ORANGEBOT.AI

Exponential Growth/Decay Calculator

Exponential growth/decay formula: x(t) = x₀ × (1 + r)t, where x₀ is the initial value, r is the growth rate (r > 0) or decay rate (r < 0) in percent and t is the time. Enter the values and press Calculate.

The value at time t appears here after you press Calculate.

How to use this exponential growth/decay calculator

  1. Enter the initial value x₀ — the amount at time t = 0 (negative values are allowed).
  2. Enter the growth/decay rate r in percent. Positive r grows the value, negative r decays it (for example 4 means +4% per interval and -50 means it halves each interval).
  3. Enter the time t — the number of intervals. Fractions and negative times are accepted too; t = 0 simply returns the initial value.
  4. Press Calculate. The result field shows x(t) = x₀ × (1 + r)^t with up to 14 significant digits.
  5. Press Reset to clear all fields and the result.

The exponential growth/decay formula is x(t) = x₀ × (1 + r)t, where x(t) is the value at time t, x₀ is the initial value at t = 0, r is the growth rate when r > 0 or the decay rate when r < 0 (entered here in percent, so 4% = 0.04), and t is the time in intervals.

For example, starting from x₀ = 50 with a 4% growth rate over t = 90 intervals gives x(90) = 50 × (1 + 0.04)90 ≈ 1706. For decay, an initial 100 decaying at 50% per interval drops to 100 × (1 − 0.5)3 = 12.5 after 3 intervals. A rate of exactly -100% takes the value to 0, and any invalid or non-real input (such as text in a number field, or a result that overflows to infinity) is reported with a clear message instead of a silent wrong answer.

The whole calculation runs in your browser; nothing is uploaded anywhere. More math tools are in Math & Statistics.