Free · Doubling time · 72 ÷ rate

Rule of 72 calculator

The Rule of 72 estimates how long money doubles at a given return: years ≈ 72 ÷ rate. Works for stocks, savings, inflation, debt — any compounding rate.

Where Rule of 72 actually drifts · Snowballr exact-formula comparison vs 72/r approximation

Most accurate near 8% — error under 0.4 years

At 8% the rule gives 9.00 yrs vs exact 9.01 yrs. At 4% it overshoots by 0.3 yrs. At 20% it undershoots by 0.2 yrs. Below 2% and above 25%, switch to ln(2)/ln(1+r) for sub-month precision.

We pair the Rule of 72 estimate with the exact answer on every result so you can see the drift in real time instead of just trusting the shortcut.

Doubling time by rate

Annual rate	Rule of 72 estimate	Exact doubling time
2%	36.0 yrs	35.0 yrs
4%	18.0 yrs	17.7 yrs
6%	12.0 yrs	11.9 yrs
7%	10.3 yrs	10.2 yrs
8%	9.0 yrs	9.0 yrs
10%	7.2 yrs	7.3 yrs
12%	6.0 yrs	6.1 yrs
20%	3.6 yrs	3.8 yrs

Rule of 72 is most accurate near 8% — exact at lower or higher rates drifts slightly.

Practical Rule of 72 uses

Stocks at 10% nominal: double every ~7.2 years. $10k → $20k → $40k → $80k by year 21.6.
S&P 500 real (7%): double every ~10.3 years in purchasing power.
HYSA at 4.5%: double every ~16 years.
Inflation at 3%: prices double every ~24 years. Your $5 coffee becomes $10 by 2050.
Credit card debt at 22%: doubles in ~3.3 years if you pay nothing.

Why Rule of 72 works

To double: (1+r)^t = 2
                  t = ln(2) / ln(1+r)
                  t ≈ 0.693 / r  (for small r)
                  t ≈ 69.3 / rate%

72 is used instead of 69.3 because it's evenly divisible
by 1, 2, 3, 4, 6, 8, 9, 12 — convenient mental math.

Rule of 72 Calculator FAQ

What is the Rule of 72?

A mental-math shortcut for estimating doubling time: years to double ≈ 72 ÷ annual return rate. At 8% return, money doubles every 9 years. At 6%, every 12 years. Works for any compounding rate, in either direction (investments doubling, inflation eroding).

How accurate is the Rule of 72?

Within 1–2% for rates between 4% and 12%, where most real-world investments live. Less accurate at very low (1–2%) and very high (20%+) rates. For more precision: use ln(2) ÷ ln(1+r) = exact years to double.

Can I use the Rule of 72 for monthly compounding?

Use the effective annual rate. A 6% APR compounded monthly = 6.17% APY → ~11.7 years to double. If you use the nominal 6%, you'd get 12 years — close enough for mental math but the APY version is technically correct.

Does the Rule of 72 work for inflation?

Yes — and it's depressing. At 3% inflation, prices double in 24 years. At 4%, in 18 years. Same math, opposite direction: your $100 today buys what $50 buys in 24 years if inflation runs at 3%.

What's the Rule of 70 or Rule of 69?

Alternative approximations. Rule of 69 (or 69.3) is exact for continuous compounding. Rule of 70 is sometimes used for higher precision at moderate rates. Rule of 72 dominates because 72 has many factors — easier to divide mentally.

How do I use the Rule of 72 in real life?

Quick sanity checks. 'My HYSA pays 4.5% — money doubles in 16 years.' 'Stocks should double in 7 years at historical 10%.' 'My 22% credit card balance will double if I ignore it for 3.3 years.' Useful for fast intuition without a calculator.

Related calculators

Compound interest calculator

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S&P 500 calculator

Doubling at 10% historical.

Inflation calculator

Doubling of prices over time.

Rule of 72 deep-dive

Full theory and examples.

Methodology, sources, and editorial standards

The rule of 72 calculator on this page uses the same closed-form math published by the U.S. Securities and Exchange Commission's consumer-investor portal at Investor.gov and the Consumer Financial Protection Bureau. Every number you see is generated client-side in your browser — no data is sent to our servers, no account is required, and no personally identifiable information is stored or shared. The calculation assumes constant rates and contributions over the modeled period; real-world returns, fees, and tax treatment vary year to year, and the figures presented are educational projections, not personalized financial advice.

We cite primary data sources directly within the FAQs and snapshot block above. Historical return assumptions are drawn from NYU Stern's historical returns database (Aswath Damodaran) and Robert Shiller's S&P 500 dataset. Inflation comparisons rely on the Bureau of Labor Statistics CPI series. Mortgage and credit-card market data come from Freddie Mac's PMMS and the Federal Reserve's G.19 release, respectively. Where we publish our own multi-scenario research, the dataset is available under a Creative Commons CC-BY 4.0 license at snowballr.io/data.

Snowballr is an independent, ad-supported publication. We do not sell financial products, accept affiliate commissions on bank, brokerage, or loan products, or take payment for editorial placement. Our editorial standards describe how we source, fact-check, and update every calculator and guide. The full master sources index lists every primary reference used across the site, organized by topic. For corrections, updates, or fact-checking inquiries, contact us via the contact page; we typically respond within 24–48 hours.

Important disclaimer: This calculator is provided for educational purposes only. It does not constitute investment, tax, accounting, legal, or financial-planning advice and should not be used as the sole basis for any decision about your money. Compound projections, debt-payoff schedules, and retirement estimates depend on assumptions that will change in real life — investment returns are not guaranteed, market downturns can extend recovery timelines, fees and taxes reduce realized growth, and inflation erodes the real purchasing power of nominal balances. Before making a financial decision based on any number you calculate here, consult a fiduciary financial advisor, a licensed tax professional, or both, as appropriate to your situation. Past performance does not guarantee future results.

Who uses this calculator

The rule of 72 calculator is used by three distinct audiences, each for a different question. New investors and savers use it to answer the foundational "what could this become?" question — they enter conservative monthly amounts and realistic return assumptions to see whether building meaningful wealth on a normal salary is actually possible. The answer, for almost every income level, is yes; the math just requires patience and consistency that intuition resists. Mid-career professionals use the same tool to stress-test their retirement plan against catch-up contributions, late-career raises, and the trade-off between paying down debt and investing in tax-advantaged accounts.

Pre-retirees and recent retirees use the calculator to validate withdrawal sustainability and to model what happens if a market downturn coincides with the start of retirement. Educators, financial coaches, and personal-finance bloggers use Snowballr's calculators in their teaching because every input is visible, every formula is documented, and the year-by-year breakdown lets learners see exactly where compounding pulls ahead of contributions. We support that use case explicitly under our Creative Commons license — you can embed any calculator on your own site using the snippet generator at /widgets and cite Snowballr per the citation guide.

Common assumptions and how to interpret the numbers

The output is only as accurate as the inputs and the assumptions that bridge them to real life. Three categories of assumption deserve the most scrutiny. Returns are nominal unless explicitly labeled real (inflation-adjusted); a seven-percent nominal return is closer to four-percent real, which materially changes long-horizon projections. Inflation itself averaged just under three percent in the U.S. from 1928 through 2024 but ran above five percent in roughly fifteen of those years and below zero in three. Average expense ratios for index funds dropped from roughly one-and-a-half percent in 2000 to under a tenth of a percent today, but actively managed mutual funds still average about half a percent — which translates to a quarter of the final balance lost to fees over a thirty-year horizon at typical contribution rates.

Taxes affect both contributions and withdrawals in ways the headline number does not show. Pre-tax contributions in a traditional 401(k) or IRA receive a deduction today but trigger ordinary income tax on withdrawal. Roth contributions are post-tax today but grow and withdraw tax-free. Taxable brokerage accounts pay tax annually on dividends and at sale on capital gains. If you are comparing projected balances across account types, equalize by reducing pre-tax balances by your expected retirement tax rate and adding back the dividend drag on the taxable account; otherwise the comparison is misleading. Our 401(k) vs Roth IRA comparison walks through this explicitly with worked examples at three tax-bracket scenarios.

For inputs you are uncertain about, run the calculator twice with a high and a low value to see how sensitive the answer is to your assumption. If a two-percent rate change moves the final balance by less than ten percent, the assumption is not very load-bearing. If it moves the balance by forty percent or more, that input dominates the model and deserves the most careful estimation. The single highest-leverage input in almost every compound-interest scenario is time — every additional year compounds geometrically — followed by rate, then contribution, then starting principal in roughly that order.