Exponential Growth Calculator
Enter an initial amount, a growth rate, and a number of periods to get the final amount from continuous exponential growth — plus the total change over time.
Final amount and total change
Enter the starting value, rate, and time and the calculator returns the final amount from A = P · e^(r·t) and the total change (final minus initial).
Rate as a decimal
Enter the growth rate as a decimal — 0.05 means 5% per period. Use a negative rate, such as -0.03, to model decay instead of growth.
What is exponential growth?
Growth that compounds on itself
The exponential growth calculator turns three numbers — an initial amount, a growth rate, and a span of time — into the value after continuous exponential growth, A = P · e^(r·t), along with the total change over the period. Exponential growth is what happens when a quantity increases by a constant fraction of its current size in every instant, so the amount added keeps getting bigger. It is the maths behind compound interest, population increase, and viral spread, and the same formula runs in reverse — with a negative rate — to model decay such as radioactive half-life or a depreciating asset.
Enter an initial amount, a growth rate as a decimal, and a number of periods to get the final amount and the total change instantly.
The final amount is the initial amount multiplied by e (about 2.71828) raised to the growth rate times the time, and the total change is simply the final amount minus the initial amount.
A = P · e^(r·t)Because the exponent r·t sits in the power of e, the result accelerates: each period builds on the one before, so doubling the time more than doubles the gain. Keep the rate and the time in matching units — a yearly rate with a number of years, a daily rate with days — and the answer stays consistent.
Suppose you start with 1000 and it grows continuously at a rate of 0.05 (5%) for 10 periods.
Multiply the rate by the time
0.05 × 10 = 0.5 — the exponent that drives the growth.
Raise e to that exponent
e^0.5 ≈ 1.648721 — the growth factor over the whole period.
Multiply by the initial amount
1000 × 1.648721 = 1648.721271 — the final amount. The total change is 1648.721271 − 1000 = 648.721271.
The two outputs answer two different questions. The final amount (1648.72 above) is where the quantity ends up after the full span of continuous growth, and the total change (648.72) is how much it gained along the way — the headline number for anything you care about as a net increase. When the rate is negative the model becomes exponential decay: the final amount falls below the initial amount and the total change comes back negative, showing the loss. The crucial feature of the curve is that growth feeds on itself, so the absolute gain in later periods dwarfs the early ones even though the rate never changes. That is exactly why long-term compound interest and unchecked population growth produce numbers that feel surprisingly large, and why small differences in the rate compound into big differences over time.
The formula is exact, but a couple of practical points are worth keeping in mind.
Continuous model and constant rate
This calculator uses the continuous growth model, A = P · e^(r·t), which compounds at every instant — discrete growth that compounds once per period uses A = P · (1 + r)^t instead and gives a slightly smaller result. The model also assumes the rate stays constant for the whole span; real populations, markets, and resources eventually slow as limits are reached, so treat very long projections as a best case rather than a forecast.