Exponential Growth Prediction Calculator
Given a starting value and one observed measurement, this calculator fits an exponential growth (or decay) model and predicts the value at any future or past time. Useful for population forecasting, bacterial growth, radioactive decay, and financial projections.
Value predicted by the fitted exponential model
- 1
Growth rate r = ln(Pₜ ÷ P₀) ÷ t₁
ln(200 ÷ 100) ÷ 5 = 0.138629 - 2
r × t₂
0.138629 × 10 = 1.386294 - 3
e^(r × t₂)
e^(1.386294) = 4 - 4
Predicted value = P₀ × e^(r × t₂)
100 × 4 = 400
How does this calculator work?
Two data points (P₀ at t = 0, Pt at t = t₁) uniquely determine a continuous exponential model: r = ln(Pt/P₀)/t₁, then predict P(t₂) = P₀·e^(r·t₂). The calculator also shows the growth rate per period, doubling time (growth) or half-life (decay), and a plot of the fitted curve.
Formula
How this is calculated
The calculator fits a continuous exponential model P(t) = P₀ · e^(rt) to exactly two known data points: the initial value P₀ at time 0 and an observed value Pt at time t₁. From these two points the growth rate r is uniquely determined as r = ln(Pt / P₀) / t₁. A positive r means growth; a negative r means decay. The predicted value at any other time t₂ is then P₀ · e^(r·t₂).
This is a single-rate, single-model extrapolation. It assumes the growth rate r is constant throughout — a strong assumption that is realistic only over limited time windows. Bacterial populations, early-stage viral spread, and radioactive decay approximately follow this model; long-term human populations and economies deviate significantly because rates change over time.
The doubling time (for growth, r > 0) is ln(2) / r; the half-life (for decay, r < 0) is ln(2) / |r|. Both are shown automatically. Because only two points are used, there is no goodness-of-fit metric — for multi-point data, use the exponential regression calculator instead.
Frequently asked questions
The calculator handles decay automatically. If Pt < P₀, the computed rate r will be negative, giving an exponential decay model P(t) = P₀·e^(rt) with t < 0. The half-life is shown in the secondary stats.
Very accurate if the quantity truly grows exponentially at a constant rate. In practice, a two-point fit offers no way to detect curvature or rate changes. For better accuracy, collect more observations and use the exponential regression calculator to fit and assess goodness-of-fit via R².
Any consistent unit — years, days, hours, seconds. Enter t₁ and t₂ in the same unit, and the computed rate r will be expressed per that unit. The predicted value is unitless (or in whatever unit your P values are).
Also known as
TG we-Calculate Editorial Team. (2026). Exponential Growth Prediction Calculator [Online calculator]. TG we-Calculate. https://we-calculate.com/calculator/exponential-growth-prediction-calculator
TG we-Calculate Editorial Team. "Exponential Growth Prediction Calculator." TG we-Calculate. 2026. https://we-calculate.com/calculator/exponential-growth-prediction-calculator.
TG we-Calculate Editorial Team, "Exponential Growth Prediction Calculator," TG we-Calculate, 2026. [Online]. Available: https://we-calculate.com/calculator/exponential-growth-prediction-calculator
@misc{wecalculate_exponential_growth_prediction_calculator, title = {Exponential Growth Prediction Calculator}, author = {{TG we-Calculate Editorial Team}}, howpublished = {\url{https://we-calculate.com/calculator/exponential-growth-prediction-calculator}}, year = {2026}, note = {TG we-Calculate} }
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