Exponential Growth/Decay Calculator
Exponential Growth/Decay Calculator
Enter a starting value, a rate per period (use a negative rate for decay), and the number of periods. This calculates the final value after exponential growth or decay compounds over that time — the same underlying math behind compound interest, population growth, and radioactive decay.
The defining feature of exponential change is that growth compounds on an ever-larger base: with growth, the absolute increase gets bigger each period because the percentage rate applies to a bigger starting point every time, while with decay the absolute decrease gets smaller as the shrinking base leaves less to decay from. This same compounding formula describes wildly different real-world phenomena — savings account balances, viral spread rates, and the half-life decay of radioactive material — because they all follow the identical mathematical pattern of a fixed percentage change applied repeatedly.
- Formula: final value = initial value × (1 + rate/100)^periods, where a positive rate compounds growth and a negative rate compounds decay.
- Growth accelerates, decay decelerates: exponential growth means the absolute increase gets larger each period (since it's a percentage of an ever-growing base), while exponential decay means the absolute decrease shrinks each period.
- Same formula covers many real scenarios: compound interest, population growth, viral spread, and radioactive/drug decay are all modeled by this same exponential structure — only the interpretation of "rate" and "period" changes.
How do I model decay instead of growth?
Enter a negative rate — for example, a 5% decay per period is entered as −5, which the formula handles automatically by shrinking the value each period instead of growing it.
Why does the total change percentage differ from the rate per period?
The rate per period compounds over multiple periods, so the total change over all periods combined is always larger (in magnitude) than any single period's rate — that's the nature of compounding.
Exponential Growth/Decay Calculator
Enter a starting value, a rate per period (use a negative rate for decay), and the number of periods. This calculates the final value after exponential growth or decay compounds over that time — the same underlying math behind compound interest, population growth, and radioactive decay.
The defining feature of exponential change is that growth compounds on an ever-larger base: with growth, the absolute increase gets bigger each period because the percentage rate applies to a bigger starting point every time, while with decay the absolute decrease gets smaller as the shrinking base leaves less to decay from. This same compounding formula describes wildly different real-world phenomena — savings account balances, viral spread rates, and the half-life decay of radioactive material — because they all follow the identical mathematical pattern of a fixed percentage change applied repeatedly.
- Formula: final value = initial value × (1 + rate/100)^periods, where a positive rate compounds growth and a negative rate compounds decay.
- Growth accelerates, decay decelerates: exponential growth means the absolute increase gets larger each period (since it's a percentage of an ever-growing base), while exponential decay means the absolute decrease shrinks each period.
- Same formula covers many real scenarios: compound interest, population growth, viral spread, and radioactive/drug decay are all modeled by this same exponential structure — only the interpretation of "rate" and "period" changes.
How do I model decay instead of growth?
Enter a negative rate — for example, a 5% decay per period is entered as −5, which the formula handles automatically by shrinking the value each period instead of growing it.
Why does the total change percentage differ from the rate per period?
The rate per period compounds over multiple periods, so the total change over all periods combined is always larger (in magnitude) than any single period's rate — that's the nature of compounding.