01
What is X% of Y?
Use this for commissions, budgets, fees or any time you need a slice of a total.
Formula: divide the percentage by 100, then multiply by the number: (20 ÷ 100) × 70 = 14.
Make percentages make sense.
Fourteen practical calculators and four clear guides for the numbers that show up in shops, investments, reports, invoices and classrooms.
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02
X is what percent of Y?
Compare a part to its whole — useful for completion rates, scores and budgets.
Formula: divide the part by the whole, then multiply by 100: (18 ÷ 24) × 100 = 75%.
03
Percentage change
Measure how much a value rose or fell relative to where it started.
Formula: subtract the old value from the new, divide by the absolute old value, then multiply by 100.
04
Percentage difference
Compare two values when neither one is the starting point or baseline.
Formula: absolute difference ÷ average of the two absolute values × 100.
05
Add or subtract a percentage
Adjust a number upward or downward by a chosen rate.
Formula: multiply the starting number by (1 + percentage ÷ 100) to add, or (1 − percentage ÷ 100) to subtract.
06
Reverse percentage
Work backward to find the original value before a percentage increase or decrease.
Formula: final value ÷ (1 + rate) after an increase, or final value ÷ (1 − rate) after a decrease.
07
Discount & sale price
See exactly how much you save and what you pay after a discount.
Formula: original price × (1 − discount percentage ÷ 100).
08
Tip & bill split
Calculate the tip, total bill and each person’s share.
Formula: tip = bill × tip rate. Add the tip to the bill, then divide by the number of people.
09
Sales tax
Add tax to a subtotal or work backward from a tax-inclusive total.
Formula: to add tax, multiply by (1 + tax rate). To remove included tax, divide by (1 + tax rate).
10
Margin & markup
Compare profit to selling price (margin) and to cost (markup).
Key difference: margin divides profit by selling price. Markup divides the same profit by cost.
11
Commission
Calculate commission earned and total pay from a sales amount and rate.
Formula: sales amount × commission rate. Add any base pay to get total pay.
12
Repeated percentage change
See how growth or decline compounds over multiple periods.
Formula: starting value × (1 + rate ÷ 100)periods. Repeated percentage changes compound; they do not simply add.
13
CAGR
Find the compound annual growth rate between a starting and ending value.
Formula: (ending value ÷ starting value)1 ÷ years − 1, then multiply by 100. CAGR smooths the change into one annual rate.
14
Grade needed on a final
Find the score required on a final exam to reach your target course grade.
Formula: (target − current × remaining-course weight) ÷ final-exam weight.
Percentage formulas, without the guesswork.
Percent change uses the starting value
A move from 40 to 50 is a 25% increase because the difference, 10, is divided by the starting value, 40.
(new − old) ÷ |old| × 100
40 → 50+25%
50 → 40−20%
Not oppositesDifferent bases
Percent vs. percentage points
If a rate moves from 20% to 25%, it rose by 5 percentage points. Relative to the original 20%, that is a 25% increase.
Change vs. difference
Use percentage change when one value is the starting point. Use percentage difference when two values are peers and neither is the baseline.
Margin is not markup
With a cost of 60 and a price of 100, profit is 40. Margin is 40 ÷ 100 = 40%; markup is 40 ÷ 60 = 66.67%.
Common percentage formulas
- Percent of a number
- (percentage ÷ 100) × number
- Percentage change
- (new − old) ÷ |old| × 100
- Percentage difference
- |a − b| ÷ ((|a| + |b|) ÷ 2) × 100
- Reverse increase
- final ÷ (1 + rate ÷ 100)
- Sale price
- price × (1 − discount ÷ 100)
- Gross margin
- (price − cost) ÷ price × 100
- Commission
- sales × commission rate ÷ 100
- CAGR
- [(ending ÷ starting)^(1 ÷ years) − 1] × 100
Go beyond the answer.
Use these original, step-by-step guides when you want to understand the method, check a result or do the math without a calculator.
Percentage change
How to calculate percentage increase and decrease
Choose the right starting value, follow the formula and work through increases, decreases and reverse calculations.
Read the step-by-step guide →Sales taxHow sales tax is calculated, with examples
Add tax to a subtotal, remove included tax and understand combined rates, taxable bases and rounding.
Read the sales-tax guide →Rates and reportingPercentage vs. percentage points, explained simply
See why a five-point rise can be a much larger percent change, with examples from rates, polls and discounts.
Learn the difference →Everyday mathHow to calculate tips quickly
Use fast mental shortcuts for 10%, 15%, 18%, 20% and 25%, then total or split the bill correctly.
Read the tipping guide →Quick answers
How do I calculate a percentage without a calculator?
To find X% of a number, convert X to a decimal by dividing it by 100, then multiply. For example, 15% of 80 is 0.15 × 80 = 12.
How do I reverse a percentage increase?
Divide the final value by 1 plus the percentage rate as a decimal. If a total is 120 after a 20% increase, the original was 120 ÷ 1.20 = 100.
What is the difference between percentage change and percentage difference?
Percentage change compares a new value with a known starting value. Percentage difference compares two values symmetrically, using their average as the reference.
What is CAGR?
Compound annual growth rate is the steady annual rate that would turn a starting value into an ending value over a number of years. It smooths the path between those values and does not show year-to-year volatility.
Why can a percentage decrease not exceed 100%?
A 100% decrease reduces a positive starting value to zero. A result below zero can exist, but describing that move as a decrease of more than 100% usually needs extra context.
How many decimal places are used?
Results are rounded for readability to a maximum of six decimal places. Calculations use the full unrounded values internally.
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