Exponential Growth Calculator

Use our exponential growth calculator to find the final value, initial value, growth rate, or time.

Calculate:

• Final Value
• Initial Value
• Growth Rate
• Time

x_{t}=x_{0} \times \left ( 1 + r \right ) ^{t}

Initial Value x₀:

Growth Rate r:

%

Elapsed Time t:

x_{t}=x_{0} \times \left ( 1 + r \right ) ^{t}

Growth Rate r:

%

Elapsed Time t:

Final Value x_t:

x_{t}=x_{0} \times \left ( 1 + r \right ) ^{t}

Initial Value x₀:

Elapsed Time t:

Final Value x_t:

x_{t}=x_{0} \times \left ( 1 + r \right ) ^{t}

Initial Value x₀:

Growth Rate r:

%

Final Value x_t:

×

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Final Value:

Final Value:

x_t =

 

Initial Value:

x₀ =

 

Growth Rate:

r =

 

Time:

t =

 

Learn how we calculated this below

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By

Joe Sexton

Joe is the creator of Inch Calculator and has over 20 years of experience in engineering and construction. He holds several degrees and certifications.

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Reviewed by

Aditya Dua, PhD

Aditya holds a PhD in electrical engineering from Stanford University and specializes in signal processing, algorithms, and machine learning.

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Cite As:

Sexton, J. (n.d.). Exponential Growth Calculator. Inch Calculator. Retrieved November 17, 2024, from https://www.inchcalculator.com/exponential-growth-calculator/

How to Calculate Exponential Growth

Exponential growth is the growth of a value by the same percentage over a number of time periods, where the percentage of growth during each period includes the effect of growth accumulated over previous periods.

Exponential growth is the mechanism behind things such as compound interest (positive exponential growth) and half-life decay (negative exponential growth, or decay).

You can calculate the amount of growth in a value over time using the exponential growth formula.

Exponential Growth Formula

The formula to find a value using the exponential growth formula is:

The final value x_t is equal to the initial value x₀ times 1 plus the growth rate r raised to the power of the number of time periods t.

By using a negative growth rate, you can also calculate the amount of exponential decay in a value.

The initial value grows over time if growth rate r > 0 and decreases (decays) over time if r < 0.