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Notes on doubling, compounding, and growth

Short reads that turn growth rates into intuition. Each post is meant to be useful in five minutes or less.

We write about exponential growth in the wild: investing, business, biology, and the back-of-the-envelope math you can run in your head. If you want to try the numbers as you read, the Doubling Time Calculator is one click away.

Latest posts

What Is Doubling Time?

A clear, jargon-free explanation of doubling time: the meaning, the intuition behind it, and where it shows up in finance, biology, and populations.

How to Calculate Doubling Time

Four ways to calculate doubling time: by hand with the formula, on a scientific calculator, in a spreadsheet, and with our free online calculator.

The Doubling Time Formula

What the doubling time formula really says, why ln(2) shows up, and how to use the discrete and continuous versions correctly, with worked examples.

Exponential Growth & Doubling

How exponential growth and doubling time connect: compound rates, continuous compounding, graph interpretation, and what those curves really mean.

Rule of 70 vs Rule of 72

A practical comparison of the Rule of 70 and the Rule of 72, with a clear guide for when each shortcut wins and how each compares to the exact formula.

Doubling Time in Finance

How to use doubling time in finance: investment returns, compound interest, retirement planning, savings growth, and the cost of inflation over time.

Population Doubling Time

Population doubling time across demographics and biology: how cities, species, bacteria, and infectious diseases grow and what doubling periods reveal.

Continuous Growth Rate Formula

Where the continuous growth rate formula comes from, why e shows up, how to derive doubling time from it, and when to choose continuous over discrete.

Doubling Time in Real Life

Five short examples that turn doubling time into intuition: savings, startups, populations, cells, and bandwidth, with the rate and the math.