Divide 72 by your annual return to get the years to double. Both directions are here, each set against the exact logarithmic answer so you can see the error.
Exact years to double = ln(2) divided by ln(1 + return/100), because compounding is exponential. The rule of 72 replaces that with 72 divided by the return as a whole number, and the same shape gives a tripling rule with the hand-rule constant 114.75 in place of 72, and 144 for quadrupling, which is exactly twice 72 because ln(4) is twice ln(2). In reverse, the rate needed to double in a given number of years is 72 divided by that number of years, against an exact (2 raised to 1/years, minus 1) times 100. 72 is the chosen numerator because it divides cleanly by 2, 3, 4, 6, 8, 9, 12, 18 and 24, and its small cushion above ln(2)×100 = 69.31 cancels the bias of annual rather than continuous compounding near the middle of the range.
At 8% the rule says 72 ÷ 8 = 9.00 years to double; the exact answer is ln(2) ÷ ln(1.08) = 9.01 years, so the rule is out by 0.07%. Tripling at the same rate: 114.75 ÷ 8 = 14.34 years against an exact 14.27, an error of 0.48%. Run backwards, a 10-year deadline needs 72 ÷ 10 = 7.20% by the rule and 7.18% exactly, a gap of 0.02 percentage points. Away from the middle the rule drifts: at 2% it claims 36.00 years where the exact figure is 35.00 (2.85% too slow), and at 20% it claims 3.60 where the truth is 3.80 (5.31% too quick). A negative error means the rule flatters you.
Every figure rests on one rate you typed in yourself. Markets do not deliver a constant percentage: an 8% average assembled from +30% and −14% years does not double on schedule, because volatility pulls geometric growth below the arithmetic mean, and because the order of those years changes what each deposit or withdrawal does to you. The rule is also nominal. Inflation is not in it, so a doubling of dollars is not a doubling of buying power, and neither are taxes, fees, currency moves or the timing of cash flows. At a 0% or negative return nothing doubles and the arithmetic stops meaning anything.
An arithmetic convenience. No return is predicted or guaranteed here. Do your own research and, where relevant, seek qualified advice.