How long does it take your money to double? That single question drives almost every long-term financial decision — choosing between a savings account, a bond fund, or an index portfolio; judging whether a startup's growth rate is really explosive; even reading a headline that says "population growing at 2% per year." This doubling time calculator gives you the exact answer in years and months, alongside the popular Rule of 72 estimate, so you can sanity-check the math in seconds.
The exact formula is t = ln(2) / ln(effectiveFactor), where effectiveFactor depends on how often the growth compounds. With annual compounding effectiveFactor = 1 + r; with monthly compounding effectiveFactor = (1 + r/12)^12; with continuous compounding effectiveFactor = exp(r). The Rule of 72 shortcut — 72 divided by the percentage rate — is a close approximation that works best between about 4% and 15%. This calculator shows both, so you can see how far off the quick rule really is at any given rate, and how compounding frequency moves the exact answer.
How to Use
- Enter the Annual Growth Rate as a percentage. A savings account might earn 0.5%, a high-yield account 4–5%, a broad stock index 7–10% long-term, and a hot startup might claim 20% or more.
- Pick the Compounding Frequency from the dropdown — Annual (compounded once per year), Monthly (compounded 12 times per year), or Continuous (compounded infinitely often). The choice changes the effective annual growth factor and therefore the exact doubling time; more frequent compounding doubles your money faster.
- Optionally enter an Initial Amount. This is only used to display the dollar value you reach after one doubling; the doubling time itself does not depend on the starting number.
- Read the result card. Doubling Time is the exact figure in years; Doubling Time (months) converts it into whole months for easier planning.
- Compare the Rule of 72 Estimate against the exact number. At low rates the rule slightly overestimates; at high rates it slightly underestimates — usually within a few percent, which is why it has survived for over a century.
- Slide the growth rate upward. Notice that small changes near the low end barely move the doubling time, while a jump from 10% to 20% cuts it almost in half. That non-linearity is the most important intuition this tool gives you.
The Doubling Time Formula
When a quantity grows at a constant nominal rate r, the factor by which it grows in one year depends on how often that growth is compounded:
- Annual compounding: it grows by the factor (1 + r) each year.
- Monthly compounding: each month it grows by (1 + r/12), so over a full year it multiplies by (1 + r/12)^12.
- Continuous compounding: it grows by the factor exp(r) each year (the limit of compounding infinitely often).
We want that one-year factor raised to the power t to equal 2, the moment the original amount has doubled:
effectiveFactor^t = 2
Taking natural logarithms of both sides and solving for t gives:
t = ln(2) / ln(effectiveFactor)
Where ln(2) ≈ 0.6931. For example, at 7% per year with annual compounding, r = 0.07, effectiveFactor = 1.07, ln(1.07) ≈ 0.06766, and t ≈ 0.6931 / 0.06766 ≈ 10.24 years. With monthly compounding the effective factor is (1 + 0.07/12)^12 ≈ 1.0723, and t drops to about 9.93 years. With continuous compounding the effective factor is exp(0.07) ≈ 1.0725, and t ≈ 9.90 years. The Rule of 72 gives 72 / 7 = 10.29 years for all three — a quick estimate that ignores compounding frequency.
If the growth rate is zero or negative, the denominator ln(1 + r) becomes zero or undefined. A quantity that does not grow never doubles; a quantity that shrinks never doubles either. The calculator returns an error in those cases rather than a nonsense number.
Why the Rule of 72 Works
Because ln(2) ≈ 0.6931, the exact formula can be rewritten as t ≈ 0.6931 / r. Multiplying numerator and denominator by 100 turns r into a percentage, giving t ≈ 69.31 / (percent rate). That number 69.3 is awkward to divide by in your head, so financial writers settled on 72 — it is divisible by 2, 3, 4, 6, 8, 9, and 12, making mental arithmetic easy — and the tiny extra bias cancels out most of the error for typical interest rates between 6% and 10%. For rates outside that band, prefer the exact doubling time shown on this page.
Examples
Example 1 — The classic 7% portfolio. A broad S&P 500 index fund returning 7% per year, with a $100,000 starting balance. The exact doubling time is 10.24 years, or about 123 months. The Rule of 72 says 10.29 years. After one doubling the balance reaches $200,000; after two doublings — about 20.5 years — it reaches $400,000 without adding a cent of new money.
Example 2 — A $1,000,000 nest egg growing at 5%. At 5% annually the exact doubling time is 14.21 years (Rule of 72: 14.4 years). A $1,000,000 initial amount grows to $2,000,000 in just under 15 years. This is the math behind the common claim that a 5% real return turns a million into two million before retirement.
Example 3 — High-growth startup revenue. A SaaS company growing 20% per year doubles in only 3.80 years (Rule of 72: 3.60 years). At 30% growth the doubling time drops to roughly 2.64 years. Compare that to a 2% savings account, which needs about 35 years to double — the contrast explains why compound growth rates matter so much for early-stage investing.
Example 4 — A low-yield savings account. At 0.5% per year, doubling takes nearly 139 years. Slide the growth rate down to 0.5% on this page and watch the years column stretch past a century: this is the clearest possible illustration of why cash loses purchasing power to inflation even when it nominally "grows."
FAQ
How long does it take to double money at 7%?
At 7% annual compound growth, money doubles in approximately 10.24 years (about 123 months). The Rule of 72 gives a quick estimate of 10.29 years. This assumes the 7% return is reinvested annually and that the rate stays constant.
What is the Rule of 72?
The Rule of 72 is a mental shortcut: divide 72 by the percentage growth rate to get the approximate doubling time in years. For example, at 8% growth, 72 / 8 = 9 years. It is accurate to within about half a year for rates between 4% and 15%, and slightly overestimates at low rates while underestimating at high rates.
Does doubling time depend on the starting amount?
No. Doubling time depends only on the growth rate, not on whether you start with $100 or $1,000,000. A 7% return doubles $100 to $200 in the same 10.24 years it doubles $1,000,000 to $2,000,000. The initial amount input on this page is only used to show the dollar figure you reach.
What growth rate do I need to double in 5 years?
Rearranging the formula, you need roughly 14.39% annual compound growth to double in 5 years (because ln(2) / ln(1.1439) ≈ 5). The Rule of 72 gives a quick answer of 72 / 5 = 14.4%. Plug 14.4 into this calculator to confirm.
What if my growth rate is negative or zero?
A negative growth rate means the quantity is shrinking, not growing, so it will never double. A zero rate means the quantity stays flat forever. Both cases produce an error on this calculator rather than a meaningless number. Use this tool only for positive compound growth.
Is this calculator for investments or population growth too?
The math is identical for any quantity growing at a constant percentage rate: investments, GDP, population, bacterial cultures, social-media followers, or revenue. If something grows at r% per year, this calculator tells you how many years until it doubles.
How do I turn annual growth into monthly doubling time?
Multiply the doubling time in years by 12. For example, at 7% annual compounding, 10.24 years × 12 = 122.9 months. The result card shows this conversion directly.
Does compounding frequency change the doubling time?
Yes, and the effect is small but real. More frequent compounding raises the effective annual growth factor, so the money doubles sooner. At 7% nominal: annual compounding doubles in about 10.24 years, monthly in about 9.93 years, and continuous in about 9.90 years. The Rule of 72 estimate (10.29 years) is the same for all three, which is why it is only an approximation.
Disclaimer
This doubling time calculator is provided for informational purposes only and does not constitute financial, investment, tax, or legal advice. Results are based on constant annual compound growth and the inputs you enter; real investment returns are volatile, non-constant, and affected by fees, taxes, inflation, and market timing. Past growth rates do not guarantee future results. Always consult a qualified financial professional before making investment decisions.