How to Calculate Doubling Time: 4 Methods

Step-by-step formula

The exact discrete formula is T = ln(2) divided by ln(1 plus r), where r is the rate as a decimal per period. The continuous version drops the inner log: T = ln(2) divided by r. The Rule of 70 and Rule of 72 are approximations that divide 70 or 72 by the rate as a percentage.

Method 1: by hand

You need two natural log values: ln(2) is about 0.693 and ln(1 plus r) for your chosen rate. For a 7 percent rate, ln(1.07) is about 0.0677. Divide 0.693 by 0.0677 and you get roughly 10.24 years. The hand method is fine for one or two calculations but tedious when you need to compare many rates.

Method 2: scientific calculator

Almost any scientific calculator or smartphone calculator app has an LN or natural log key. Enter 2, press LN, write down the result. Enter (1 + your rate as a decimal), press LN. Divide the first by the second. Done in under thirty seconds with no manual log lookups.

Method 3: spreadsheet

In Excel, Google Sheets, or Numbers, the formula =LN(2)/LN(1+r) gives the discrete answer. Put your growth rate as a decimal in a cell, reference it, and the doubling time appears. The spreadsheet version is ideal when you want to compute doubling times for many scenarios at once, or to build a sensitivity table that shows how the result changes as the rate moves.

Method 4: online calculator

The Doubling Time Calculator on this site runs the exact formula, the Rule of 70 estimate, and the Rule of 72 estimate at the same time. Type a rate, label the period, and read all three values together. The continuous mode also plots a growth curve so you can see the shape of the exponential.

Worked example: 7 percent

Annual growth rate of 7 percent. r = 0.07. Discrete formula: T = ln(2) / ln(1.07) = 0.693 / 0.0677 = 10.24 years. Rule of 70: 70 / 7 = 10.00 years. Rule of 72: 72 / 7 = 10.29 years. All three answers sit within a quarter of a year of each other, which is typical for rates in this range. See Rule of 70 vs Rule of 72 for how to choose between the two shortcuts.