Exponential Growth Calculator
Exponential growth happens when a quantity is multiplied by the same factor every period. Interest, population and radioactive decay all follow the same shape once the numbers are set up.
Final value
1,628.8946
- Total growth
- 628.8946
- Growth multiple
- 1.6289
- Doubling time in periods
- 14.2067
Values update as you type. This calculator covers the single scenario its formula assumes — see Common Mistakes for what it leaves out.
The formula this calculator uses
A = P x (1 + r)^t, where r can be negative for decay
- A
- The final value
- P
- The starting value
- r
- The rate per period, negative for decay
- t
- The number of periods
How to check the result by hand
- 1
Write the rate as a fraction
Five percent is 0.05. The formula needs the fraction, not the percentage, so divide by one hundred first.
- 2
Add one to the rate
One plus 0.05 is 1.05. This is the factor the value is multiplied by each period, and it is the base of the exponent.
- 3
Raise the factor to the number of periods
1.05 to the power of ten is 1.62889463. Raising to a power is repeated multiplication, which is exactly what compounding means.
- 4
Multiply by the starting value
One thousand times 1.62889463 is 1628.89462678, so the value has grown by 628.89462678 over the ten periods.
- 5
Check the doubling time
Log of two divided by log of 1.05 is 14.20669908 periods, which the rule of 72 approximates as 72 over 5, or about 14.4.
For worked examples, common mistakes and the limits of this formula, read the full How To Calculate Exponential Growth page.