The basic percentage formula
The word percent originates from the Latin phrase per centum, meaning "by the hundred." A percentage is simply a ratio or fraction whose denominator is standardized to 100.
The fundamental formula:
Percentage = (Part / Whole) × 100
To find the part when you already know the percentage:
Part = (Percentage / 100) × Whole
Quick example: Finding 15% of 240
Part = (15 / 100) × 240
Part = 0.15 × 240
Part = 36
15% of 240 is 36.
Percentage increase: How to calculate growth
Use this formula when a value has increased from an initial base and you want to express that growth as a percentage:
Percentage Increase = ((New Value − Original Value) / Original Value) × 100
Example: SaaS subscription growth
A company had 1,200 active subscribers last month and grew to 1,500 subscribers this month:
- Increase = ((1,500 − 1,200) / 1,200) × 100 = (300 / 1,200) × 100 = 25%
The subscriber base increased by 25%.
Percentage decrease: How to calculate decline
When a value drops from an original reference point:
Percentage Decrease = ((Original Value − New Value) / Original Value) × 100
Example: Website page weight reduction
An asset was compressed from 450 KB down to 180 KB:
- Decrease = ((450 − 180) / 450) × 100 = (270 / 450) × 100 = 60%
The file size was reduced by 60%.
Crucial distinction: Percent vs. Percentage Points
One of the most widespread statistical misunderstandings in news and business reporting is confusing percent change with percentage points:
- Percentage Points: The simple arithmetic difference between two percentage values (B − A).
- Percent Change: The relative change compared to the original starting baseline.
Classic Example: If a central bank interest rate rises from 4% to 5%:
- The interest rate rose by 1 percentage point (5% − 4% = 1 point).
- However, the interest rate rose by 25 percent ((5 − 4) / 4 × 100 = 25%).
Mixing these up can distort financial reporting significantly!
The cumulative percentage trap: Why +20% then −20% is NOT zero
A common intuitive trap is assuming that gaining 20% and then losing 20% brings you back to where you started.
Let's test this on $100:
- Step 1 (+20%): $100 × 1.20 = $120
- Step 2 (−20%): $120 × 0.80 = $96
You end up with $96, a net loss of 4%!
Why does this happen? The second percentage is calculated on a larger base ($120), so the 20% deduction ($24) is larger than the original 20% gain ($20).
To fully recover from a loss, you must gain a higher percentage than you lost:
| If you lose... | You need to gain... to break even |
|---|---|
| 10% | 11.1% |
| 20% | 25.0% |
| 33.3% | 50.0% |
| 50% | 100.0% |
| 75% | 300.0% |
Percentage difference between two numbers
When comparing two independent values where neither number is the "original" baseline (for example, comparing salaries between two job candidates), use Percentage Difference:
Percentage Difference = (|Value A − Value B| / Average of A and B) × 100
Example: Comparing 80 and 100
- Difference = (|80 − 100| / ((80 + 100) / 2)) × 100 = (20 / 90) × 100 ≈ 22.2%
Mental math shortcuts for everyday life
| Percentage | Shortcut Rule | Mental Example |
|---|---|---|
| 10% | Move the decimal point 1 place left | 10% of 350 = 35 |
| 5% | Find 10%, then divide by 2 | 10% of 80 is 8; 8 / 2 = 4 |
| 20% | Find 10%, then double it | 10% of 45 is 4.5; 4.5 × 2 = 9 |
| 25% | Divide by 4 | 25% of 120 = 30 |
| 50% | Divide by 2 | 50% of 74 = 37 |
| 1% | Move the decimal point 2 places left | 1% of 4,200 = 42 |
Percentage formulas for Excel and Google Sheets
| Goal | Formula in Cell | Notes |
|---|---|---|
Find % of a number (Rate in A2, Total in B2) | =A2 * B2 | If A2 is formatted as percentage (e.g. 15%) |
% Change between two values (Old in A2, New in B2) | =(B2 - A2) / A2 | Format cell as Percentage |
| Total after % increase | =A2 * (1 + B2) | E.g. Price in A2, +5% in B2 |
| Total after % decrease | =A2 * (1 - B2) | E.g. Price in A2, -20% in B2 |
Summary
- Calculate percentages using
(Part / Whole) × 100. - Understand the vital difference between percent change and percentage points.
- Remember that sequential percentage gains and losses do not cancel out.
- To perform all four major percentage calculations instantly in your browser, check out our Percentage Calculator. For retail markdowns and shopping, visit our How to Calculate a Discount guide.