Exponential Smoothing Calculator

Exponential smoothing blends the latest actual with the previous forecast: for sales 10, 12, 13, 12, 15, 16 with α = 0.3, the forecast for period 7 is 13.59676.

Actual values (oldest first):

Smoothing constant α (0 to 1):

Initial forecast F₁:

Usually the first actual value.

Forecast for the next period =

13.59676

Precision

Full answer, then cut to fewer decimals (not rounded):

13.59676
13.5967
13.596
13.59
13.5

MAE: 2.39784
MSE: 6.81837
RMSE: 2.6112
MAPE: 17.0851 %

Exponential smoothing, α = 0.3
Period	Actual	Forecast	Error
1	10	10	0
2	12	10	2
3	13	10.6	2.4
4	12	11.32	0.68
5	15	11.524	3.476
6	16	12.5668	3.4332
7	—	13.5968	—

Step-by-step solution

Fₜ₊₁ = α Aₜ + (1 − α) Fₜ
F7 = 0.3 × 16 + 0.7 × 12.5668 = 13.59676

Exponential Smoothing Formula

Fₜ₊₁ = α Aₜ + (1 − α) Fₜ

α smoothing constant (0–1), Aₜ actual, Fₜ forecast for period t

Worked Example

Sales of 10, 12, 13, 12, 15, 16 with α = 0.3 and F₁ = 10:

Fₜ₊₁ = α Aₜ + (1 − α) Fₜ
F7 = 0.3 × 16 + 0.7 × 12.5668 = 13.59676

MSE: 6.81837 · RMSE: 2.6112 · MAPE: 17.0851 %

Exponential smoothing, α = 0.3
Period	Actual	Forecast	Error
1	10	10	0
2	12	10	2
3	13	10.6	2.4
4	12	11.32	0.68
5	15	11.524	3.476
6	16	12.5668	3.4332
7	—	13.5968	—

Choosing the smoothing constant α

Simple exponential smoothing weights the latest actual by α and the previous forecast by 1 − α. A high α (0.5–0.9) reacts quickly to changes but also to noise; a low α (0.1–0.3) gives a steadier forecast that lags real shifts. Choose α by comparing forecast errors such as MAD or MAPE on past data. The method suits series without trend or seasonality; for those, use Holt’s or Holt–Winters smoothing.

Frequently asked questions

How do I choose α?

A larger α (e.g. 0.5–0.9) reacts faster to changes; a smaller α (0.1–0.3) smooths noise. Pick the α with the lowest error on past data.

What should F₁ be?

Commonly the first actual value, or the average of the first few periods. Its influence fades as more periods are smoothed.

Does simple exponential smoothing handle trends?

No: it lags behind a trend. Holt’s method (double exponential smoothing) adds a trend term, and Holt–Winters adds seasonality.

Sources

NIST/SEMATECH e-Handbook of Statistical Methods, National Institute of Standards and Technology .

Last reviewed: 2026-10-15. Factors are stored exactly and computed with 50-digit decimal arithmetic. See how we verify conversion factors.

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APA

Scientific Converters. (2026, October 15). Exponential Smoothing Calculator. Retrieved October 25, 2026, from https://scientificconverters.com/calculators/exponential-smoothing-calculator/

IEEE

Scientific Converters, "Exponential Smoothing Calculator," scientificconverters.com. Accessed: Oct. 25, 2026. [Online]. Available: https://scientificconverters.com/calculators/exponential-smoothing-calculator/