Doubling Time Calculator

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Choose how you want to calculate: from a known growth rate, from observed start/end values, or as a quick Rule-of-70/72 estimate.
Continuous uses ln(2)/r; discrete uses ln(2)/ln(1+r). For most finance and population contexts, discrete is the right choice.
The constant percentage increase per period (year, day, hour, etc.).
% per period
Doubling timeFast doubling
9.9periods

Time for the quantity to double at the given growth rate

Rule of 70 estimate10periods
Rule of 72 estimate10.29periods
Rule of 70 error0.99%
Rule of 72 error3.87%
Exact doubling time9.9
Rule of 7010
Rule of 7210.29

Doubling time: 9.90 periods

  • At a 7% continuous growth rate, the quantity doubles every 9.90 periods.
  • Rule of 70 gives 10.00 periods (error: +0.99%); Rule of 72 gives 10.29 periods (error: +3.87%).
  • Rule of 70 is more accurate for this rate. Rule of 72 tends to be closer for rates above 8%; Rule of 70 tends to be closer for rates below 5%.
  • These calculations assume a constant growth rate. Real-world growth rates fluctuate, so treat the result as an estimate rather than a guarantee.

Next stepApply this to finance: an investment growing at 7% per year doubles roughly every 10 years (the Rule of 72 gives 72/7 = 10.3 years). For bacteria or populations, switch to the continuous model for better accuracy.

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