Rule of 72 — Doubling Time Calculator
Estimate how long it takes for an investment or balance to double at a given annual return rate. Compare the Rule of 72 shortcut against the exact compound-interest answer side-by-side.
Years to double (Rule of 72)
10.3 years
Years to double (exact compound math)
10.2 years
Rule of 72 over/undershoot
0.0 years
Balance when doubled
$20,000
Years to triple (exact)
16.2 years
Years to quadruple (exact)
20.5 years
Balance Growth — Watching Your Money Double
How to read your result
The 'Years to double (Rule of 72)' is the simple shortcut — divide 72 by your annual rate (as a whole number, not decimal). At 7%, the rule says 72 / 7 ≈ 10.3 years. The number is meant to be done in your head; it's a check, not a forecast.
The 'Years to double (exact compound math)' is the textbook answer: log(2) divided by log(1 + rate). It assumes annual compounding. For most retail rates between 4% and 12%, the rule's estimate is within a few months of this exact answer — close enough to use as a reasonableness check.
'Rule of 72 over/undershoot' is the gap between the two, in years. It's positive when the rule overshoots (says more years than reality) and negative when it undershoots. The gap stays small near 8% — that's by design — and grows at very low or very high rates.
The chart shows the actual balance growing year over year, with a horizontal green line at twice your starting balance. The first time the blue curve crosses the green line is the exact doubling year — usually a fraction of a year off from the Rule of 72 estimate.
When to use this tool
- ›Doing fast 'is this rate good?' math without a calculator — for example, sizing whether a HYSA at 4.5% will double a savings cushion in your time horizon.
- ›Sanity-checking a long-term retirement projection. If a fund manager promises 'doubles every five years,' the Rule of 72 implies a sustained 14.4% return — high enough to deserve scrutiny.
- ›Teaching compound interest intuitively. The rule is the cleanest way to internalize that the math is exponential — small rate differences become big at longer horizons.
- ›Comparing inflation against your savings rate. If inflation is 3% and your HYSA pays 5%, the gap is 2% — a doubling time of about 36 years for real purchasing power, much slower than the nominal doubling time.
Methodology
The Rule of 72 is an arithmetic shortcut that approximates the exact doubling time for an annually-compounded investment. The exact formula is years = log(2) / log(1 + r), where r is the rate as a decimal. Setting this expression equal to 72/r% and solving algebraically shows the rule is exact only near a specific rate (~7.85%); elsewhere it has a small but predictable error.
We compute the exact answer using natural logarithm — JavaScript's Math.log — so the result reflects standard annual compounding. The chart series uses balance = principal × (1 + r)^year, the same compounding model. Continuous compounding (e^(rt)) would change the exact answer by a few weeks at typical rates and is not used here.
The doubled-balance threshold is just twice the principal — it does not adjust for inflation. To translate this into real (inflation-adjusted) doubling time, use the Inflation-Adjusted Real Return tool to find your real rate, then plug that rate back into this calculator.
Limits we acknowledge: the rule assumes a constant rate over the full horizon. Real-world returns fluctuate year to year, so the doubling time you actually experience may be shorter or longer than either number reported here. Use this tool for back-of-envelope work, not for retirement planning.
Site-wide methodology framework: /methodology/ · Pre-publication standards: /editorial-standards/
FAQ
Why 72 specifically and not 70 or 75?
Because 72 has an unusual number of small integer divisors — 1, 2, 3, 4, 6, 8, 9, 12 — which makes the mental math fast for the rates that matter most (3%, 4%, 6%, 8%, 9%, 12%). Mathematically, the 'true' constant for the rule is about 69.3 (which equals 100 × log(2)), so the Rule of 70 is slightly more accurate at very low rates. For the 5–12% range that retail investors actually see, 72 is the better-fitting whole number.
How accurate is the Rule of 72?
Within about 2% relative error across rates from 1% to 20%. At 8% it is essentially exact (the rule says 9 years; the exact answer is 9.006 years). At 2% the rule says 36 years; the exact answer is 35.0 — about a year short. At 20% the rule says 3.6 years; exact is 3.8 — about two months long. For practical decisions, the gap rarely changes the answer.
Does the rule work for inflation or debt as well?
Yes — it works for any compounding rate, positive or negative. At 3% inflation, your purchasing power halves in roughly 72/3 = 24 years. At a 22% credit-card APR, an unpaid balance doubles in about 72/22 ≈ 3.3 years. The rule does not care whether the rate is helping you or hurting you.
Why does my actual investment balance not double exactly when the rule predicts?
Three reasons. (1) Real returns are volatile, not a smooth fixed rate. (2) Most products compound more frequently than annually — daily, monthly — which slightly accelerates doubling and the rule does not adjust for this. (3) Fees, taxes, and contributions or withdrawals all change the trajectory. The Rule of 72 answers a clean theoretical question; reality is messier.
What is the Rule of 114 or Rule of 144?
The same idea applied to tripling and quadrupling. 114 / rate ≈ years to triple (because 114 ≈ 100 × log(3)). 144 / rate ≈ years to quadruple (which is also exactly twice the doubling time). This calculator shows the exact tripling and quadrupling years using the log formula so you can see how close the Rule of 114 / 144 estimate would be.
When does this tool become misleading?
When the rate is far outside the 1–20% range, when contributions or withdrawals are significant compared to principal, or when the time horizon is short enough that fees and taxes dominate the math. For long-term retirement and savings planning, layer this insight onto the Compound Interest and Inflation-Adjusted Real Return tools rather than relying on the Rule of 72 alone.