Exponential Growth & Decay Calculator

Exponential growth happens when something increases by the same percentage each period, like a population or an investment; exponential decay is the same with a decreasing percentage, like a medicine leaving the body. This calculator finds the final amount, the doubling time or half-life, and draws the curve.

Try:

How to use the exponential growth & decay calculator

  1. Enter the starting amount.
  2. Enter the rate per period (use a negative rate for decay) and the number of periods.
  3. Press Calculate to see the final amount and the curve.

Formula

A=A0(1+r)tA = A_0(1 + r)^t
tdouble=ln⁡2ln⁡(1+r)t_{\text{double}} = \frac{\ln 2}{\ln(1 + r)}

Worked example: 500 growing 8% for 10 periods

  • Starting amount: 500
  • Rate per period (%) — negative for decay: 8
  • Number of periods: 10

✓ Answer checked

A≈1079.4625A \approx 1079.4625
Doubling time
9.00647 periods
Growth factor per period
1.081.08
Total change
115.892%
123456789101120040060080010001200start 500t = 10: 1079.46A(t)
Exponential growth: the amount doubles every 9.006 periods (dashed line).
Step-by-step working (3 steps)

  1. Growth factor

    A change of 8% per period means multiplying by 1.08 each period.

    1+8100=1.081 + \frac{8}{100} = 1.08

  2. Exponential formula A = A₀(1 + r)ᵗ

    Multiply the starting amount by the factor 10 times.

    A=A0(1+r)t=500×1.0810≈1079.4625A = A_0 (1 + r)^t = 500 \times 1.08^{10} \approx 1079.4625

  3. Doubling time Logarithms

    Solve (1 + r)ᵗ = 2 (or ½) with logarithms.

    t=ln⁡2ln⁡1.08≈9.00647t = \frac{\ln 2}{\ln 1.08} \approx 9.00647
Formulas used
A=A0(1+r)tA = A_0(1 + r)^t
tdouble=ln⁡2ln⁡(1+r)t_{\text{double}} = \frac{\ln 2}{\ln(1 + r)}
How this was checked
  • ✓ Working back with logarithms from the final amount gives the original number of periods.

Frequently asked questions

What is the difference between growth and decay?

Growth multiplies by more than 1 each period (a positive rate); decay multiplies by less than 1 (a negative rate).

How do I find the half-life?

Solve (1 + r)ᵗ = ½ with logarithms: t = ln(0.5) ÷ ln(1 + r).

Is this the same as compound interest?

Yes, compound interest is exponential growth. Use the compound interest calculator for interest added several times a year.

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