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Exponential Growth Calculator

Project a value forward at a constant growth rate and see the final amount, the multiplier and the doubling time.

Formula
x(t) = x₀ × (1 + r)^t · doubling time = ln 2 ÷ ln(1 + r)

How to use it

  • Enter the starting value, the growth rate per period and how many periods.
  • Use a negative rate for exponential decay.
  • Doubling time tells you how many periods it takes to grow 2×.

Examples

1000 at 5% for 10 periods1628.89
Growth 7%Doubles in about 10.2 periods

Exponential growth compounds a fixed percentage rate onto an ever-larger base, so the absolute increase gets bigger every period even though the rate stays constant: x(t) = x₀ × (1 + r)^t. It's the model behind population growth, investment returns, viral spread and — with a negative rate — radioactive decay and depreciation.

Worked example — user base growth

An app starts with 1,000 users and grows 5% a month. After 10 months: 1,000 × 1.05¹⁰ ≈ 1,629 users. Linear thinking (adding 50 users a month, the month-1 increase) would predict only 1,500 — exponential growth pulls ahead because each month's 5% is calculated on the larger, already-grown total, not the original 1,000.

Doubling time and the rule of 72

Doubling time — how many periods until the value doubles — is ln 2 ÷ ln(1 + r). At 7% a year, that's ln 2 ÷ ln 1.07 ≈ 10.24 years. The rule of 72 (72 ÷ rate) is the classic mental shortcut: 72 ÷ 7 ≈ 10.3, close enough for a back-of-envelope estimate at typical growth rates.

Questions people ask

What is the rule of 72?

A shortcut: divide 72 by the percentage growth rate to estimate the doubling time. At 8% that predicts 9 periods, against an exact 9.006.

Is anything sent to a server?

No. Every calculation runs in your browser, so nothing you type is uploaded and the page keeps working offline once it has loaded.

Runs entirely in your browser. Nothing you type is uploaded, logged or shared.

Last updated 17 August 2026