Need to project data that's slowing down? This logarithmic extrapolation calculator fits a logarithmic curve to your data, ideal for diminishing returns scenarios.
Logarithmic Extrapolation Calculator
Using the calculator
Enter at least two data points with positive X values, then specify your target X. The calculator fits a logarithmic curve and projects the Y value.
You'll see the R² fit quality and the equation y = a + b × ln(x) being used.
Heads up: Logarithmic fits require X > 0 (zeros and negatives can't be log-transformed). And the farther you project, the less reliable the estimate.
What is logarithmic extrapolation?
Logarithmic extrapolation models diminishing returns — large early gains that taper off over time. The formula:
y = a + b \times \ln(x)
Growth continues forever but at an ever-decreasing rate. Doubling X adds a constant amount to Y rather than doubling it.
When to use logarithmic extrapolation
Logarithmic extrapolation works best for:
- Learning curves: Skill improvement that plateaus
- Market saturation: Product adoption or pandemics that slow as a susceptible population runs out (see, uhh, COVID-19 and logarithmic growth charts)
- Diminishing returns: Additional inputs yielding smaller outputs
So: virus susceptibility, product growth... different causes, similar curve: both pandemics and products can slow as the available pool runs out.
For constant growth, use linear extrapolation. For percentage growth, use exponential extrapolation.
