Rule of 72 calculator

What the Rule of 72 is

The Rule of 72 is a mental-math shortcut for estimating how long it takes an amount to double at a given annual rate of return: divide 72 by the rate. At 8% annual growth, money doubles in about 72 / 8 = 9 years. No calculator required — just division most people can do in their head.

Why it works

The exact doubling time for compound interest is ln(2) / ln(1 + r), where r is the rate as a decimal. For small r, ln(1 + r) is very close to r itself, and ln(2) ≈ 0.693 — so the exact formula is approximately 0.693 / r. Multiplying both the numerator and the rate by 100 (to work in whole percentage points instead of a decimal) turns 0.693 into 69.3. The Rule of 72 rounds that up to 72 because 72 divides evenly by more small numbers (2, 3, 4, 6, 8, 9, 12), making the mental math even easier — at a small cost in accuracy.

Where it's accurate

The approximation is closest in the roughly 6–10% range, which is also where 72 happens to split most evenly against typical interest rates. Below that range, and especially above it, the gap between ln(1 + r) and r widens, and the Rule of 72 increasingly over- or understates the true doubling time. The calculator below shows the exact answer alongside the approximation for any rate, and the optional chart overlay makes the growing gap visible at the extremes.

Where you'd actually use this

• Sizing up retirement savings. If a 401(k) averages 7% a year, it roughly doubles every ~10 years — a fast way to picture where a balance is headed decades out.
• Comparing accounts at a glance. A savings account at 2% doubles in 36 years; an investment account at 8% doubles in 9. No spreadsheet needed to see which is doing the work.
• Gut-checking debt. The same math runs in reverse: a credit card sitting at 24% APR effectively doubles what you owe in about 3 years if it's never paid down.
• Sanity-checking a pitch. If someone promises your money will double in 3 years, that's implying roughly a 24% annual return — worth asking what's supposed to produce that.