ROI Percentage Calculator
Measure investment returns as a percentage of the original investment.
Understanding the Calculation
Percentage calculations involve:
- Base Value: The original or total amount
- Percentage Rate: The proportion expressed as a percent
- Result: The calculated value based on your inputs
Common Formulas
- Finding a percentage: (Part ÷ Whole) × 100 = %
- Finding the part: Whole × (% ÷ 100) = Part
- Percentage change: ((New - Old) ÷ Old) × 100 = % Change
Practical Applications
Use percentage calculations for:
- Financial planning and budgeting
- Academic performance tracking
- Business metrics and KPIs
- Health and fitness goals
- Shopping and discount calculations
ROI and Its Limits
``
ROI = (gain − cost) ÷ cost × 100
`
Simple, and it omits the single most important variable: time. A 50% ROI over one year and a
50% ROI over ten are the same number and completely different investments.
| Investment | ROI | Period | Annualised |
|---|---|---|---|
| A | 50% | 1 year | 50% |
| B | 50% | 5 years | 8.4% |
| C | 100% | 10 years | 7.2% |
Use CAGR whenever periods differ:`
CAGR = (ending ÷ beginning)^(1 ÷ years) − 1
`
ROI also ignores risk. Comparing a 12% ROI on a startup with a 5% ROI on Treasuries as though
the numbers are commensurable is the most common error in the whole category.
The Four Percentage Questions
Almost every percentage problem is one of these, and mixing them up is the most common
arithmetic error there is:
| Question | Formula | Example |
|---|---|---|
| What is X% of Y? | Y × (X ÷ 100) | 15% of 80 = 12 |
| X is what % of Y? | (X ÷ Y) × 100 | 12 is 15% of 80 |
| X is Y% of what? | X ÷ (Y ÷ 100) | 12 is 15% of 80 |
| % change from X to Y | ((Y − X) ÷ X) × 100 | 80 → 92 is +15% |
Percentage Points Are Not Percent
A rate moving from 4% to 5% is one percentage point, and a 25% increase. Both
statements are true and they are not interchangeable — headlines routinely use the smaller
one when reporting a rise and the larger one when reporting a fall.
Increases and Decreases Do Not Cancel
| Start | Change | Result |
|---|---|---|
| 100 | +50%, then −50% | 75 |
| 100 | −50%, then +50% | 75 |
| 100 | −20%, then +25% | 100 |
The reason is that the second percentage applies to a different base. To reverse a −20% you
need +25%, not +20%. This is why a stock that falls 50% must double to break even, and why
"we cut costs 30% then grew 30%" leaves you 9% down.Reversing a Percentage
To find the price before a 20% discount, divide by 0.8 — do not add 20%:
`
before = after ÷ (1 − discount)
$80 ÷ 0.8 = $100 ✓
$80 × 1.2 = $96 ✗
``
The same asymmetry applies to tax, tips, markups and platform fees.