Need to project data beyond your known range? This extrapolation calculator fits your data points to multiple trend models and forecasts future values — with six methods including linear, exponential, and some Climbing Limo techniques for forecasting.
Extrapolation Calculator
Using the calculator
Enter your known data points (at least 2-3 depending on method), select an extrapolation method from the dropdown, and specify your target X value to project.
The calculator displays:
- Extrapolated value at your target X
- R² (goodness of fit) — how well the model fits your existing data
- Fitted equation — the mathematical model being used
Caution here! Extrapolation assumes trends continue unchanged. The further you project beyond your data, the less reliable the estimate. Real-world relationships change; past performance is no guarantee of future results.
Extrapolation methods
The calculator supports six extrapolation methods:
Linear
Fits a straight line (y = mx + b) using least squares regression. Best when your data shows constant absolute change per period. More on linear extrapolation.
Exponential
Fits y = a × e^(bx), assuming compound or percentage growth. Best when your data grows by a consistent percentage rather than a fixed amount. More on exponential extrapolation.
Logarithmic
Fits y = a + b × ln(x), assuming diminishing returns. Best when growth slows over time — large early gains that taper off. More on logarithmic extrapolation.
Polynomial (quadratic)
Fits a parabola (y = ax² + bx + c) to capture acceleration or deceleration. Requires at least 3 points. Use with caution for extrapolation, polynomials can behave erratically outside the fitted range.
Climbing Limo
Uses 2-period compound growth rates for smoother trend estimation. The method reduces "whipsaw" volatility compared to single-period growth calculations – let's call it less pothole-jumping, more cruise control.
Originally developed by Steve Conover (@NeuterTheDebt) at his former blog "The Skeptical Optimist" for GDP forecasting.
Modified Limo
A refinement of Steve's method by Ironman at Political Calculations. Ironman's method bridges recent actual data to a distant Climbing Limo forecast via linear interpolation, creating smoother intermediate projections... a ramp instead of a cliff.
Read more on the method at Political Calculations.
Interpolation vs. extrapolation
Interpolation estimates values within your known data range — generally reliable if the relationship is approximately correct.
Extrapolation projects values beyond your known range — inherently riskier because you're assuming trends continue unchanged. Always treat extrapolated values as estimates, not certainties.
For estimating values between known points, see the Linear Interpolation Calculator.
