About the Exponential Growth Calculator
Exponential growth happens when something increases by the same percentage each period, so each step adds more than the last. Populations, viruses, savings and followers can behave this way, and so can decay, such as a drug leaving the body. This exponential growth calculator solves the standard formula for whichever of the four quantities you are missing: the value after some time, the growth rate, the time needed to reach a target, or the starting value. It supports growth added each period and continuous growth, and shows the doubling time or half-life with a short table of the first periods.
Updated October 2026
How to use the Exponential Growth Calculator
- 1Choose what you want to find: final value, rate, time or starting value.
- 2Choose whether growth is added each period or is continuous.
- 3Fill in the values it asks for. Use a negative rate for decay.
- 4Read the answer, the doubling time or half-life and the table of periods.
- 5Copy the result to use elsewhere.
Where exponential growth appears
- Compound interest on savings and debt
- Bacteria or viral spread in early stages
- Population growth with plenty of food and space
- Radioactive decay, where each step removes a fixed share
- Social media or subscriber growth under a steady percentage gain
Limits of the model
Nothing grows exponentially forever. Populations meet limits of food, space and disease, and sales reach saturation. Real data often follows a curve that starts exponential and then levels off, called logistic growth. Use the result as a projection under a fixed rate, not as a prediction of what will happen, and test how sensitive it is by trying slightly different rates.
Related tools
The CAGR Calculator finds a rate between two values, the Compound Interest Calculator handles savings, the Half-Life Calculator covers decay, the Log Calculator solves for time by hand, and the Percentage Calculator handles simple changes. For the constant e itself, see the Euler's Number digit generator.
Features
- Solves for value, rate, time or starting value
- Periodic and continuous growth
- Handles decay with negative rates
- Doubling time or half-life shown
- Table of the first periods
- Any time unit: years, days, hours
- Runs in your browser
Frequently asked questions
What is the exponential growth formula?
For growth added each period, the value after t periods is the starting value times (1 plus the rate) raised to the power t. For continuous growth it is the starting value times e raised to the power (rate times t). A population of 1,000 growing 5 percent a year becomes about 1,629 after 10 years.
How do I calculate doubling time?
Divide the natural logarithm of 2, about 0.693, by the natural logarithm of (1 plus the rate). At 7 percent growth per period the doubling time is about 10.2 periods. The quick rule of 72 gives 72 divided by the percentage rate, which is about 10.3 here.
What is the difference between periodic and continuous growth?
Periodic growth jumps at the end of each period, like yearly interest. Continuous growth is spread smoothly over time, as with a population that grows all the time. For the same rate, continuous growth ends higher, because the rate is applied at every instant.
How do I model exponential decay?
Enter a negative rate, such as minus 3 percent per period. The formula works the same way and the value shrinks, and the doubling time becomes a half-life, the time for the value to fall to half. Radioactive decay and the cooling of a drink both follow this pattern.
How is exponential growth different from linear growth?
In linear growth the same amount is added each period, so a graph is a straight line. In exponential growth the same percentage is added, so the amounts get larger over time and the graph curves upward. Over long periods exponential growth becomes much larger.
Can I use any time unit?
Yes. The periods may be years, months, days or hours, as long as the rate is for that same period. If the rate is 2 percent per day, the number of periods must be days.