Exponential Growth & Decay Calculator (Free)

Use this free exponential growth and decay calculator to model continuous or periodic change. Enter the starting amount, the rate, and the time to get the final amount, the growth factor, the doubling time or half-life, and a graph.

Two models

Continuous growth uses A = A₀·e^(kt); periodic growth uses A = A₀·(1 + r)^t. Use a negative rate for decay.

How to use it

1. Choose continuous or periodic.
2. Enter the initial amount, the rate (as a percent), and the time.
3. Press Compute.

Related: the Compound Interest Calculator and more free math calculators.

Frequently asked questions

What is the difference between continuous and periodic?

Continuous compounding uses e^(kt) and applies growth at every instant; periodic uses (1+r)^t and applies it once per period.

How do I model decay?

Use a negative rate (for example −5). The tool then reports a half-life instead of a doubling time.

What is doubling time?

The time for the amount to double; for decay it instead reports the half-life.

Check the model with a worked example

Starting with 1,000 and growing 5% per period for 10 periods, the periodic model gives 1,000 × 1.05¹⁰ ≈ 1,628.8946. A continuous rate of 5% over 10 time units gives 1,000 × e^0.5 ≈ 1,648.7213. The same entered percentage produces different amounts because the two models interpret the rate differently.

For 10% periodic decay over three periods, enter −10 as the rate and 3 as the time: 1,000 × 0.9³ = 729. The half-life is ln(0.5) ÷ ln(0.9) ≈ 6.5788 periods, a positive duration.

Check units, rates and assumptions

• Enter 5 for 5%, rather than 0.05. The calculator converts the percentage to a decimal internally.
• Match the time to the rate: an annual rate needs time in years, while a monthly rate needs months.
• For a standard positive-amount model, use an initial amount above zero and nonnegative elapsed time. A periodic decay rate must be greater than −100%, so the multiplier stays positive.
• A zero rate leaves the amount unchanged; there is no finite doubling time or half-life.
• Constant percentage change is a modeling assumption. A fitted curve does not establish that real populations, investments or other quantities will follow it indefinitely.

Use the result to explain the change

Before computing, predict whether the amount should rise, fall or remain unchanged. Then write the model, substitute the values and include units in the answer. For the decay example, 729 is 72.9% of the starting amount; the total decrease is 27.1%, not 30%, because each period uses the remaining amount.

For the underlying formulas and the difference between additive and multiplicative change, see OpenStax College Algebra 2e: Exponential Functions.