Rule of 72 Calculator
A fast way to estimate how long it takes to double your money at a steady annual return, or what annual return you would need to double in a chosen number of years. See the classic 72 ÷ rate shortcut next to the exact compound-interest answer—useful for students, beginners, and back-of-the-envelope planning.
You have an annual return %; we estimate doubling time.
Rule of 72: years ≈ 72 ÷ R where R is the rate in percent per year (e.g. 8% → about 9 years).
Rule of 72 — years to double
9.00 yr
Exact (annual compounding)
9.01 yr
Absolute difference
0.01 yr
Rule of 72 vs exact (scale comparison)
Understanding the Rule of 72
Compound interest means you earn return on both principal and accumulated interest. Over time, money can grow faster than a straight line—the Rule of 72 compresses that idea into one easy relationship: for many common annual rates, the product of the rate (in percent) and the doubling time (in years) is close to 72. That is why years ≈ 72 ÷ rate and rate ≈ 72 ÷ years show up in textbooks, wealth apps, and introductory finance lessons.
Where the “72” comes from
Starting from (1 + r)t = 2, take natural logs: t = ln(2) / ln(1 + r). For small r, approximations link r × t to ln(2) ≈ 0.693, and scaling to whole-number percentages leads people to use 72 instead of 69.3 for easier mental math—especially because 72 has many divisors (2, 3, 4, 6, 8, 9, 12).
Quick examples (Rule of 72)
- 6% p.a. → 72 ÷ 6 ≈ 12 years to double.
- 8% p.a. → 72 ÷ 8 ≈ 9 years.
- Double in 10 years → 72 ÷ 10 ≈ 7.2% p.a. implied return.
Limits and real-world caveats
The rule assumes a steady rate and ignores taxes, fees, risk, and cash flows. Market returns bounce around; FD rates change. Treat the Rule of 72 as a conversation starter or classroom demo, then use detailed tools when you need precision—for example the compound interest calculator, CAGR calculator, or SIP calculator for rupee-level plans.
Formulas (summary)
- Rule of 72 (years): T72 ≈ 72 ÷ R, with R = annual rate in %.
- Rule of 72 (rate): R72 ≈ 72 ÷ T, with T = years to double.
- Exact years (annual compounding): t = ln(2) / ln(1 + r), r = R/100.
- Exact rate (annual compounding): r = 21/T − 1.
Other uses (inflation intuition)
Some guides use the same shortcut to illustrate how long until money loses half its purchasing power if prices rise steadily: roughly 72 ÷ inflation rate (as a percent). It is still a model, not a forecast. For rupee inflation scenarios on a lump sum, our inflation calculator is a direct complement.
Frequently asked questions
What is the Rule of 72?
The Rule of 72 is a mental shortcut for compound growth: if money grows at a fixed annual rate R% (as a percentage), the time in years to roughly double is about 72 ÷ R. You can also flip it: the rate % needed to double in T years is about 72 ÷ T. It is an estimate, not a substitute for exact compound-interest math.
How accurate is the Rule of 72?
It is usually closest for annual rates roughly between 6% and 10%. At very low or very high rates the error grows. This page shows both the Rule of 72 answer and the exact figure from annual compounding.
What is the exact formula for years to double?
For annual compounding, if the annual rate is r as a decimal (e.g. 8% → 0.08), the number of years t to double solves (1+r)^t = 2, so t = ln(2) / ln(1+r). The Rule of 72 approximates this in a form that is easy to do in your head.
Why is the number 72 used?
72 is a convenient composite number with many divisors, which makes mental division easy. Mathematically, ln(2) ≈ 0.693, and approximations tie rate × time near 0.72 for typical rates—scaled to percentage points, people use 72 in practice.
Can the Rule of 72 be used for inflation?
As a teaching analogy, some use 72 ÷ inflation rate to guess how many years until prices roughly double. That assumes a steady inflation rate and is still only a rough guide; real inflation varies by category and year.
Does the Rule of 72 include taxes and fees?
No. It works on a single stated rate. In real portfolios, taxes, expense ratios, and cash flows change outcomes—use a net or after-fee return if you want a planner-style estimate.
Is the ZeroKhata Rule of 72 calculator free?
Yes. It is free to use with no sign-up or payment.