Exponential Growth & Decay Calculator NZ

This calculator models exponential growth and decay, working out how a quantity changes over time when it grows or shrinks by a fixed percentage each period. Exponential change is one of the most important patterns in nature, finance and science, because so many things grow or decay in proportion to their current size: money earning compound interest, populations of people, animals or bacteria, the spread of information, and the decay of radioactive material or a drug in the bloodstream. Unlike linear change, which adds the same amount each step, exponential change multiplies by the same factor each step, which is why it starts slowly and then accelerates dramatically, or, for decay, falls quickly at first and then tails off. This tool captures both. You enter the starting value, the percentage rate per period, positive for growth or negative for decay, and the number of periods, and the calculator returns the final value, the total change, the growth or decay factor, and the doubling time for growth or half-life for decay, the time it takes for the quantity to double or halve. The results update as you type, so you can explore how even a modest rate compounds into a large change over many periods. Use it for finance and investment projections, population and biology problems, radioactive decay, or any situation that compounds. The doubling time and half-life are especially useful intuitions: a quantity growing at a steady rate always takes the same time to double again, no matter how large it has become, which is the surprising power of exponential growth. The calculation uses the standard compound formula and is rounded for display.

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1,628.89
final value
Total change+628.89
Doubling time14.2 periods
Growth factor1.629

Final = start x (1 + rate/100)^periods. Positive rate grows; negative rate decays. Doubling time (growth) or half-life (decay) is shown. Rounded for display.

How it works

Each period the quantity is multiplied by one plus the rate as a decimal, so after a number of periods the final value is the starting value times that factor raised to the power of the periods. The doubling time, for growth, is the natural log of two divided by the natural log of the growth factor; for decay it becomes the half-life.

Worked example

Starting with 1,000 and growing 5 percent per period for 10 periods, the final value is 1,000 times 1.05 to the power 10, which is about 1,628.89, a total increase of 628.89. At 5 percent per period the quantity doubles roughly every 14.2 periods, regardless of how large it grows.

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Frequently asked questions

What is exponential growth?

Exponential growth is when a quantity increases by a fixed percentage of its current size each period, so it multiplies rather than adds. This makes it start slowly then accelerate sharply. Compound interest, populations and viral spread all follow this pattern.

What is doubling time?

Doubling time is how long a growing quantity takes to double. For steady exponential growth it stays constant no matter how large the quantity gets, and equals the natural log of two divided by the natural log of the growth factor. For decay, the equivalent is the half-life.

How do I model decay?

Enter a negative rate, such as minus 10 percent, for decay. The quantity then shrinks by that percentage each period, falling quickly at first and tailing off. The calculator shows the half-life, the time for the quantity to fall to half its value.