Doubling Time Calculator
Enter a constant growth rate and get the exact doubling time from t = ln(2) / r — plus the popular rule-of-70 estimate so you can sanity-check it in your head.
Exact and shortcut at once
Enter one growth rate and the calculator returns the exact doubling time (ln(2) / r) and the rule-of-70 estimate (0.7 / r) side by side.
Use a decimal rate
Write the rate as a decimal — 0.05 for 5%, 0.07 for 7% — and the answer comes back in the same period as the rate (years in, years out).
What is doubling time?
How long until it doubles
The doubling time calculator answers one intuitive question: if something grows at a steady rate, how long until there is twice as much of it? Doubling time is the number of periods a quantity takes to double when it grows at a constant, compounding rate. It turns an abstract percentage into a tangible horizon — "7% a year" becomes "doubles in about a decade." It applies to populations, investments and compound interest, inflation, bacteria, epidemics, and traffic: anywhere growth compounds on itself.
Enter a growth rate as a decimal to get the exact doubling time and the rule-of-70 estimate instantly.
The exact doubling time is the natural logarithm of two divided by the growth rate, and the rule of 70 is the quick approximation that lands right next to it.
t = ln(2) / rBecause ln(2) ≈ 0.693, dividing 0.7 by the rate instead — the rule of 70 — gives an answer just a hair higher. At 7% the exact figure is 9.9 years while the rule of 70 says 10, close enough for mental math. Keep the rate and the period consistent: a yearly rate yields years, a monthly rate yields months.
Suppose an investment grows at 7% per year, so r = 0.07.
Take the natural log of two
ln(2) = 0.693 — the constant on top of every doubling-time formula.
Divide by the growth rate
0.693 ÷ 0.07 = 9.9 — the exact doubling time in years.
Check with the rule of 70
0.7 ÷ 0.07 = 10 years, almost the same — a fast way to verify the result.
The formula is exact, but it rests on one assumption worth keeping in mind.
Assumes a constant, positive growth rate
Doubling time only makes sense when the rate stays constant and positive. Real populations and markets speed up and slow down, so treat the result as a steady-state estimate, not a guarantee. A rate of zero or below has no doubling time — a quantity that is flat or shrinking never doubles — so the calculator returns nothing there. Keep the rate and its period consistent, and enter the rate as a decimal.