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Compound Annual Growth Rate — result sheet
Convert a beginning value, ending value, and elapsed years into a smoothed annual growth rate, including declines and total losses when there are no intervening cash flows.
Inputs used
Results
Visual chart
Breakdown
Calculation steps
Returned data table
Formula and methodology
Formula: CAGR (%) = ((endValue / startValue)^(1 / years) - 1) x 100; total change (%) = (endValue / startValue - 1) x 100.
CAGR is the constant annual growth rate that connects two values over the entered duration. It is an effective annualized rate, unlike the nominal annual input used by the monthly interest tools. It suppresses volatility and is misleading if deposits or withdrawals changed the balance between the endpoints.
This result follows the calculator's declared inputs, precision, validation boundaries, and model limits.
Input contract
- Beginning value — Must be positive; zero has no defined growth ratio.; minimum 0.01; maximum 1000000000000
- Ending value — Zero is treated as a total loss (-100%).; minimum 0; maximum 1000000000000
- Elapsed time — years; Fractional years are used exactly; this is not restricted to whole months.; minimum 0.01; maximum 100
Worked example
| Input | Value |
|---|---|
| Beginning value | 10000 |
| Ending value | 16105.1 |
| Elapsed time | 5 |
CAGR: 10.00%; total change: 61.05%; value increase: 6105.10.
Assumptions and limits
- Beginning value is positive, ending value is nonnegative, and elapsed years are positive and no more than 100; fractional years are used exactly.
- No intervening deposits, withdrawals, or separate distributions occur. Use one consistent currency or consistently defined value unit.
- This is a smoothed historical or hypothetical endpoint rate, not a forecast or measure of volatility; a zero ending value gives -100%, and numerical overflow is rejected.
Calculator note
Source and methodology
Use the official WorldCalculate methodology policy for the source, formula, precision, and boundary standards behind this calculator.
Planning estimate, not financial, medical, legal, or professional advice. © WorldCalculate — reuse with attribution. Built and curated by Hassan ALRowaie.
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