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Period Change vs Annualized Percent Change

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Direct answer

A total change over several years is not an annual rate. Under a compound-growth assumption, annualized change is (final/initial)^(1/years) − 1.

Formula and method

Annualized rate = [(final ÷ initial)^(1/n) − 1] × 100%

This page must show the formula exactly as the calculator or worked method uses it. Inputs remain unrounded during the calculation; rounding applies only to the displayed answer unless a domain-specific rule requires otherwise.

Step-by-step calculation

  1. Confirm initial and final are positive and comparable.
  2. Measure the exact period length n in years.
  3. Divide final by initial.
  4. Take the nth root, subtract 1 and convert to a percentage.

Worked examples

Two years

100 to 121 over 2 years: 1.21^(1/2) − 1 = 10% per year.

Three years

200 to 266.2 over 3 years is about 10% annualized.

Total versus annual

A 21% total rise over two years is not 21% per year and not exactly 10.5% per year.

Interpretation and edge cases

  • Annualization assumes compounding and smooths variation; it does not describe each year.
  • Zero or negative endpoints invalidate this ratio-based formula.
  • This is mathematical information, not financial advice.

Frequently asked questions

Is annualized return the same as average return?

No. Annualized return is a geometric growth rate.

Can I annualize a monthly rate?

Yes, with a compound assumption: (1+r)^12−1.

What if the period is 18 months?

Use n=1.5 years.

Sources and transparency

The formulas and examples were evidence-checked on 2026-09-10. This is educational mathematical content. It does not replace a field-specific standard, accounting policy, laboratory method, contractual definition or professional judgment. CalculatorGeek should display a named human reviewer only after a real reviewer has completed and documented that review.

Use this resource

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Open the Percent Change CalculatorRun the calculation with your own inputs, then return here to interpret it.

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