Percentages show up everywhere — discounts, grades, tips, taxes, statistics, and spreadsheets. The underlying math is simple once you understand three core operations: finding a percentage of a number, finding what percentage one number is of another, and calculating percentage change.
This guide covers all three, plus reverse percentages, mental math shortcuts, and the mistakes that trip people up most often.
Quick Answer
To calculate a percentage, use one of these formulas:
- X% of a number =
(X ÷ 100) × Number - What percent A is of B =
(A ÷ B) × 100 - Percentage change =
((New − Old) ÷ |Old|) × 100
Example: 15% of 200 = (15 ÷ 100) × 200 = 30.
Key Takeaways
- Most percentage tasks reduce to three formulas: of, ratio, and change.
- The base value controls the result; changing the base changes the percentage amount.
- Equal up/down percentages do not cancel because they apply to different bases.
- For reverse percentages, divide by the multiplier (
1 + ror1 − r), not by adding/subtracting the percent directly.
The Three Core Percentage Calculations
Every percentage problem falls into one of three types. Here's each formula with its plain-English translation.
1. What Is X% of a Number?
Formula: Result = (Percentage ÷ 100) × Number
This answers: "What is 15% of 200?"
Steps:
- Convert the percentage to a decimal: 15 ÷ 100 = 0.15
- Multiply: 0.15 × 200 = 30
So 15% of 200 is 30.
More examples:
- 25% of 80 = 0.25 × 80 = 20
- 8% of 50 = 0.08 × 50 = 4
- 120% of 60 = 1.20 × 60 = 72 (percentages can exceed 100%)
Use our percentage calculator to check any of these instantly.
2. What Percentage Is One Number of Another?
Formula: Percentage = (Part ÷ Whole) × 100
This answers: "What percent of 200 is 50?"
Steps:
- Divide the part by the whole: 50 ÷ 200 = 0.25
- Multiply by 100: 0.25 × 100 = 25%
So 50 is 25% of 200.
More examples:
- 30 out of 120 = (30 ÷ 120) × 100 = 25%
- 7 out of 20 = (7 ÷ 20) × 100 = 35%
- 180 out of 150 = (180 ÷ 150) × 100 = 120% (the part can be larger than the whole)
3. What Is the Percentage Change Between Two Numbers?
Formula: Percentage Change = ((New Value − Old Value) ÷ |Old Value|) × 100
A positive result means an increase. A negative result means a decrease.
Percentage increase example: Your rent went from $1,200 to $1,350. ((1350 − 1200) ÷ 1200) × 100 = (150 ÷ 1200) × 100 = 12.5% increase
Percentage decrease example: A stock dropped from $80 to $68. ((68 − 80) ÷ 80) × 100 = (−12 ÷ 80) × 100 = −15% (15% decrease)
For quick calculations, use the percentage change calculator.
Reverse Percentage: Finding the Original Number
Sometimes you know the result after a percentage was applied and need to find the original.
Formula: Original = Result ÷ (1 ± Percentage ÷ 100)
Use + for increases and − for decreases.
After an Increase
A shirt costs $69 after a 15% markup. What was the base cost?
$69 ÷ (1 + 0.15) = $69 ÷ 1.15 = $60
After a Decrease
A laptop is $680 after a 20% discount. What was the original price?
$680 ÷ (1 − 0.20) = $680 ÷ 0.80 = $850
This is one of the most commonly misunderstood percentage operations. A 20% discount off $850 gives you $680 — but adding 20% to $680 gives you $816, not $850. The base number matters.
Mental Math Shortcuts
You don't need a calculator for most everyday percentages. These shortcuts work because percentages are just fractions of 100.
The Building Blocks
Find 10% and 1% first. Everything else builds from those:
- 10% — move the decimal one place left. 10% of $85 = $8.50
- 1% — move the decimal two places left. 1% of $85 = $0.85
Common Percentages from Building Blocks
| Percentage | Shortcut | Example ($85) |
|---|---|---|
| 5% | Half of 10% | $4.25 |
| 10% | Move decimal left | $8.50 |
| 15% | 10% + 5% | $8.50 + $4.25 = $12.75 |
| 20% | 10% × 2 | $17.00 |
| 25% | Divide by 4 | $21.25 |
| 33% | Divide by 3 | $28.33 |
| 50% | Divide by 2 | $42.50 |
| 75% | 50% + 25% | $63.75 |
The Flip Trick
X% of Y = Y% of X. Always.
8% of 50 is the same as 50% of 8 = 4.
This is useful when one direction is easier to compute mentally. 4% of 75 is hard. 75% of 4 = 3. Same answer.
Quick Tip Calculation
For a 15% restaurant tip: find 10% (move decimal), then add half of that.
- Bill: $73
- 10% = $7.30
- 5% = $3.65
- 15% tip = $10.95
For 20%, just double the 10% figure: $7.30 × 2 = $14.60.
Percentage vs. Percentage Points
These terms sound similar but mean different things.
- Percentage change is relative to the starting value.
- Percentage points describe the absolute difference between two percentages.
Example: An interest rate goes from 3% to 5%.
- That's a change of 2 percentage points (5 − 3 = 2).
- But it's a 66.7% increase ((5 − 3) ÷ 3 × 100 = 66.7%).
Confusing these is a common source of misunderstanding in news reporting and financial discussions.
Common Percentage Mistakes
1. Adding Successive Percentages
A 20% increase followed by a 20% decrease does not return you to the original value.
- Start: $100
- After 20% increase: $120
- After 20% decrease: $120 × 0.80 = $96
You're down 4%, not back to even. The second percentage applies to the new, larger base.
2. Dividing by the Wrong Number
"What percentage is 40 of 160?" requires dividing 40 by 160 (the whole), not 160 by 40.
- Correct: 40 ÷ 160 = 0.25 = 25%
- Wrong: 160 ÷ 40 = 4 = 400% (this answers a different question)
Always divide the part by the whole.
3. Using the Wrong Base for Reverse Percentages
If something costs $80 after a 20% discount, the original is not $80 + 20% of $80.
- Wrong: $80 × 1.20 = $96
- Correct: $80 ÷ 0.80 = $100
The discount was 20% of the original price ($100), not 20% of the sale price.
4. Confusing Percentage Of with Percentage Off
- 25% of $80 = $20 (the amount itself)
- 25% off $80 = $80 − $20 = $60 (the price you pay)
The preposition changes the answer entirely.
Percentages in Everyday Situations
Discounts and Shopping
A store advertises "30% off." On a $120 item:
Savings = $120 × 0.30 = $36 You pay = $120 − $36 = $84
For stacked discounts (e.g., 30% off + extra 10% coupon), each applies to the reduced price, not the original. See our discount calculator for step-by-step breakdowns.
Grades and Scores
You scored 38 out of 45 on a test.
(38 ÷ 45) × 100 = 84.4%
Sales Tax
An item costs $65 in a state with 7.5% tax.
Tax = $65 × 0.075 = $4.88 Total = $65 + $4.88 = $69.88
Tip Calculation
For a $52 dinner with a 20% tip:
Tip = $52 × 0.20 = $10.40 Total = $62.40
Markups and Margins
A retailer buys a product for $40 and sells for $60.
- Markup = ((60 − 40) ÷ 40) × 100 = 50% (based on cost)
- Margin = ((60 − 40) ÷ 60) × 100 = 33.3% (based on selling price)
Markup and margin use different bases. Our markup calculator and margin calculator handle the conversions.
Percentage Formulas Reference
| Problem | Formula | Example |
|---|---|---|
| X% of a number | (X ÷ 100) × Number | 15% of 200 = 30 |
| What % is A of B | (A ÷ B) × 100 | 50 of 200 = 25% |
| % increase | ((New − Old) ÷ Old) × 100 | 80 → 100 = 25% |
| % decrease | ((Old − New) ÷ Old) × 100 | 100 → 80 = 20% |
| Original before increase | Result ÷ (1 + X/100) | $69 after 15% up = $60 |
| Original before decrease | Result ÷ (1 − X/100) | $680 after 20% off = $850 |
| Percentage points | Simply subtract the two percentages | 5% − 3% = 2 pp |
FAQ
How do I calculate a percentage of a number?
Divide the percentage by 100 and multiply by the number. For example, 25% of 200: divide 25 by 100 to get 0.25, then multiply by 200 to get 50.
How do I find what percentage one number is of another?
Divide the part by the whole and multiply by 100. For example, 30 out of 120: 30 ÷ 120 = 0.25 × 100 = 25%.
How do I calculate percentage increase?
Subtract the old value from the new value, divide by the old value, and multiply by 100. Formula: ((New − Old) ÷ Old) × 100. Example: from $80 to $100 = ((100 − 80) ÷ 80) × 100 = 25% increase.
How do I calculate percentage decrease?
Subtract the new value from the old value, divide by the old value, and multiply by 100. Formula: ((Old − New) ÷ Old) × 100. Example: from $50 to $35 = ((50 − 35) ÷ 50) × 100 = 30% decrease.
What is the difference between percentage and percentage points?
Percentage points are the arithmetic difference between two percentages. A rate going from 3% to 5% rose by 2 percentage points but by 66.7% in percentage terms. Percentage points are absolute; percentages are relative.
Why doesn't a 50% increase followed by a 50% decrease return to the original?
Because each percentage is calculated on a different base. A 50% increase on $100 = $150. A 50% decrease on $150 = $75, not $100. The second operation uses the new value as its base.
How do I calculate a percentage in Excel or Google Sheets?
For X% of a number: =A1*0.25 (for 25%). For percentage of total: =A1/B1 and format the cell as percentage. For percentage change: =(B1-A1)/A1 and format as percentage.
How do I find the original price before a discount?
Divide the sale price by (1 minus the discount as a decimal). Example: A product costs $72 after 10% off. Original = $72 ÷ 0.90 = $80.
What does "percent" literally mean?
"Percent" comes from Latin per centum, meaning "by the hundred." 25% literally means 25 per 100, or 25/100, or 0.25.
Is there a shortcut for calculating percentages in my head?
Yes. Find 10% by moving the decimal one place left, then combine. For 15%, find 10% and add half of it. For 25%, divide by 4. You can also use the flip trick: X% of Y equals Y% of X — pick whichever is easier to compute.
How do I convert a fraction to a percentage?
Divide the numerator by the denominator and multiply by 100. For example, 3/8 = 0.375 × 100 = 37.5%.
How do I convert a decimal to a percentage?
Multiply by 100. For example, 0.72 = 72%. Move the decimal point two places to the right.
Try It Yourself
Use our percentage calculator to compute any percentage instantly — whether you need X% of a number, what percentage one number is of another, or the percentage change between two values.
For more specific calculations:
- Percentage Change Calculator — compute percent increase or decrease
- Discount Calculator — apply single or stacked discounts
- Markup Calculator — find selling price from cost and markup
- Margin Calculator — calculate profit margins