What is the CAGR formula?

CAGR = (end value ÷ start value)^(1 ÷ years) − 1. Multiply by 100 for a percent.

Why is CAGR lower than total growth divided by years?

Because each year’s growth builds on the previous years’ growth. Dividing total growth by the number of years ignores that compounding, so it overstates the steady yearly rate.

Can CAGR be negative?

Yes. If the end value is below the start value, CAGR is negative. 1,000 falling to 800 over 2 years is about −10.56% per year.

What is the rule of 72?

A shortcut: 72 ÷ the yearly growth rate (in percent) ≈ years to double. At a CAGR of about 7.18%, 72 ÷ 7.18 ≈ 10 years, which matches 100 → 200 in 10 years. It is an approximation that works best for rates between roughly 4% and 12%.

CAGR Calculator (Compound Annual Growth Rate)

CAGR is the single steady yearly rate that would turn your starting value into your ending value. It is the honest way to say “how fast did this grow per year” when growth compounds — revenue, a portfolio, a city’s population, a price index.

Written and maintained by Ricardo Rodrigues · Last updated October 7, 2026 · What changed

Who this calculator is for

This page is for investors summarising a holding, small-business owners describing revenue growth, students meeting the CAGR formula in a finance or economics course, and anyone who has to compare growth over periods of different length.

If you already know the rate and want to project forward, use the compound interest calculator. If you have only two values and no time dimension, the percentage change calculator is enough.

CAGR calculator

Compound annual growth rate: the steady yearly rate that turns the start value into the end value.

Start value

End value

Years between them

CAGR

9.86% / year

Total growth 60% over 5 years · simple average 12% / year

CAGR = (end ÷ start)^(1 ÷ years) − 1

Value each year at a constant CAGR
Year	Value at constant CAGR
0	10,000.00
1	10,985.61
2	12,068.35
3	13,257.82
4	14,564.51
5	16,000.00

Step-by-step for your numbers

Growth multiple = end ÷ start = 16,000.00 ÷ 10,000.00 = 1.6.
Take the 5th root (raise to 1 ÷ 5): 1.6^(1/5) = 1.09856.
Subtract 1 and multiply by 100: CAGR = 9.86% per year.
Compare: total growth is 60%, and simply dividing by 5 years gives 12% — higher than the CAGR because it ignores compounding.

Comparison table

CAGR for a given total growth and period
Total growth	3 years	5 years	10 years
25%	7.72%	4.56%	2.26%
50%	14.47%	8.45%	4.14%
100%	25.99%	14.87%	7.18%
200%	44.22%	24.57%	11.61%

Doubling (100% total growth) over 10 years is about 7.18% a year, not 10%.

About this cagr

The compound interest calculator on this site runs forward: you know a rate and want the future value. CAGR runs backwards: you know where something started and where it ended, and you want the steady yearly rate that connects them. It is the right summary for anything that compounds, because it is the one rate that, applied every year, reproduces the real end value exactly.

The page also prints the simple average (total growth divided by years) next to the CAGR on purpose. The gap between the two is the compounding effect, and seeing it for your own numbers is the quickest way to stop over-reading “we grew 60% in five years, so 12% a year.”

How to use each field

Start value: The value at the beginning of the period. Must be above zero — growth from zero has no rate.
End value: The value at the end. Use the same units and the same basis (both nominal, or both inflation-adjusted) as the start value.
Years between them: The length of the period, not the number of data points. From January 2020 to January 2025 is 5 years even though it spans six calendar years. Fractions are allowed: 18 months is 1.5.

When to use this calculator

You have a start value, an end value and a number of years, and you want one yearly growth figure to quote.
You want to compare two investments or businesses that ran over different lengths of time.
Someone quoted an average yearly return and you want to check whether it is the compounded rate or a simple average.

Worked examples

Example calculations for CAGR
Question	Answer
10,000 → 16,000 over 5 years	CAGR ≈ 9.86% / year
100 → 200 over 10 years	CAGR ≈ 7.18% / year
100 → 50 → 100 over 2 years	CAGR 0% (average of yearly returns says 25%)
10,000 → 12,000 over 3 years	CAGR ≈ 6.27% / year

Walkthroughs

An investment that fell and recovered

100 falls 50% to 50 in year one, then rises 100% back to 100 in year two. The average of the two yearly returns is (−50% + 100%) ÷ 2 = +25%. But you have exactly what you started with.

CAGR: (100 ÷ 100)^(1/2) − 1 = 0%. This is the classic example of why arithmetic averages of returns mislead, and why CAGR (a geometric average) is the honest summary.

Comparing two periods of different length

Business A grew revenue from 200,000 to 300,000 in 4 years. Business B grew from 200,000 to 350,000 in 7 years. B’s total growth (75%) beats A’s (50%), but per year A grew about 10.67% and B about 8.33%.

CAGR puts both on the same yearly footing. It still ignores how bumpy each path was, so pair it with the actual yearly figures when the decision matters.

Formula

Goal	Formula
CAGR	(end ÷ start)^(1 ÷ years) − 1
End value from CAGR	start × (1 + CAGR)^years
Total growth	(end ÷ start − 1) × 100

CAGR = (end ÷ start)^(1/years) − 1. For 10,000 growing to 16,000 in 5 years: 16,000 ÷ 10,000 = 1.6; 1.6^(1/5) ≈ 1.09856; subtract 1 → about 9.86% per year. Check: 10,000 × 1.09856^5 ≈ 16,000.

The simple average would be 60% ÷ 5 = 12% a year. Applying 12% for five years actually gives 10,000 × 1.12^5 ≈ 17,623, overshooting the real end value. That overshoot is why the simple average is the wrong number to quote for compounding growth.

The year-by-year table shows the smoothed path at the constant CAGR. It is not your real history — just the steady path that ends in the same place. It is shown only for whole numbers of years up to 30.

Mistakes this page will not catch for you

Treating CAGR as what happened each year

CAGR is a smoothed rate. The real path may have been +40%, −10%, +5%. Two investments with the same CAGR can have very different bumps along the way, and CAGR says nothing about that volatility.

Ignoring money added or withdrawn

If you added savings during the period, the end value includes your deposits, and the CAGR of the account balance overstates the return on the money. For accounts with contributions you need a money-weighted return (such as XIRR in a spreadsheet), which this page does not compute.

Comparing nominal and real figures

A price index or salary series that is not adjusted for inflation gives a nominal CAGR. To get a real growth rate, divide (1 + nominal CAGR) by (1 + average inflation) and subtract 1 — the inflation guide walks through this.

FAQ

What is the CAGR formula?: CAGR = (end value ÷ start value)^(1 ÷ years) − 1. Multiply by 100 for a percent.
Why is CAGR lower than total growth divided by years?: Because each year’s growth builds on the previous years’ growth. Dividing total growth by the number of years ignores that compounding, so it overstates the steady yearly rate.
Can CAGR be negative?: Yes. If the end value is below the start value, CAGR is negative. 1,000 falling to 800 over 2 years is about −10.56% per year.
What is the rule of 72?: A shortcut: 72 ÷ the yearly growth rate (in percent) ≈ years to double. At a CAGR of about 7.18%, 72 ÷ 7.18 ≈ 10 years, which matches 100 → 200 in 10 years. It is an approximation that works best for rates between roughly 4% and 12%.