they are not reversible: a 20% increase followed by a 20% decrease does not return you to the starting value, because the 20% decrease is computed from the larger new value.
Are there quick mental math tricks for common percentages?
Yes. 10% of a number is simply the number with the decimal point moved one place left (10% of 80 = 8). 1% moves it two places (1% of 80 = 0.8). From there you can build others: 20% = double 10%, 5% = half of 10%, 15% = 10% + 5%. To find 50%, just halve the number; for 25%, take half of that half.
What is the difference between a percentage and a percentile?
A percentage is a share of a whole expressed out of 100 (you answered 85% of questions correctly). A percentile ranks a value relative to others in a dataset: scoring in the 85th percentile means you did as well as or better than 85% of people, regardless of the raw score. Percentages compare parts to a whole; percentiles compare one value to the rest of a distribution.
How do I calculate a tip using percentages?
Multiply the bill by the tip percentage expressed as a decimal. For an 18% tip on a $45 check: 45 × 0.18 = $8.10, so the total is $53.10. A common shortcut is to find 10% (move the decimal one place left → $4.50), then add roughly double that for ~20%, or take a bit less than double for ~18%.