Exponential Growth Calculator

Exponential growth describes a quantity whose change is proportional to its current size. Unlike linear growth, which adds the same amount each period, exponential growth multiplies by the same factor. That compounding effect means the absolute increase becomes larger as the quantity grows. The model appears in savings balances, populations, bacterial cultures, technology adoption, radioactive decay, and many other processes. For growth that happens at distinct intervals, the calculator uses A = P(1 + r)^t. P is the initial value, r is the rate per period written as a decimal, t is the number of periods, and A is the final amount. A rate entered as 5 is converted to 0.05 before calculation. Negative percentages model decay. A discrete rate of -100% reduces the quantity to zero, while a lower rate is not meaningful for this model because its multiplier becomes negative. Continuous growth uses A = P e^(rt), where e is Euler's number. This form models change occurring at every instant rather than at yearly, monthly, or other separate checkpoints. Continuously compounded interest and idealized biological processes are common examples. At the same nominal positive rate, continuous growth produces a slightly larger result than growth compounded once per period. The rate and time units must agree. If the rate is annual, time must be entered in years; if the rate is monthly, time must be in months. Mixing an annual rate with a month count exaggerates the answer. The calculator leaves units open so it can model money, people, cells, mass, or any other positive starting quantity, but users must keep those units consistent. Exponential models are powerful approximations, not promises that growth can continue forever. Real populations encounter limited resources, investments experience changing returns, and physical systems may follow more detailed decay laws. Use the result to understand the mathematical consequence of a constant rate, compare scenarios, and check hand calculations. For planning decisions, pair the calculation with realistic assumptions about changing rates, fees, constraints, and uncertainty.