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Exponential Smoothing Calculator

Work out exponential smoothing instantly with clear inputs, formula shown and shareable results.

About Exponential Smoothing Calculator

Simple exponential smoothing updates the level as previous forecast plus alpha times the last error, which is equivalent to an exponentially decaying weighted average of all past observations. Because there is no trend term, the forecast is flat for every horizon. Alpha controls responsiveness: the weight on an observation k periods old is alpha(1-alpha)^k, giving a half-life of ln(0.5)/ln(1-alpha).

Formula

Simple exponential smoothing

L(t) = F(t) + alpha x (A(t) - F(t)); forecast for any horizon = L(t); half-life = ln(0.5) / ln(1 - alpha)

Worked example

With the default values below, Exponential Smoothing Calculator returns Forecast for the next period of 140.100. Change any input above and every figure here is recalculated in your browser.

Inputs used

Most recent actual value
145
Previous forecast
138
Smoothing factor alphaaccepts 0.01–1
0.3
Periods ahead to projectminimum 1
3

Results

Forecast for the next period
140.100
Correction applied from the last error
2.100
Forecast at the chosen horizon
140.100
Half-life of the weighting in periods
1.94

Step by step

  1. 1Values used
  2. 2Simple exponential smoothing
  3. 3Forecast for the next period= 140.100
  4. 4Correction applied from the last error= 2.100
  5. 5Forecast at the chosen horizon= 140.100
  6. 6Half-life of the weighting in periods= 1.94

Assumptions and limits

  • The result is derived only from the 4 inputs listed above. Anything not among them is not part of the calculation.
  • In particular, this calculator does not take inflation or fees or charges into account.
  • Figures are rounded for display to 3 decimal places, so totals built from several rounded parts can differ slightly from the unrounded arithmetic.

How these calculators are built and tested is described on the Methodology page. If a figure looks wrong, please report it.

Frequently Asked Questions

How should alpha be chosen?

Fit it by minimising one-step-ahead squared error on historical data. Values from 0.1 to 0.3 suit stable series; higher values track volatile series but amplify noise.

Why is the forecast flat?

Simple smoothing models level only. Add Holt's trend term for a sloping forecast and a seasonal term for repeating patterns.

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