The Rule of 72 Calculator runs the famous mental shortcut properly: enter a growth rate and it returns the Rule of 72 doubling estimate beside the exact compound-growth answer, the difference in days, an accuracy score, and a year-by-year growth schedule; or enter a target number of years and it returns the required rate both ways. An optional starting amount turns the schedule into real money.
How It Works
The rule divides 72 by the percentage rate to estimate doubling years. The exact answer comes from solving the compound-growth equation, years = ln(2) / ln(1 + r). The calculator shows both, quantifies the gap in days, and builds the growth table out to the doubling point (capped at 60 years), so the shortcut's error is something you can see rather than something a footnote admits.
Worked examples
At 8%, the rule says 9.0 years and the exact answer is 9.01 years, a difference of a few days: this is the rate region where the rule is nearly perfect. At 6%, the rule says 12.0 years against an exact 11.90, erring by about five weeks. At 24%, the rule says 3.0 years against an exact 3.22, erring by about eleven weeks: the rule underestimates doubling time at high rates and overestimates it at very low ones, crossing near-perfect accuracy around 8%. In reverse, doubling in 10 years needs 7.2% by the rule and 7.18% exactly.
Why 72 works at all
The honest constant for continuous compounding is about 69.3 (100 x ln 2). Seventy-two wins its place for two reasons: it corrects upward in the direction annual compounding needs at typical interest rates, and it divides cleanly by 2, 3, 4, 6, 8, 9, and 12, making mental arithmetic effortless. The same family gives the rule of 114 for tripling and 144 for quadrupling. Where precision matters, at rates far from 8% or over many doublings where errors compound too, the exact column in this calculator is the one to quote.
Uses beyond investing
Doubling logic applies to anything growing at a steady percentage: inflation halving purchasing power (at 4% inflation, money loses half its value in about 18 years by the inverted rule), population and user growth, debt balances growing when payments stall, and fee drag (a 2% annual fee halves your would-be terminal wealth relative to the no-fee path over about 36 years). The calculator's schedule makes the debt case vivid: run a credit-card rate through it and the doubling arrives in under four years, which is the whole argument for paying it first.
Limitations
The model assumes one constant compounded annual rate and no contributions, withdrawals, taxes, or fees beyond the rate you enter. Real returns vary year to year, and variable returns double money on a path the constant-rate formula only approximates (the CAGR page covers that distinction). Rates must be positive; a zero or negative rate never doubles anything.
Frequently Asked Questions
How accurate is the rule of 72?
Within a few percent of the exact answer across the 4 to 12% band where it is usually applied, best near 8%. The calculator quantifies the exact error for your rate in days and as an accuracy percentage.
Does the rule work for halving and decay?
Yes, symmetrically: at a steady -4% annual decline, value halves in about 72/4 = 18 years. It is the standard quick estimate for inflation's erosion of cash and for depreciation schedules.
Why not always use the exact formula?
In a spreadsheet, do. The rule survives because most doubling questions are asked away from one, in meetings and negotiations, where a two-second estimate that is 98% right beats a precise answer nobody computes.