Forecasting Calculator (Moving Average & Exponential Smoothing)
Free forecasting calculator for time series. Paste your historical data and compute forecasts using simple moving average and single exponential smoothing. Get next-period forecast, error metrics (MAD, MAPE) and an inline chart.
Full original guide (expanded)
Forecasting Calculator (Moving Average & Exponential Smoothing)
Paste your historical time series (one value per line, oldest to newest) and compute forecasts using simple moving average or single exponential smoothing. The tool also shows error metrics (MAD, MAPE) for the in-sample fit.
number of periods to average
0.1=slow, 0.5=fast
Blue: actual, Orange: forecast (from first available point). Only first 24 points shown.
Next forecast
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MAD
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MAPE (%)
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Method
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| t | Actual | Forecast | Error | |Error| | |PE| % |
|---|
How the calculator works
1. Simple Moving Average
\( \hat{Y}_{t+1} = \dfrac{Y_t + Y_{t-1} + \dots + Y_{t-m+1}}{m} \)
where m is the window size.
Use this when your data is fairly stable. A larger window means smoother forecasts but slower reaction to changes.
2. Single Exponential Smoothing
\( F_t = \alpha Y_{t-1} + (1-\alpha) F_{t-1} \)
with starting \( F_1 = Y_1 \) (simple initialization).
Use this when you want the most recent data to matter more. α close to 1 makes the forecast very reactive.
Error metrics
- MAD (Mean Absolute Deviation): average of |error|.
- MAPE: average of |error|/actual, as percentage.
Formula (LaTeX) + variables + units
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\( \hat{Y}_{t+1} = \dfrac{Y_t + Y_{t-1} + \dots + Y_{t-m+1}}{m} \) where m is the window size.
\( F_t = \alpha Y_{t-1} + (1-\alpha) F_{t-1} \) with starting \( F_1 = Y_1 \) (simple initialization).
- No variables provided in audit spec.
- NIST — Weights and measures — nist.gov · Accessed 2026-01-19
https://www.nist.gov/pml/weights-and-measures - FTC — Consumer advice — consumer.ftc.gov · Accessed 2026-01-19
https://consumer.ftc.gov/
Last code update: 2026-01-19
- Initial audit spec draft generated from HTML extraction (review required).
- Verify formulas match the calculator engine and convert any text-only formulas to LaTeX.
- Confirm sources are authoritative and relevant to the calculator methodology.