CAGR Calculator
Find the smoothed annual growth rate over multiple periods.
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
Compound Annual Growth Rate
CAGR is the constant annual rate that would take you from the starting value to the ending value over the period:
``
CAGR = (ending ÷ beginning)^(1 ÷ years) − 1
`
$10,000 growing to $25,000 over 8 years is a 12.1% CAGR.
Its value is that it makes different periods comparable, which raw returns do not. Its
limitation is that it smooths away all the volatility:
| Year | Portfolio A | Portfolio B |
|---|---|---|
| Start | $10,000 | $10,000 |
| Path | steady 12% | +60%, −30%, +45%, −20%… |
| End (8 yr) | $24,760 | $24,760 |
| CAGR | 12.1% | 12.1% |
Identical CAGR, radically different experience — and a different outcome for anyone who needed
to withdraw during a drawdown.CAGR also differs from average annual return. A +50% year followed by a −50% year averages 0%
and leaves you down 25%; CAGR reports the −13.4% that actually happened.
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.