Math
Exponential Growth Calculator
Model exponential growth or decay. Solve for final amount, time, rate, or starting value. Discrete or continuous, with doubling and halving times.
Exponential Growth Calculator
Given starting amount, rate, and time, find the final amount.
Per-period growth: N(t) = N0 x (1 + r)^t.
Any positive quantity (population, balance, sample size).
Use a negative value for decay (for example, -3 for -3%).
Number of periods in the same unit as the rate.
Final amount
162.889463
Growth
Growth factor (N(t) / N0)
1.628895
Continuous rate (k)
0.04879 per period
Doubling time
14.206699 periods
Time to grow 1%
0.203941 periods
Time to grow 10%
1.953471 periods
Frequently Asked Questions about the Exponential Growth Calculator
What is the exponential growth formula?
For discrete growth per period, N(t) = N0 x (1 + r)^t. For continuous growth, N(t) = N0 x e^(k x t), where k = ln(1 + r). A 5% per-period discrete rate equals a continuous rate of about 4.879%.
How do I calculate doubling time?
For discrete growth, ln(2) / ln(1 + r). For continuous growth, ln(2) / k. At 5% per period that is ln(2) / ln(1.05), about 14.207 periods. The rule of 72 (72 divided by the percent rate) is a quick mental shortcut.
How do I model exponential decay?
Use a negative rate. A 3% loss per period becomes r = -0.03, giving N(t) = N0 x 0.97^t. Starting from 100 with r = -3% over 10 periods leaves about 73.74.
What is the difference between discrete and continuous compounding?
Discrete applies the rate once per period; a 5% annual rate compounded yearly turns $100 into $105 after one year. Continuous assumes infinitely small intervals; the same $100 becomes about $105.13 after one year.
How do I solve for the rate when I know the start and end amounts?
With initial 100, final 200, and 10 periods, the discrete rate is r = (200 / 100)^(1 / 10) - 1 = 2^0.1 - 1, about 7.177% per period. The continuous equivalent is k = ln(200 / 100) / 10 = ln(2) / 10, about 6.931%.