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Year-over-Year Change & Multi-Year CAGR

Compare two annual values and calculate compound annual growth, absolute change and total growth across a chosen number of years.

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Calculator inputs

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How to use this calculator

  1. Enter the known values in the units shown. Results update as you type.
  2. Where results are editable, change one to solve backwards. Lock a value to hold it fixed.
  3. Use the worked example to check the method. Reset restores the starting fields.

Use the result with context

Results are estimates for planning and education. Confirm rates, taxes, fees, and legal requirements with the relevant institution or a qualified professional before making a financial decision.

Formula and method

A rise from 100 to 120 is 20% year-over-year growth. Growth from 100 to 144 over two years has a 20% CAGR and 44% total growth.

YoY = 100 × (new/old − 1); CAGR = 100 × [(final/initial)^(1/years) − 1]

Worked example

Enter these known values and leave the other values blank.

Value in initial year
100
Value in final year
120
Value in initial year
100
Value in final year
144
Elapsed years
2
Year-over-year % change
20 %
Compound annual growth rate
20 %
Difference
44
Total growth
44 %

Assumptions and limitations

  • Starting values and elapsed years are positive. Ending values may be zero; negative ending values are outside this compound-growth model.
  • For CAGR, enter elapsed years between measurements, not the number of year labels in an inclusive list.
  • CAGR smooths the endpoints into a constant annual rate. It does not reveal the intervening path or adjust for cash flows, inflation, taxes or fees.
  • A zero endpoint corresponds to a total loss of 100%. It does not determine a unique elapsed period when solving backwards at a rate of minus 100%.

Common questions

Is CAGR the average of yearly percentage changes?

No. It is the constant compounded rate connecting the starting and ending values over the entered years.

Can the final value be zero?

Yes. The change is minus 100%. The starting value must remain positive because it is the comparison denominator.

References

Bookify allows zero ending values and requires growth rates to remain at least minus 100% in this nonnegative-endpoint model.

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