Exponential Growth Calculator
Calculate exponential growth or decay using A = P(1+r)^t (discrete) or A = Pe^(rt) (continuous). Shows final value, growth factor, and doubling time. See also our Compound Interest Calculator and CAGR Calculator.
How to Calculate Exponential Growth
- Choose the growth model (discrete or continuous).
- Enter the initial value (starting amount).
- Enter the growth rate as a percentage (use negative for decay).
- Enter the number of time periods.
- Click Calculate to see the final value and growth metrics.
Formula
Discrete Growth: A = P × (1 + r)^t
Continuous Growth: A = P × e^(rt)
Where:
A = Final amount
P = Initial amount (principal)
r = Growth rate (as decimal)
t = Time periods
e = Euler's number (2.71828...)
Doubling Time (discrete): t₂ = ln(2) / ln(1 + r)
Doubling Time (continuous): t₂ = ln(2) / rExample
Initial value: $1,000, Growth rate: 5% per year, Time: 10 years
Discrete: A = 1000 × (1 + 0.05)^10 = 1000 × 1.6289 = $1,628.89
Growth factor: 1.6289
Total growth: $628.89 (62.89%)
Doubling time: ln(2) / ln(1.05) = 14.21 years
Exponential Growth Reference Table
| Rate | Doubling Time | 10-Year Factor | $1000 after 10yr |
|---|---|---|---|
| 1% | 69.66 years | 1.1046 | $1,104.62 |
| 2% | 35.00 years | 1.2190 | $1,218.99 |
| 3% | 23.45 years | 1.3439 | $1,343.92 |
| 5% | 14.21 years | 1.6289 | $1,628.89 |
| 7% | 10.24 years | 1.9672 | $1,967.15 |
| 10% | 7.27 years | 2.5937 | $2,593.74 |
| 15% | 4.96 years | 4.0456 | $4,045.56 |
| 20% | 3.80 years | 6.1917 | $6,191.74 |
Frequently Asked Questions
What is the difference between discrete and continuous growth?
Discrete growth compounds at fixed intervals (yearly, monthly). Continuous growth compounds infinitely often, using the natural exponential function e^(rt). Continuous growth always yields a slightly higher result.
How do I calculate exponential decay?
Use a negative growth rate. For example, -5% means the quantity decreases by 5% each period. The formula works the same way.
What is the Rule of 72?
The Rule of 72 is a quick approximation: divide 72 by the growth rate percentage to estimate doubling time. At 6% growth, doubling takes approximately 72/6 = 12 years.
Where is exponential growth used?
Population growth, compound interest, bacterial growth, radioactive decay, viral spread, and technology adoption all follow exponential patterns.
What is the growth factor?
The growth factor is the ratio of final value to initial value (A/P). A growth factor of 2 means the quantity doubled; 0.5 means it halved.