Exponential Growth Calculator
Model continuous growth or decay (populations, interest, radioactive decay).
Calculator
Use the Exponential Growth Calculator
Result
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Formula
A = P × e^(r × t)
Step-by-step
- 1
Enter the initial amount
Starting quantity P.
- 2
Enter rate and time
Continuous rate r and elapsed periods t.
Worked example
Example input: initial: 100, rate: 0.05, time: 10
Result: 164.872
Related tools
- Compound Interest
Annual compounding variant.
- Natural Log
The inverse operation.
Frequently asked questions
What formula does the growth calculator use?
The continuous growth law: initial amount times e raised to rate x time. The example 100 at 0.05 for 10 period-units returns 164.872, straight from e to the power 0.5. The base constant here is e, about 2.718, the number that turns steady percent into smooth curve growth.
Why enter 0.05 instead of 5?
This calculator takes the rate as a decimal share per period, matching the exponent math directly: 0.05 means 5 percent continuous growth. Entering 5 would mean 500 percent per period.
When does the continuous model describe reality?
Idealized cultures, unchecked compound processes, and physics-style growth fit it well; real populations eventually meet ceilings and the model stops matching. Use it as the pure-math baseline.