Percent Growth Rate Calculator

The Percent Growth Rate Calculator computes the growth rate, final value, initial value, or time for a given dataset. Input three known variables to find the missing one. Use the advanced mode to calculate average growth rate over multiple periods.

The Percent Growth Rate Calculator helps assess growth trends in finance, population studies, and other fields. The basic mode focuses on single-period growth, while the advanced mode calculates average growth across multiple periods. It is ideal for business planning, investment analysis, and economic forecasting.

Formula

Basic Growth Rate Formula:

r = \left( \left( \frac{x(t)}{x_0} \right)^{\frac{1}{t}} – 1 \right) \times 100

Final Value Formula:

x(t) = x_0 \times (1 + \frac{r}{100})^t

Initial Value Formula:

x_0 = \frac{x(t)}{(1 + \frac{r}{100})^t}

Time Formula:

t = \frac{\ln \left( \frac{x(t)}{x_0} \right)}{\ln \left( 1 + \frac{r}{100} \right)}

Advanced Growth Rate Formula:

r_{\text{avg}} = \left( \left( \frac{x(t)}{x_0} \right)^{\frac{1}{\text{Periods}}} – 1 \right) \times 100

Variable	Description
$r$	Growth rate per year (percentage).
$x(t)$	Final value after $t$ years.
$x_0$	Initial value.
$t$	Time in years.
Periods	Number of time periods (advanced).

Solved Calculations

Example 1:
Find the growth rate:

Final Value: $200
Initial Value: $100
Time: 3 years

Step	Calculation	Result
Formula	$r = \left( \left( \frac{x(t)}{x_0} \right)^{\frac{1}{t}} – 1 \right) \t$
Substitution	$r = \left( \left( \frac{200}{100} \right)^{\frac{1}{3}} – 1 \right)$
Result	$r$	26.01%

Example 2 (Advanced):
Find the average growth rate over 5 periods:

Final Value: $500
Initial Value: $100

Step	Calculation	Result
Formula	$r_{\text{avg}} = \left( \left( \frac{x(t)}{x_0} \right)^{\frac{1}{5}} – 1 \right) \times$
Substitution	$r_{\text{avg}} = \left( \left( \frac{500}{100} \right)^{\frac{1}{5}} – 1 \right) \times 100$
Result	$r_{\text{avg}} = 38$	38.17%