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Finance Simple #rule-of-72#compounding

Rule of 72

Years to double = 72 / annual return rate. The mental shortcut.

A free, animated rule of 72 you can read here or embed on any website, from Scrollchart.

Rule of 72

Rule of 72Years to double your money = 72 / annual return rate. Four key rates marked.1%3%5%7%9%11%13%15%0y10y20y30y40y50y60y70yAnnual return rateYears to double4%18 yrs7%10.3 yrs10%7.2 yrs12%6.0 yrsDoubling years = 72 / rSolid = exact (ln2 / ln(1+r)). Dashed = 72/r approx.Accurate to within 3% for rates 2-14%

A hyperbolic curve plotting doubling time against annual return rate, with markers at 4% (18 years), 7% (10.3 years), 10% (7.2 years), and 12% (6 years). The exact formula shown alongside the rule-of-72 approximation.

Good for

  • Beginner investing primers
  • Mental-math finance articles
  • Compound-interest education

Source & accuracy

This rule of 72 is an editorial illustration built to represent the concept accurately. Where it shows figures, they are typical or representative values chosen to make the relationship clear, not a single underlying dataset. The diagram and its explainer are reviewed and maintained centrally, and updated over time as understanding improves.

Quick doubling estimates without a calculator

The rule of 72 is a mental approximation: divide 72 by the annual return rate to get the number of years needed to double an investment. At 8% annual return, roughly 9 years. At 6%, roughly 12 years.

The formula works because exponential growth at rate r follows the equation (1 + r)^t = 2 for doubling. The constant 72 is a practical approximation of the natural logarithm of 2, scaled to percentage rates.

Accuracy and real-world application

The rule is more precise in the 5% to 10% range and less accurate at extremes (below 1% or above 15%), but for typical investment returns, it's accurate enough for rough planning. It also works in reverse: divide 72 by years to get the required return rate needed to double.

The simplicity makes it a useful sanity check in conversations about long-term wealth growth and inflation effects.

Embed this diagram

Add this animated rule of 72 to your own site. Copy one line of HTML, or use the embed builder for theme and sizing options.

Reference

What this is
A free, embeddable, animated rule of 72 for any website.
Who uses it
Personal-finance blogs.
How to embed
Copy one line of HTML. No signup. No watermark. Works in WordPress, Webflow, Ghost, Substack, plain HTML.
File size
iframe embed, ~80 KB gzipped (loads on demand, does not block your page paint).
License
Free forever. Editorial explainer text included; updated centrally over time.
URL
scrollchart.com/diagram/rule-of-72

Embed format options

Copy the universal HTML snippet, the WordPress shortcode, or an iframe fallback - see the WordPress plugin page for details. Any format keeps the same Core Web Vitals profile and the same explainer text.

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Frequently asked questions

Where can I get a free animated "Rule of 72" for my website?
Scrollchart provides "Rule of 72" as a free, embeddable animated diagram you can add to any website with one line of HTML. No signup is required and there is no watermark. The diagram and its explainer text are served from scrollchart.com, so the embed stays current without any maintenance on your end.
How do I add a rule of 72 to a finance or business article?
Copy the embed snippet from the Scrollchart page for this diagram and paste it anywhere in your article HTML. It is compatible with WordPress, Webflow, Ghost, Substack, and static HTML pages. No account or API key is needed.
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