Exponential Growth Prediction Calculator (fit a growth rate to your data, then forecast)

Understanding the exponential growth prediction calculator — concept and principle

This calculator fits a constant growth rate to a series of observed values taken at equal time steps and uses it to forecast ahead. It reports the fitted growth per period, the fitted values, R² of the fit, the doubling time and a comparison with the simple first-to-last average rate. Use it for sales, users, prices or populations that have been growing by a roughly steady percentage.

How it is calculated

Model: y_t = y₀·e^(kt), so ln y_t = ln y₀ + k·t, a straight line

Fit that line by least squares with t = 0, 1, 2, …

Growth per period r = e^k − 1; doubling time = ln 2 ÷ k

Forecast h periods after the last of n values = y₀·e^(k(n − 1 + h))

Simple average rate = (last ÷ first)^(1/(n − 1)) − 1

• R² of the log fit shows how close the data are to a constant rate.

The principle

Constant percentage growth becomes a straight line on a logarithmic scale. Fitting that line uses every observation, so one unusual value has less effect than in the simple first-to-last calculation, which ignores everything in between. The slope of the line is the continuous rate k, and the exponential of the intercept is the fitted starting level.

Worked example

Default inputs: 1,200, 1,350, 1,490, 1,700, 1,880, 2,110; predict 6 periods ahead.

1. Fitted growth per period = 11.94 %; fitted starting value 1,200.84; fitted last value 2,110.46.
2. R² of the log-linear fit = 0.9991, very close to steady growth.
3. Doubling time = 6.146 periods.
4. Forecast 6 periods after the last value (t = 11): 1,200.84 × 1.1194¹¹ = 4,151.91.
5. Simple average growth first → last = 11.95 %, giving 4,153.4 for comparison.

How to read the result

The two methods agree here because the data are smooth. A large gap between them would mean the middle values do not follow the trend. Treat forecasts far ahead with caution: six periods ahead is already more than half the length of the data, and small changes in the rate compound quickly.

Common mistakes

• Using unequal time steps between observations.
• Forecasting far beyond the observed range.
• Including zero or negative values, which have no logarithm.
• Assuming a high R² guarantees the trend will continue.

Frequently asked questions

How do I predict exponential growth from data?

Fit a straight line to the logarithms of the values, then extend it and convert back.

Why not just use the first and last values?

That ignores the values in between; the fit uses all of them.

What does R² tell me here?

How closely the data follow a constant percentage growth rate.

Sources: NIST/SEMATECH e-Handbook of Statistical Methods, §4.1.4.1 Linear Least Squares Regression