Exponential Growth Calculator
Growth or decay, with doubling time and half-life.
Work out Exponential Growth. Growth or decay, with doubling time and half-life. Handles the cases the shortcuts get wrong.
Negative for decay.
Final value
1,967.1514
+96.72% over 10 periods
Doubling takes 10.24 periods at this rate. The rule of 72 estimates it as 10.29 — close, and the error grows with the rate. The exact figure is ln(2) ÷ ln(1 + r), which is what this uses.
How the Exponential Growth Calculator works
Growth or decay at a constant rate, with the doubling time or half-life that follows. The rule of 72 approximates doubling time well for small rates and drifts as they rise; the exact figure is ln(2) ÷ ln(1 + r), which is what this uses.
Also known as: exponential decay calculator · doubling time calculator · growth rate calculator · compound growth calculator
Doubling time and the rule of 72
Doubling time is ln(2) ÷ ln(1 + r), which at 7% gives 10.24 periods.
The rule of 72 approximates this as 72 ÷ 7 = 10.29 — close enough for mental arithmetic. It works because ln(2) is about 0.693 and, for small rates, ln(1+r) is about r; the 72 rather than 69 compensates for the curvature and happens to divide nicely.
The approximation drifts as rates rise. At 25% the rule gives 2.88 periods against a true 3.11.
Growth and decay
1,000 growing at 7% for ten periods reaches 1,967 — not the 1,700 that ten lots of 7% would suggest, because each period's growth is calculated on the larger balance.
Decay works identically with a negative rate, and never quite reaches zero: each period removes a share of what remains rather than a fixed amount. That is why half-life is constant — falling from 100 to 50 takes exactly as long as falling from 50 to 25.
The reason exponential growth defeats intuition is that the absolute increase grows every period. Very little appears to happen for a long stretch, and then a great deal happens quickly.
Frequently asked questions
What is the exponential growth formula?
Final = initial × (1 + r)ⁿ. A thousand growing at 7% for ten periods reaches 1,967.
How do I find doubling time?
ln(2) ÷ ln(1 + r). At 7% that is 10.24 periods. The rule of 72 estimates it as 72 ÷ 7 = 10.29 — close enough for mental arithmetic, and less accurate as rates rise.
What is the difference between growth and decay?
The sign of the rate. Decay never quite reaches zero, because each period removes a share of what remains rather than a fixed amount — which is why half-life is constant.
Why is exponential growth so hard to intuit?
Because the absolute increase grows every period. Nothing much appears to happen for a long time, and then a great deal happens quickly.
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