Exponential Growth Calculator
Calculate exponential growth over time using initial value and growth rate
Enter as percentage (e.g., 5 for 5% growth per period)
How to Use This Calculator
Enter Initial Value
Input the starting value (P₀). This is the value at time t = 0. For example, an initial population, starting investment, or initial quantity.
Enter Growth Rate
Input the growth rate as a percentage per period. For example, if something grows by 5% each year, enter 5. Negative values represent decay.
Enter Time Periods
Input the number of time periods (t) over which growth occurs. This should match the unit of your growth rate (years, months, days, etc.).
Calculate
Click "Calculate Growth" to see the final value after the specified time periods, total growth, and growth factor.
Formula
P(t) = P₀ × (1 + r)t
Where:
- P(t) = value after t periods
- P₀ = initial value (at t = 0)
- r = growth rate per period (as decimal, so 5% = 0.05)
- t = number of time periods
Example 1: Population Growth
Initial population: 1,000
Growth rate: 5% per year
Time: 10 years
P(10) = 1,000 × (1 + 0.05)10 = 1,000 × 1.0510 ≈ 1,629
Example 2: Investment Growth
Initial investment: $5,000
Annual return: 8%
Time: 20 years
P(20) = 5,000 × (1.08)20 ≈ $23,305
Example 3: Bacterial Growth
Initial bacteria: 100
Growth rate: 50% per hour
Time: 6 hours
P(6) = 100 × (1.5)6 = 100 × 11.39 ≈ 1,139
About Exponential Growth Calculator
The Exponential Growth Calculator helps you calculate how a quantity grows over time when it increases by a constant percentage rate each period. This type of growth is called exponential because the growth rate is proportional to the current value. Exponential growth is common in population growth, compound interest, bacterial reproduction, and many other natural and financial phenomena.
When to Use This Calculator
- Finance: Calculate compound interest and investment returns over time
- Population Biology: Model population growth for humans, animals, or plants
- Microbiology: Calculate bacterial or viral growth rates
- Business: Project revenue growth, customer acquisition, or market expansion
- Economics: Analyze economic growth rates and inflation effects
Why Use Our Calculator?
- ✅ Instant Results: Get accurate growth calculations immediately
- ✅ Multiple Metrics: See final value, total growth, and growth factor
- ✅ Flexible Units: Works with any time period (years, months, days, etc.)
- ✅ Educational: Understand exponential growth through examples
- ✅ 100% Free: No registration or payment required
- ✅ Accurate: Precise mathematical calculations
Common Applications
Compound Interest: If you invest $10,000 at 6% annual interest, after 30 years: P(30) = 10,000 × (1.06)30 ≈ $57,435. Your investment grows almost 6-fold!
Population Growth: If a city has 50,000 people and grows at 3% annually, after 25 years: P(25) = 50,000 × (1.03)25 ≈ 104,689 people - more than doubling.
Bacterial Growth: If bacteria double every 20 minutes (100% growth rate per 20 min), after 2 hours (6 periods): P(6) = 1 × (2)6 = 64 times the original amount.
Tips for Best Results
- Make sure the time unit matches your growth rate (e.g., if rate is per year, time should be in years)
- Enter growth rate as a percentage (5 for 5%, not 0.05)
- For decay (negative growth), use a negative growth rate
- Large time periods with high growth rates can produce very large results
- Remember: Exponential growth accelerates over time - the growth gets faster as the value increases
Frequently Asked Questions
What is exponential growth?
Exponential growth occurs when a quantity increases by a constant percentage rate over equal time periods. Each period, the growth is proportional to the current value, causing accelerating growth over time.
How is exponential growth different from linear growth?
Linear growth adds a constant amount each period (e.g., +100 per year), while exponential growth multiplies by a constant factor each period (e.g., ×1.05 per year, or +5%). Exponential growth accelerates over time.
Can I use negative growth rates?
Yes! Negative growth rates represent exponential decay. For example, -10% means the quantity decreases by 10% each period. This is useful for radioactive decay, depreciation, or population decline.
How do I calculate doubling time?
The doubling time is approximately 70 divided by the growth rate percentage. For 5% growth: doubling time ≈ 70/5 = 14 periods. More precisely: t = ln(2)/ln(1+r).
What if growth rate changes over time?
This calculator assumes a constant growth rate. If the rate changes, you'll need to calculate each period separately or use a more complex model with variable rates.