Exponential Growth Calculator
Calculate exponential growth and decay: P(t) = P₀ × e^(rt). Model population growth, compound interest, radioactive decay, and more.
This free online exponential growth calculator provides instant results with no signup required. All calculations run directly in your browser — your data is never sent to a server. Enter your values below and see results update in real time as you type. Perfect for everyday calculations, homework, or professional use.
Positive for growth, negative for decay
Results
Final Value P(t)
1648.7213
How to Use This Calculator
Enter your input values
Fill in all required input fields for the Exponential Growth Calculator. Most fields include unit selectors so you can work in your preferred unit system — metric or imperial, whichever matches your problem.
Review your inputs
Double-check that all values are correct and that you have selected the right units for each field. Incorrect units are the most common source of calculation errors and can produce results that are off by factors of 2, 10, or more.
Read the results
The Exponential Growth Calculator instantly computes the output and displays results with units clearly labeled. All calculations happen in your browser — no loading time and no data sent to a server.
Explore parameter sensitivity
Try adjusting individual input values to see how the output changes. This is a quick and effective way to develop intuition about how different parameters influence the result and to identify which inputs have the largest effect.
Formula Reference
Exponential Growth Calculator Formula
See calculator inputs for the governing equation
Variables: All variables and their units are labeled in the calculator interface above. Input fields accept values in multiple unit systems — select your preferred unit from the dropdown next to each field.
When to Use This Calculator
- •Use the Exponential Growth Calculator when you need a quick mathematical result without writing out all the steps manually, saving time on repetitive calculations.
- •Use it to verify hand calculations on tests or assignments and catch arithmetic mistakes.
- •Use it when teaching or explaining mathematical concepts to others, demonstrating how changing inputs affects the result.
- •Use it to explore the behavior of mathematical functions across a range of inputs.
About This Calculator
The Exponential Growth Calculator is a free mathematical calculation tool for students, educators, and professionals who need quick, reliable results. Calculate exponential growth and decay: P(t) = P₀ × e^(rt). Model population growth, compound interest, radioactive decay, and more. The underlying algorithms implement well-established mathematical formulas and numerical methods. Results are computed instantly in the browser. This tool is useful for learning, verification of hand calculations, and rapid exploration of mathematical relationships. All computation happens locally — no data is sent to a server.
About Exponential Growth Calculator
Exponential growth and decay describe processes where the rate of change is proportional to the current value. The formula P(t) = P₀e^(rt) models continuous exponential change, where P₀ is the initial value, r is the growth rate (positive for growth, negative for decay), and t is time. This model applies to an extraordinary range of phenomena: bacterial growth, compound interest, radioactive decay, population dynamics, viral spread, drug metabolism, and Newton's law of cooling. The doubling time (how long until a growing quantity doubles) and half-life (how long until a decaying quantity halves) are constant for exponential processes — a distinctive property. This calculator computes the final value along with the doubling time or half-life.
The Math Behind It
Formula Reference
Exponential Growth
P(t) = P₀ × e^(rt)
Variables: P₀ = initial value, r = rate, t = time
Doubling Time
T₂ = ln(2) / r
Variables: r = growth rate (r > 0)
Half-Life
T½ = ln(2) / |r|
Variables: r = decay rate (r < 0)
Worked Examples
Example 1: Population Growth
A population of 1000 grows at 5% continuously. Find the population after 10 years.
P(10) ≈ 1648.7
Common Mistakes & Tips
- !Confusing continuous rate r with discrete rate — 5% continuous growth is not the same as 5% annual compounding.
- !Using a positive rate for decay problems (should be negative).
- !Forgetting that the doubling time formula only applies when r > 0.
Related Concepts
Used in These Calculators
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Frequently Asked Questions
What is the Rule of 70?
The Rule of 70 estimates doubling time: divide 70 by the percentage growth rate. At 7% growth, the doubling time is approximately 70/7 = 10 periods.
How does continuous growth differ from compound growth?
Continuous growth uses P₀e^(rt); compound growth uses P₀(1+r/n)^(nt) where n is compounding frequency. As n → ∞, compound growth approaches continuous growth.