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Rule of 72 calculator
The Rule of 72 estimates the time to double at a nominal annual % or the % p.a. needed to double in a given number of years. This page shows the 72 shortcut next to a single exact line (annual compounding) and Sheets/Excel copy patterns. For full schedules, contributions, and more than one compounding model, use the compound interest calculator (link in the methodology).
When to use this calculator
Fast “how long to double” and implied return mental math for classes, memos, and back-of-the-envelope spreadsheet checks before you build a full model.
- Classroom or self-study: see 72 ÷ rate vs the log-based time for a single annual compounding story.
- Sanity-check fund or savings stories that quote a long-run % and a doubling time claim.
- Copy a
LOG(2)/LOG(1+rate)or72/…line into Sheets or Excel and match this page for the same assumptions. - Move to the compound interest tool when you need balances, deposits, and multiple compounding options.
The Rule of 72 is the shortcut R × t ≈ 72 when R is a % per period and t is periods in the same unit (commonly years). It comes from a log linearization of compounding. We show both t ≈ 72 / R and, for a single annual compounding line, the closed-form time t* = ln(2) / ln(1 + r) with r = R/100.
Rule: solve for time or for %
Years to double (given %): t ≈ 72 / R where R is a simple % per year (not an APR/FEE quote). Implied % (given years): R ≈ 72 / t.
Exact (annual compounding) benchmark
With one compounding per year, doubling is the t that satisfies (1 + r) to the power t = 2, so t* = ln(2) / ln(1 + r). The implied nominal % to double in t years is (2^{1/t} − 1) × 100 .
What is out of scope here
We do not add monthly 401(k) or day-count bond conventions in v1; we keep one annual story so the page stays fast. For more cash-flow and frequency control, go to a full compound model.
The exact row is a teaching benchmark, not a guarantee; real paths have contributions, fees, and changing rates—model those in a spreadsheet or your advisor’s tools.
To project balances, contributions, and different compounding cadences, open the compound interest calculator next.
Google Sheets & Excel
English US/UK function names below. The Rule of 72 in a cell is as simple as =72/…; the exact time uses the natural log ratio (same as below). Replace the cell references (for example B2) with your own rate in decimal in the LOG pattern.
=72/B2Put the simple annual % (for example 8 for 8% ) in B2. Result is a heuristic number of years, not a bank schedule.
=LOG(2)/LOG(1+B2)Put the per-year rate as a decimal in B2 (for 8% use 0.08). Matches the exact years row on this page for annual compounding only.
=(2^(1/B2)-1)B2 = years to double. The cell is a decimal; multiply by 100 in another cell if you want a percent display. Same identity as the exact % row here.
Frequently asked questions
What is the Rule of 72?
A quick heuristic for compounding: roughly R × t ≈ 72 when R is a percent per year in the same time unit as t (for example both in years). It answers “about how long to double at R?” and “about what R to double in t?”.
What is the math behind “72 ÷ rate” and “72 ÷ years”?
From the shortcut R × t ≈ 72, you solve t ≈ 72 / R to estimate years to double, or R ≈ 72 / t to estimate the % to double in t years. The % in the rule is a simple per-year teaching rate (see APY FAQ for contrast).
Why the number 72 and not 70 or 69?
72 is easy to divide mentally (many small divisors) and happens to be a good middle ground for a common r and t line-up around many % in teaching. You may see 69.3 or other variants—same idea, different accuracy tradeoff.
Is the Rule of 72 “accurate”?
It is an approximation—it is often decent for yearly % in a mid range, and can miss more at very high or very low % . Always compare the 72 result with the exact (annual compounding) line (or a full model) for anything material.
What is the “exact (annual compounding)” row?
We assume one compound of the stated yearly rate: doubling time is t* = ln(2) / ln(1 + r) with r = R/100; the implied R for a fixed t is (2^{1/t}−1) × 100 . It is a close-form line so you can match Sheets/Excel without a rule-of-thumb error.
Is this the same as APY from a bank or fund?
Not always. A stated APY (annual percentage yield) already reflects compounding inside that yield figure. The rule line here uses a simple % per year story for the heuristic—see your statement’s definitions, or the exact line with an explicit compounding model when in doubt.
What about “Rule of 72 / monthly” searches?
The classic 72 line is in annual % and years. If interest is credited monthly or daily, the time to double for the same nominal label changes—our v1 exact line keeps one annual benchmark so the page does not add multiple pickers. Use a full compound calculator to layer m>1 in production models.
How do I do this in Excel or Google Sheets (English names)?
Rule: =72/B2 with % as a number in B2 (8 for 8% ). Exact years with r in decimal in B2 (0.08): =LN(2)/LN(1+B2) in U.S. Excel and Sheets—see the copy cards. Implied return as a decimal: =(2^(1/B2)-1); format the cell as % for a percent display. In non-English Excel, find LN in your language pack via Formulas → Insert function.
When should I use the compound interest calculator instead?
Use the compound interest tool for ending balance, monthly contributions, daily vs monthly compounding, and longer schedules—it is a cash-flow engine. This page is doubling and hurdle-rate intuition only, with one annual compounding line for a reality check on the 72 rule.
Does the rule include inflation or “real” returns?
Not by default. The % and t you enter are nominal math in this teaching setup. A “real” (inflation-adjusted) story needs its own model—treat the lines here as a stylized compounding check, not a macro forecast.
Is this a stand-in for a retirement, tax, or advisor plan (401(k), PER, etc.)?
No. It is a teaching calculator. Government benefits, workplace plans, taxes, and jurisdiction rules are out of scope; use official portals and qualified professionals for decisions with money on the line.
Is this financial or tax advice?
No. It is educational and illustration-only. Outcomes in real portfolios and loans include fees, taxes, and timing that this page does not model—verify material choices with a licensed advisor or tax pro when you need to.