How to calculate growth rate and CAGR

By: Patrick Myers Patrick Myers is the CEO and Founder of Calculator Academy. He has over eight years of experience developing online calculators and holds a B.S. in Mechanical Engineering. His work focuses on formula implementation, calculator accuracy, unit conversions, and creating practical tools that are easy to use.

Last Updated: September 26, 2026

Distinguish total percentage growth from a compounded rate per period. Follow a 1,000-to-1,500 example over five years, check CAGR backward, and see why simple averages and reversed changes differ.

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The calculation

Total growth (%) = (final − start) / start × 100. CAGR (%) = [(final / start)^(1/n) − 1] × 100, where n is the positive number of equal periods.

Worked example

Start 1,000, final 1,500, n=5 years: total=(1,500−1,000)/1,000×100=50%. CAGR=(1.5^(1/5)−1)×100≈8.4472% per year. Using the unrounded factor, 1,000×(1+CAGR/100)^5=1,500. Compounding 10% yearly instead gives 1,610.51.

Total percent change requires a nonzero starting value. For the usual CAGR interpretation, use comparable positive endpoints and a positive period count. The result is a smoothed equivalent rate, not evidence of steady actual growth or a prediction. Deposits and withdrawals must be treated separately when measuring investment performance. Reversing 1,500→1,000 gives −33.3333%, because the baseline is now 1,500.

Video chapters

  • 0:00 — One increase, two growth rates
  • 0:14 — Measure change against the starting value
  • 0:32 — Turn the total into a growth multiple
  • 0:50 — Compute and verify CAGR
  • 1:11 — Why fifty divided by five is different
  • 1:30 — A decrease uses a new baseline
  • 1:50 — State the period and the limits
  • 2:17 — Choose the growth rate you mean
Read the full transcript

A value rises from one thousand to fifteen hundred over five years. Is its growth rate fifty percent, or about eight point four five percent a year? Both can be correct. One describes the whole change; the other describes an equivalent compounded rate.

For total growth, subtract the starting value from the final value. Fifteen hundred minus one thousand is five hundred. Divide that change by the starting one thousand to get zero point five. Multiply by one hundred: the total increase is fifty percent. The starting value is the reference size.

The final value is one point five times the starting value. If an equal growth factor repeats each year, five copies of that factor must multiply to one point five. Take the fifth root, then subtract one. This is the compound annual growth rate, usually called C A G R.

Divide fifteen hundred by one thousand to get one point five. Raise it to the one-fifth power: about one point zero eight four four seven two. Subtract one and convert to a percent. The answer is about eight point four four seven two percent per year. Check it by compounding the unrounded factor five times: one thousand becomes fifteen hundred.

Fifty percent divided by five gives ten percent per year as a simple average of the total change. But ten percent compounded each year would turn one thousand into about sixteen hundred ten point five one. Each increase then grows from a larger base. Ten percent is not the compounded rate connecting our two endpoints.

Reversing the endpoints also changes the denominator. From fifteen hundred back to one thousand, the change is minus five hundred. Divide by fifteen hundred, then multiply by one hundred: about minus thirty-three point three three percent. A fifty-percent rise is not undone by a fifty-percent fall. The reference value changed.

Use the same quantity, units, and measurement basis at both endpoints. For total percent change, the starting value cannot be zero. The usual C A G R calculation uses positive starting and final values, and a positive number of periods. Five years gives a yearly rate. Five months gives a monthly rate. C A G R smooths the journey; it does not prove growth was steady. For investments, extra deposits or withdrawals need separate treatment.

So choose your question first. For the entire increase or decrease, divide final minus start by start, and multiply by one hundred. For an equivalent compounded rate per period, take final divided by start to the one-over-periods power, subtract one, and convert to a percent. One thousand to fifteen hundred over five years is fifty percent total growth, or about eight point four five percent compounded per year.

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