Exponential Growth Calculator
Calculate growth or decay at a steady rate: the final amount, starting amount, rate or time, plus the doubling time.
Result
1,628.894627
- Total change
- 62.8895%
- Doubling time or half-life
- 14.206699 periods to double
- Growth factor per period
- 1.05
The amount after the time is shown above.
Calculation breakdown
| Step | Formula | Result |
|---|---|---|
| Result | 1,000 × (1 + 5%) ^ 10 | 1,628.894627 |
How it works
Choose what to find, then enter the other values. Time is in the same unit as the rate.
Worked example
1,000 growing 5% a period for 10 periods:
- Growth factor per period: 1.05
- Final amount: 1,000 × 1.05^10 = 1,628.89
- Doubling time: ln 2 ÷ ln 1.05 = 14.2067 periods
Sources
Frequently asked questions
What is the exponential growth formula?
With a steady rate r per period, the amount after t periods is x₀ × (1 + r)^t. Starting with 1,000 and growing 5% a period for 10 periods gives 1,628.89. With continuous growth the formula is x₀ × e^(rt).
How do you find the doubling time?
Divide ln 2 by ln(1 + r). At 5% growth per period it takes about 14.2 periods to double. The calculator shows the doubling time, or the half-life when the rate is negative.
What is the difference between per-period and continuous growth?
Per-period growth applies the rate in steps, such as once a year. Continuous growth compounds at every instant, which gives a slightly larger result for the same rate, 1,648.72 against 1,628.89 after 10 periods at 5%.
How do I find the rate or the time?
Choose Rate or Time at the top. The rate is the (final ÷ start) to the power of 1 ÷ time, minus 1. The time is ln(final ÷ start) ÷ ln(1 + r).
Can I use this for decay?
Yes. Enter a negative rate, such as −10%. The amount shrinks each period, and the calculator shows the half-life.