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Exponential Growth Calculator

Project how a quantity grows or shrinks at a steady percentage rate. Enter the starting value, the rate per period and the number of periods to get the final value, the total change, and the doubling time — or the half-life if the rate is negative.

Quick examples
%

Use a negative rate for decay.

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Final value1,628.8946
Total change
628.8946
Total percent change
62.89%
Growth factor per period
1.05 ×
Doubling time
14.2067 periods
Half-life
—

Value period by period

PeriodValueChange in period

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      Formula

      Per-period growth: x(t) = x₀ × (1 + r)ᵗ
      Continuous growth: x(t) = x₀ × e^(r × t)
      Doubling time = ln 2 ÷ ln(1 + r), or ln 2 ÷ r for continuous growth
      Half-life = ln 2 ÷ −ln(1 + r) when r is negative

      How to use it

      1. Enter the starting value.
      2. Enter the growth rate per period as a percentage; use a negative number for decay.
      3. Enter the number of periods, in the same unit of time as the rate.
      4. Choose per-period or continuous growth and read the final value. The table lists every period.

      Worked examples

      1,000 growing 5% per period for 10 periods

      Final value
      1,628.8946
      Total change
      628.8946
      Total percent change
      62.89%
      Doubling time
      14.2067 periods

      500 decaying 3% a year for 20 years

      Final value
      271.8972
      Half-life
      22.7566 periods

      1,000 growing continuously at 2% for 35 periods

      Final value
      2,013.7527
      Doubling time
      34.6574 periods

      Doubling time and the rule of 70

      A quick estimate of doubling time is 70 divided by the percentage rate. At 5% that gives 14 periods; the exact figure is 14.21. The shortcut works well for rates up to about 10%.

      For decay the same idea gives the half-life: something losing 3% a year halves in about 22.8 years.

      Getting the inputs right

      The rate and the number of periods must use the same unit — a monthly rate with a count of months, a yearly rate with years.

      Per-period and continuous growth are close but not equal. A continuous rate of 5% is the same as 5.127% applied once per period, because e^0.05 = 1.05127.

      Questions people ask

      What is 1,000 growing at 5% for 10 periods?

      1,628.89. That is 1,000 × 1.05¹⁰, a total increase of 62.89%.

      How long does it take to double at 5% growth?

      About 14.21 periods: ln 2 ÷ ln 1.05.

      What is the difference between linear and exponential growth?

      Linear growth adds the same amount each period; exponential growth multiplies by the same factor. Starting from 100, +10 per period reaches 200 after 10 periods, while +10% per period reaches 259.37.

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