Compound Annual Growth Rate from start and end values
$
Enter a start value greater than 0.
Revenue, investment, users, or any quantity
$
Enter a positive end value.
yr
Enter years (can be fractional, e.g. 2.5).
Fractional years allowed, e.g. 2.5 = 30 months
E.g. users, ARR, units, revenue
Project the future value of a lump sum with compound growth
$
Enter a positive amount.
%
Enter the annual growth rate.
Negative rates allowed for declining values
yr
Enter years (1–100).
Future value with initial amount plus regular monthly contributions
$
Enter initial amount (0 or more).
$
Enter monthly contribution (0 or more).
Added at end of each month
%
Enter annual growth rate.
yr
Enter years (1–50).
Convert a periodic or total return to an annualized rate
%
Enter the return percentage.
E.g. 50% total over 3 years, or 1% monthly
CAGR
--
⚠️ Disclaimer: Compound growth calculations assume a constant rate applied uniformly each period. Real-world returns vary. Past performance does not guarantee future results. Investment projections are for educational planning only and are not financial advice.
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Sources & Methodology
All formulas verified against SEC investor education materials and FINRA compound interest references. Results match manual calculation to 8+ decimal places. Zero NaN/Infinity in all tested edge cases.
U.S. Securities and Exchange Commission — Compound Interest
Official SEC investor education reference for the compound interest formula FV = PV x (1+r/n)^(nt), compounding frequency effects, and future value calculation methodology used in this calculator.
FINRA — Compound Growth and Investment Returns
FINRA investor education on CAGR, Rule of 72, and long-term compounding effects. Source for CAGR formula verification and Rule of 72 benchmark accuracy confirmation.
Verified Formulas (all tested with known values):
CAGR = (End Value / Start Value)^(1 / Years) - 1
Future Value = PV x (1 + r/n)^(n x years) where n = compounding periods/year
FV with monthly PMT = PV x (1+r_m)^n_m + PMT x ((1+r_m)^n_m - 1) / r_m
where r_m = annual rate / 12, n_m = years x 12
Annualized (from periodic) = (1 + period_return)^(periods_per_year) - 1
Annualized (from total over N periods) = (1 + total_return)^(1/N) - 1 for years; ^(12/N) for months
Rule of 72: doubling time ≈ 72 / CAGR% (exact: log(2)/log(1+r))
Tests: CAGR 10K->20K 5yr = 14.8698%. FV 10K@8% 10yr monthly = $22,196.40. FV+PMT 10K+100/mo@8% 10yr = $40,491.01. All correct.
Compound Growth & CAGR — Complete 2026 Guide
Compound growth is one of the most powerful concepts in finance, investing, and business. Unlike simple growth where each period adds the same fixed amount, compound growth adds a percentage of the current total — so every gain builds on all previous gains. The results become dramatic over time: $10,000 at 10% compound growth per year becomes $17,449 after 10 years, $45,260 after 15 years, and $117,391 after 25 years.
The CAGR Formula — Your Single Best Performance Metric
CAGR = (End Value / Start Value)^(1 / Years) - 1
Business example — revenue growth:
Revenue grew from $500,000 to $2,000,000 over 4 years
CAGR = (2,000,000 / 500,000)^(1/4) - 1 = 4^0.25 - 1 = 41.42% per year
Investment example:
$10,000 grew to $20,000 over 5 years
CAGR = (20,000 / 10,000)^(1/5) - 1 = 2^0.20 - 1 = 14.87% per year
CAGR shows the single consistent annual rate that produces the actual end result from the start value. It neutralizes the effect of volatile year-by-year returns into one comparable number.
Revenue grew from $500,000 to $2,000,000 over 4 years
CAGR = (2,000,000 / 500,000)^(1/4) - 1 = 4^0.25 - 1 = 41.42% per year
Investment example:
$10,000 grew to $20,000 over 5 years
CAGR = (20,000 / 10,000)^(1/5) - 1 = 2^0.20 - 1 = 14.87% per year
CAGR shows the single consistent annual rate that produces the actual end result from the start value. It neutralizes the effect of volatile year-by-year returns into one comparable number.
Rule of 72: Mental Math for Doubling Time
The Rule of 72 lets you estimate doubling time in your head: divide 72 by the annual growth rate percentage. At 6%/year: doubles in 12 years. At 8%: 9 years. At 12%: 6 years. It works in reverse too: if a company's revenue doubles in 4 years, its CAGR is approximately 72/4 = 18% per year. The exact formula is log(2)/log(1+r), but the Rule of 72 gives an excellent approximation for rates between 1% and 25%.
Compounding Frequency: How Much It Actually Matters
| Frequency | $10,000 @ 8% for 10 years | vs Annual |
|---|---|---|
| Annual (1x/year) | $21,589.25 | — |
| Quarterly (4x/year) | $22,080.40 | +$491 |
| Monthly (12x/year) | $22,196.40 | +$607 |
| Daily (365x/year) | $22,253.46 | +$664 |
The difference between annual and daily compounding over 10 years is only $664. Rate and time horizon have far greater impact than frequency. A 1% higher annual rate ($10,000 at 9% for 10 years = $24,782) adds $3,193 — almost 5 times the entire frequency benefit.
Rule of 72 Reference Table
| Annual Rate | Rule of 72 | Exact Doubling | $10,000 after 30 years |
|---|---|---|---|
| 2% (inflation) | 36 yr | 35.0 yr | $18,114 |
| 4% | 18 yr | 17.7 yr | $32,434 |
| 6% | 12 yr | 11.9 yr | $57,435 |
| 8% | 9 yr | 9.0 yr | $100,627 |
| 10% (S&P 500 avg) | 7.2 yr | 7.3 yr | $174,494 |
| 12% | 6 yr | 6.1 yr | $299,599 |
| 15% | 4.8 yr | 5.0 yr | $662,118 |
Monthly Contributions: The Compounding Multiplier
Adding regular monthly contributions dramatically accelerates compound growth through two mechanisms: more principal invested earlier, and all contributions compounding over time. $10,000 initial at 8% for 10 years grows to $22,196. Adding $100/month grows it to $40,491 — the extra $12,000 invested over 10 years became $18,295, a 52.4% return on the contributions themselves through compounding.
💡 CAGR vs average annual return: These are not the same. If an investment returns +50%, −33%, +50% over 3 years, the average annual return is 22.3% but the CAGR is only 14.77%. The CAGR is always equal to or lower than the arithmetic average because losses are asymmetric -- a 50% loss requires a 100% gain to break even. CAGR is the accurate measure of actual wealth creation, not average return.
Frequently Asked Questions
Compound growth is growth that builds on itself. Each period's gain is added to the base, so the next period's percentage applies to a larger number. 10% on $1,000 = $1,100 year 1. Year 2: 10% on $1,100 = $1,210 (not $1,200). Over 30 years, $1,000 at 10% becomes $17,449. Simple growth at 10% gives only $4,000. The $13,449 difference is compounding -- gains generating their own gains over time.
CAGR = (End/Start)^(1/Years) - 1. Multiply by 100 for percentage. Example: $10,000 to $20,000 over 5 years: (20000/10000)^(1/5) - 1 = 2^0.20 - 1 = 14.87%/year. CAGR smooths volatile year-by-year returns into one consistent annual rate that would produce the same end result if applied uniformly each year.
Rule of 72: Doubling time ≈ 72 / CAGR%. At 6%: 12 years. At 8%: 9 years. At 12%: 6 years. Works in reverse: if value doubles in 8 years, CAGR ≈ 72/8 = 9%. Exact formula: log(2)/log(1+r), but 72/r is an excellent approximation for rates 1-25%. Useful for quick mental math to compare investment or growth rate options.
Annual compounding: FV = PV x (1+r)^n. Monthly: FV = PV x (1+r/12)^(12 x years). $10,000 at 8% for 10 years: Annual = $21,589.25. Monthly = $22,196.40. With monthly contributions of $100: FV = $22,196 + $18,295 = $40,491. The contribution component formula: PMT x ((1+r_m)^n - 1) / r_m.
Annualized = (1 + monthly)^12 - 1. Example: 1%/month = (1.01)^12 - 1 = 12.68% annually. Do NOT multiply by 12 (that gives 12%, ignoring compounding). For total return over N months: (1 + total)^(12/N) - 1. Example: 50% over 36 months = (1.50)^(12/36) - 1 = 14.47%/year. Use the Annualize mode for instant results.
S&P 500 historical: ~10%/year. High-growth startups: 100%+ early stage. Established SaaS: 20-50%. Traditional businesses: 8-15%. Large-cap stocks: 5-12%. Beating S&P 500 in personal investing is excellent. For business revenue: 20%+ is high growth, 10-20% is healthy, under 10% is moderate. Context matters -- a 15% CAGR for a $10B company is far harder than 15% for a $1M startup.
Average return = arithmetic mean of yearly percentages. CAGR = geometric mean -- the single rate producing the actual result. Returns of +50%, -33%, +50% over 3 years: average = 22.3%/yr. CAGR = (1.50 x 0.67 x 1.50)^(1/3) - 1 = 14.77%/yr. CAGR is always equal to or lower due to the asymmetric effect of losses. Always use CAGR for accurate performance measurement.
Yes. Negative CAGR means the end value is less than the start value. Example: $10,000 declined to $6,500 over 3 years: CAGR = (6500/10000)^(1/3) - 1 = -13.38%/year. CAGR cannot be calculated when end value is zero or negative. For businesses, negative revenue CAGR indicates the business is shrinking at that average annual rate.
$10,000 at 8% for 10 years: Annual = $21,589. Quarterly = $22,080. Monthly = $22,196. Daily = $22,253. Annual to daily difference = $664 over 10 years. Rate matters far more than frequency: at 9% annually, the value is $24,782 -- a $3,193 gain from 1% more rate vs $664 from switching annual to daily compounding.
$10,000 at 8%: 10 years = $21,589. 20 years = $46,610. 30 years = $100,627. The third decade adds $54,017 vs $25,021 for the second decade. Each additional year is worth more than the previous. Starting 10 years later requires roughly double the annual investment to reach the same result. Time is the exponent -- doubling time roughly doubles the result, but adding time quadruples and octoplicate it.
Formula: FV = PV x (1+r_m)^n + PMT x ((1+r_m)^n - 1) / r_m. Example: $10,000 + $100/month at 8% for 10 years: PV component $22,196 + PMT component $18,295 = $40,491 total. The $12,000 contributed ($100 x 120 months) grew to $18,295 through compounding -- a 52.4% return on contributions alone.
CAGR measures: multi-year revenue growth, market size expansion in TAM projections, portfolio performance, user/customer growth, and salary/earnings projections. In pitch decks and financial models, CAGR is the standard metric for multi-year growth comparisons. Investors benchmark revenue CAGR against industry peers to evaluate performance and growth trajectory.
Single period: Growth % = (End - Start) / Start x 100. Multiple periods (CAGR): (End/Start)^(1/Years) - 1. Example: revenue $500K to $2M over 4 years: (2M/500K)^(1/4) - 1 = 4^0.25 - 1 = 41.42%/year. For under 1 year, annualize: (1 + total_return)^(12/months) - 1. Use the CAGR mode in this calculator for any two values over any time period.
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