What is the exponential growth formula?

A = A₀ × e^(rt), where A₀ is the initial amount, r is the continuous growth rate, t is elapsed time, and e is Euler's number (≈2.71828).

What does 'continuous' growth mean?

Continuous growth assumes compounding happens at every instant rather than at discrete intervals (like annually or monthly). It's modeled using e^(rt) and is the limiting case as the compounding frequency approaches infinity.

What is doubling time?

Doubling time is how long it takes a quantity growing exponentially to double in size, calculated as ln(2) / r. It depends only on the growth rate, not on the starting amount.

How is this different from the Percent Growth Rate Calculator?

The Percent Growth Rate Calculator finds the rate given a start value, end value, and number of periods (working backward from known data). This calculator works forward: given a known rate, it projects the future amount and doubling time.

Can the growth rate be greater than 1 (100%)?

Yes — the continuous rate r can be any positive number. A rate of r = 1 means the quantity grows by a factor of e (≈2.718) per unit of time, which is extremely fast growth.

What happens if time (t) is 0?

At t = 0, e^(r×0) = e^0 = 1, so the final amount equals the initial amount exactly — no growth has occurred yet.

How is continuous growth different from compound interest with a fixed number of compounding periods?

Compound interest with n periods per year uses A₀(1 + r/n)^(nt), which approaches the continuous formula A₀e^(rt) as n grows toward infinity. Continuous growth is the fastest possible outcome for a given nominal rate r.

Where is exponential growth used in real life?

It models population growth, compound interest and investment returns, the early spread of an epidemic or viral trend, and bacterial culture growth under unlimited resources.

Exponential Growth Calculator — Find Future Value and Doubling Time

Our Exponential Growth Calculator computes continuous exponential growth using A = A₀e^(rt), where A₀ is the initial amount, r is the continuous growth rate, and t is elapsed time. It also computes the doubling time (ln(2)/r) — how long it takes any quantity growing at that rate to double, regardless of its starting size. Useful for population growth, compound interest, viral spread modeling, and any quantity that grows proportionally to its current size.

Quick Answer

Exponential growth follows A = A₀e^(rt), where A₀ is the starting amount, r is the growth rate, and t is time. Enter your values below to get the final amount and the doubling time (ln(2)/r) for that growth rate.

Initial amount (A₀)

Growth rate (r)

Time (t)

Enter an initial amount, rate, and time, then click Calculate.

How to Use the Exponential Growth Calculator — A = A₀e^(rt) Online

1
Enter the initial amount (A₀).
2
Enter the continuous growth rate (r) as a decimal, e.g. 0.05 for 5%.
3
Enter the elapsed time (t).
4
Click 'Calculate' to get the final amount and the doubling time for this growth rate.

Why Use Exponential Growth Calculator — A = A₀e^(rt) Online?

Exponential growth describes any quantity that increases at a rate proportional to its current size — the more you have, the faster it grows — which is why populations, compound interest, and viral spread all follow this same mathematical shape. The formula A = A₀e^(rt) uses continuous compounding via Euler's number e, which is the limiting case of compounding infinitely often and is the standard form used in calculus-based growth models. The doubling time formula, ln(2)/r, is a useful shortcut that depends only on the rate, not the starting amount — this calculator computes both instantly.

Frequently Asked Questions

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