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Math

Exponential Growth Calculator

Calculate any final value from initial amount, growth rate, and time periods

Growth Parameters

Enter as a percentage, e.g. 8 for 8% annual growth.

Formula

FV = 1,000 × (1 + 0.08)10 = 2,158.925

Results

Final Value2,158.925after 10 years
Initial Value1,000starting amount
Total Growth1,158.925115.89% increase
Doubling Time9.01 yearstime to 2× value
Growth Rate8% per years
Periods10 years
Multiplier×2.1589
Total Percentage Gain115.89%
Final Value2,158.925

Growth over Time

Bar height is proportional to value at each period (showing up to 50 periods).

Period 1Period 10

Period Table

Step-by-step breakdown of value, per-period growth, and cumulative growth for each of the 10 years.

Reference

Exponential Growth Formula
FV = PV × (1 + r)^n — where PV is the present (initial) value, r is the per-period growth rate as a decimal, and n is the number of periods.
Growth Rate
The percentage or decimal rate at which the value increases each period. A rate of 8% means each period's value is 1.08× the previous.
Doubling Time
The number of periods required for the value to double, calculated as ln(2) / ln(1 + r). The Rule of 72 approximates this as 72 / rate%.
Exponential Decay
When the growth rate is negative (between −100% and 0%), the formula models decay. The half-life is the time for the value to halve: ln(0.5) / ln(1 + r).
Compound Interest
A direct application of exponential growth — e.g. an investment growing at 7% per year for 30 years: FV = PV × (1.07)^30.
Applications
Population growth, compound interest, radioactive decay, viral spread, bacterial growth, depreciation, inflation, and Moore's Law.
About

The exponential growth calculator computes the final value of any quantity that grows (or shrinks) at a constant per-period rate using the formula FV = PV × (1 + r)^n. Whether you are projecting compound investment returns, modeling population increase, estimating viral spread, or calculating radioactive decay, enter your initial value, growth rate, and number of periods to get an instant, precise answer with a full period-by-period breakdown.

FAQ
What is the exponential growth formula?+

The formula is FV = PV × (1 + r)^n, where FV is the final value, PV is the initial (present) value, r is the per-period growth rate expressed as a decimal (e.g. 0.08 for 8%), and n is the number of periods. Each period multiplies the previous value by (1 + r).

How do I calculate doubling time?+

The exact doubling time is ln(2) / ln(1 + r) periods. A quick approximation is the Rule of 72: divide 72 by the percentage growth rate. For example, at 8% per year the doubling time is roughly 72 ÷ 8 = 9 years (exact: 9.006 years).

Can this calculator handle exponential decay?+

Yes. Enter a negative growth rate (between −100% and 0%) to model decay. The tool will compute the final value and show the half-life — the number of periods required for the quantity to fall to half its starting value — using the formula ln(0.5) / ln(1 + r).

What real-world situations use exponential growth?+

Common examples include compound interest on investments, population growth, bacterial or viral spread, radioactive decay (as negative growth), inflation, asset depreciation, and Moore's Law doubling of transistor counts. Any process where a quantity changes by a fixed percentage each time step follows exponential growth.

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