Exponential Growth Calculator
Enter a starting amount, growth rate, and number of periods below to instantly get the final amount.
The Exponential Growth Formula
A = P(1 + r)ᵗ
Exponential growth compounds — each period's growth is applied to an ever-larger base — which is fundamentally different from linear growth, where the same fixed amount is added every period. Two quantities that start identical and grow at the "same rate" can end up wildly different if one grows exponentially and the other linearly.
Worked example
$1,000 growing at 5% per period, for 10 periods.
A = 1000 × (1.05)¹⁰ = 1000 × 1.6289
Final amount ≈ $1,628.89
A second example, modeling decay with a negative rate: $1,000 declining at 10% per period, for 5 periods.
A = 1000 × (0.9)⁵ = 1000 × 0.59049
Final amount ≈ $590.49
Common mistake
It's easy to assume 5% growth for 10 periods adds up to 5% × 10 = 50% total growth. It doesn't — because each period compounds on a larger base, 10 periods of 5% growth works out to about 62.9% total growth (1.05¹⁰ ≈ 1.6289), well above the simple sum.
Keep going
- Exponential growth is repeated exponentiation applied over time; the exponent calculator shows that single base-and-power calculation on its own. Exponent Calculator
Frequently Asked Questions
What is the exponential growth formula?
A = P(1 + r)ᵗ, where P is the starting amount, r is the growth rate per period (as a decimal), and t is the number of periods.
How do you model decay instead of growth?
Use a negative rate. The same formula A = P(1 + r)ᵗ works for decay when r is negative — for example, r = −0.1 for 10% decay per period.
What's a real example of exponential growth?
Compound interest, population growth, and viral spread all follow this pattern — the amount added each period grows because it's a percentage of an already-larger total.
How long does it take for exponential growth to double?
Roughly, divide 70 by the growth rate percentage — the 'rule of 70.' At 5% growth per period, doubling takes about 70 ÷ 5 = 14 periods. It's a well-known approximation, not an exact formula.
Does 5% growth for 10 periods mean 50% total growth?
No. Because each period's growth applies to a larger base than the last, 10 periods of 5% growth compounds to about 62.9% total growth, not 5% × 10 = 50%.
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