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Compound Percent Change

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Direct answer

Multiple percent changes compound because each applies to a new baseline. Multiply growth factors, then subtract 1.

Formula and method

Total change = [(1+r1)(1+r2)… − 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. Convert each percentage to a decimal rate, preserving its sign.
  2. Add 1 to each rate.
  3. Multiply the factors.
  4. Subtract 1 and convert to a percentage.

Worked examples

+10% then +20%

1.10 × 1.20 − 1 = 0.32, or +32%.

+20% then −20%

1.20 × 0.80 − 1 = −0.04, or −4%.

Three periods

+5%, −2%, +8% gives 1.05 × 0.98 × 1.08 − 1 = 11.132%.

Interpretation and edge cases

  • Adding rates ignores changing baselines.
  • Use unrounded period rates.
  • Annualizing is a separate step and requires the period length.

Frequently asked questions

Why do +20% and −20% give −4%?

The 20% loss applies to the larger post-growth value.

Does order matter?

Pure multiplication is commutative, but real fees or cash flows can make the sequence matter.

Can I average the rates?

An arithmetic average does not reproduce compounded growth.

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

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

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