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Exponential Growth Calculator

Exponential Growth Calculator

Enter the required entities and the calculator will instantly determine the exponential growth of your investment, with the steps shown.

Calculation For:


Initial value x₀:

Rate of change r:


Elapsed time t:


Final value x(t):


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When you need to find the expected growth rate of your investment, you need to use the exponential growth calculator. This can be used to measure many processes like the growth rate and also the decay of a process. 

This formula is utilized by the growth rate calculator, we also use the same formulas for calculating the decay rate of a system. The same formula is used for the exponential decay calculator. 

What is the definition of exponential growth?

The exponential growth of an object or asset is described as the growth of that object or asset after an equal interval of time. These intervals can be hours, days, weeks, months, or years.

exponential growth

Exponential growth is critical when you are investing and want to find the expected growth of your investment. You need to find the exponential growth by using an exponential growth calculator as it is simple to operate.

How we can understand the Growth/Decay formula:

The simple formula for the  Growth/Decay rate is shown below, it is critical for us to understand the formula and its various values:

$$ x\left(t\right) = x_{o} \left(1 + \frac{r}{100}\right)^{t} $$


x(t): final values at time “time=t”

x₀: initial values at time “time=0”

r: Growth rate when we have r>0 or growth or decay rate when r<0, it is represented in the %.

t: the time at various discrete time intervals and at selected time periods.

Example 1:



t= 6 year

$$ x\left(t\right) = x_{o} \left(1 + \frac{r}{100}\right)^{t} $$

x(t)=1000×(1+0.05)^6= 1,340.0956

Example 2:



t= 6 months

t=6/12=½ years =0.05 years

$$ x\left(t\right) = x_{o} \left(1 + \frac{r}{100}\right)^{t} $$

x(t)=1000×(1+0.05)^0.5= 1,024.6951

Example 3:



t= 6 days

t=6/365= 0.016438 years 

$$ x\left(t\right) = x_{o} \left(1 + \frac{r}{100}\right)^{t} $$

x(t)=1000×(1+0.05)^0.016438= 1,000.8024

All the answers are checked by the exponential growth calculator precisely. You can find any missing values in the famous like initial values, time, or exponential rate. But you need to know at one time we are only able to find one variable by the growth rate calculator.

Can time have a negative value?

Have noticed we are inserting the positive values of the time in all the above-mentioned examples of the exponential growth calculator. But it can be sometimes new for you. The value of time can also be negative like -6,-5 years, etc or any other negative values of the time. We are only finding the value of the growth rate of the positive value of the time “t”. The value of the time can also be negative which is actually the decay of a particular system. We need to use the exponential decay calculator for finding the negative value of the time “t”

We are presenting a simple example of time “t”, where we are inserting the negative value of the time:

Example of negative time 1:



t= -6 years

t=-6 years 

$$ x\left(t\right) = x_{o} \left(1 + \frac{r}{100}\right)^{t} $$

x(t)=1000×(1+0.05)^-6= 746.2154

Have you noticed when we have put down the negative value of time “t” in the exponential calculator, we are getting fewer values from the initial values? It means the final result 746.2154 would become 1000 with a rate of 5% and time values of 6 years. In this case, we have found the values of the 6 years before today.

Example of negative time 2:

What was the population of our city in 2000, let’s suppose at the present date the population is 5 million and assuming the population growth is 8% yearly.

Then we have:

x₀=5 million 


t= -20 years

$$ x\left(t\right) = x_{o} \left(1 + \frac{r}{100}\right)^{t} $$

x(t)=500,000,0×(1+0.08)^-20= 107,274.1037 

Population 20 years ago.

107,274.1037 was the actual population of your city and now it is 5 M. The exponential growth calculator helped us to find the population of our city 20 years ago and the growth rate of the population is 8% increase per year.

For understanding the process we need to reverse the values.
negative values

Reverse Example of negative time 3:

What would be the population of our city in 2020, let’s suppose at the present date the population is  107,274.1037 and the present year is 2000, assuming the population growth is 8% yearly.

Then we have:



t= 20 years

$$ x\left(t\right) = x_{o} \left(1 + \frac{r}{100}\right)^{t} $$

x(t)=107,274.1037×(1+0.08)^20= 500,000,0=5M

BY using the growth factor calculator we are able to predict the population of the city would be 5M in 2020 and we are calculating the values in 2000. We have inserted the population of the city 107,274.1037 in the population growth calculator and the growth rate of the population is 8 %. 

Important to note!

You have noticed we are finding the same values of pollution which are 5 M today in 2020 but it was 107,274.1037 back in 2000. The result was reversed when we used the population growth calculator for the negative value of time “t”. 

The effect of growth rate on growth:

The growth rate has a significant effect on the growth of an object. It affects how quickly an object is growing or decaying. The exponential growth and decay calculator helps to find the growth or decay of an object or a figure.


Considering we have an amount of $100, we are applying four values of rate 10 %, 20%, 30 %, and 40 % on this value of 100. Consider the time is constant which is 2 years time:

The Effect of growth rate on growth


Amount  Growth rate  Expected amount 
$100 10% 121
$100 20% 144
$100 30 % 169
$100 40 % 192


The time is taken constant which is 2 years time or t=2. When we inserted the values in the exponential growth calculator, we have seen a huge difference in the amount with the growth rate even within 2 years time.

The real-world implementation of the growth rate:

We use the exponential growth formula calculator to predict various real-world examples and real-time phenomena:

  • Population growth of the bacteria, viruses and even plants and animals expected growth. 
  • The age of an object by radiative decaying formula 
  • Compound interest and growth of a country.
  • Expected GDP(Gross Domestic Growth) or GNP(Gross National Growth) 
  • The price growth index and expected values of price.

Working of exponential growth calculator:

The growth rate calculator is used to find the constant exponential growth of the GDP, GNP, Price index, or the growth of germs like bacteria and viruses.


  • Enter the value of the parameter of exponential growth.
  • Need to put the values and press the calculate button.


Exponential growth and decay calculator is an efficient way to measure the growth rate of different values.

  • The out result or values of the exponential growth is displayed 
  • You can also able to find the decay rate 


Are the percentage increase and exponential growth rate the same?

Yes, both terms are the same as the percentage increase in the final term and the growth rate is describing the process.

How do you find exponential decay?

When we are using the decay or exponential decay. Then we are using the decay rate and the negative time.The growth and decay calculator enables us to find the decay of a process.

What is the exponential model it uses?

We can find the populations, interest rates, radioactive decay, and the amount of medicine in the bloodstream and in the patient’s body. We use the same formula for the exponential model as the, we can find the exponential model by the exponential model calculator. 

How do you measure the growth rate of real GDP value?

We can find the Annual growth rate of real Gross Domestic Product (GDP) per capita between two consecutive years.


The growth rate calculator is commonly used in financial and business calculations. We can find the expected growth rate of the shares values and our investments. The utilization of the growth or decay calculator is just too important to find the future of our investment.


From the source of Real Life Examples Of Exponential Growth, Microorganisms in Culture

From the source of What Is a Growth Curve?, Understanding the Growth Curve