Moving Average and Exponential Smoothing Calculator
Compare trailing simple moving averages with first-value-seeded exponential smoothing for an ordered series.
YOUR CALCULATION
Result
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Calculation steps
Work through one step at a time or reveal the complete calculation. The steps use your current inputs.
How to calculate
Average each full trailing window. Seed EMA with the first observation and apply alpha to each new value and 1−alpha to the preceding EMA. Use the last smooth value as a simple one-step baseline.
SMA=sum(last window)/window; EMA₁=x₁; EMAₜ=alpha×xₜ+(1−alpha)×EMAₜ₋₁
Worked example
For 10,12,14,16,18 and window 3, the final SMA is 16. With alpha 0.5 and first-value seed, EMA is 16.125.
Assumptions and input details
1–1000 ordered equally spaced observations. Leading SMA values without a full window stay unavailable. EMA initialization is explicitly the first value, not an initial-window mean. The last smooth value is a naive constant-level next-step baseline, not a fitted trend, confidence interval or accuracy guarantee. The chart shows the last 100 observations; the table includes all.
Using this calculator
Can I enter my own problem?
Yes. Replace the example values with your own inputs. The result, calculation steps, tables and applicable diagrams update from those inputs. Blank or invalid values clear the result; example values are never silently substituted for missing inputs.
Are the results exact?
Results use floating-point arithmetic and displayed rounding. Read the formula, assumptions and any stated data precision before interpreting the result.
Is my input uploaded?
The calculation runs in your browser. No account, file upload or external AI service is required. Inputs are not saved between page reloads.
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