Rule of 72 Calculator

• Instantly estimates doubling time at any growth rate — just divide 72 by the rate.
• Shows the precise compound-interest answer alongside the estimate, so you can see the gap.
• Also covers tripling (Rule of 114) and quadrupling (Rule of 144).
• Works the same way in reverse, to estimate how fast inflation halves purchasing power.

How to use this calculator

Enter a growth rate and, optionally, a starting amount to see the projected dollar values. The calculator returns the Rule of 72 estimate for doubling time, the precise answer from the actual compound-interest formula, and the same comparison for tripling and quadrupling.

Where the Rule of 72 comes from

The precise time to double an amount at a compounding rate r is:

years to double = ln(2) ÷ ln(1 + r)

For small rates, ln(1 + r) is closely approximated by r itself, and ln(2) ≈ 0.693. Multiplying 0.693 by 100 (to work with a percentage rather than a decimal) gives 69.3 — and 72 is used instead purely because it divides evenly by more small numbers (1, 2, 3, 4, 6, 8, 9, 12), making the mental arithmetic easier at the cost of a small amount of accuracy.

A worked example

At a 7% annual return, the Rule of 72 estimates 72 ÷ 7 ≈ 10.3 years to double. The precise compound-interest answer is about 10.24 years — the estimate is off by roughly two months, close enough for most planning purposes at this rate.

How accurate is it, really?

The Rule of 72 is most accurate in roughly the 4%–15% range, where the small-rate approximation behind it holds up well. Below that range or well above it, the gap between the quick estimate and the precise answer widens — still useful for a rough sense of scale, but worth switching to the precise figure (shown side by side here) once the exact number actually matters for a decision.

Other uses for the same trick

The same shortcut works for any multiple, using a different constant: divide by 114 instead of 72 to estimate tripling time, or 144 for quadrupling — both are simply the equivalent of ln(3) and ln(4) scaled the same way ln(2) was scaled to get 72.

It also works in reverse for a very different, less pleasant question: how fast inflation erodes purchasing power. Dividing 72 by an inflation rate estimates the number of years until money buys half as much — at 3% inflation, that's about 24 years; at 6%, about 12.

Common mistakes

Treating it as exact. It's a rounding shortcut built for mental math, not a precise formula — for anything with real money riding on the exact number, use the precise compound-interest calculation instead.

Applying it to a rate that isn't actually a steady compounding rate. The Rule of 72 assumes one consistent rate compounding the whole time — a volatile investment's average return over many years is not the same thing as a steady rate compounding smoothly, even if the arithmetic average looks similar.

Forgetting it works for inflation and fees too, not just growth. The same shortcut applies to anything that erodes value at a steady rate — inflation, and investment fees, both "double" their cumulative effect on the same kind of schedule.

Frequently asked questions