Simple & Exponential Moving Average (SMA/EMA)
Calculate trailing SMA and SMA-seeded EMA, compare all points on a line chart and export the complete series as CSV.
About this simple & exponential moving average (sma/ema)
Calculate trailing SMA and SMA-seeded EMA, compare all points on a line chart and export the complete series as CSV Computes exact algebraic and numerical metrics directly in your browser using IEEE 754 precision without round-trip latency.
Formula & calculation mechanics
The execution engine processes input tokens and applies transformations in the browser sandbox. Specifically, Trailing SMA[i] = sum(values[i−N+1…i])/N. EMA uses α=2/(N+1), starts at SMA[N−1], then EMA[i]=(1−α)EMA[i−1]+α·values[i]. Both are unavailable before N points; N=1 returns the original values. Input order is preserved, with equally spaced observations and no automatic date parsing. Different EMA initialisation conventions can give different results.
Worked numerical calculation
Scenario: What should the example produce?
Sample input:
Processing: Enter the values and integer window N. Calculate, compare the lines and select any table page. Download the complete results as CSV.
Illustrative output:
Domain range & precision boundaries
1–20000 finite points, at most 1000000 UTF-16 code units. N is a positive safe integer (at most 32 input characters); N larger than the series gives no complete averages. Native binary64 arithmetic, O(n) calculation, compensated rolling SMA. Rounding and underflow are possible; intermediate overflow is rejected. These are historical smoothing indicators, not forecasts or trading signals. No file or usage quota. Local browser calculation with no added calculation dependency, fee or external service. Works offline after loading. All points are plotted in input order without sampling. The horizontal axis is the 1-based index; all three lines share one vertical scale. Missing initial averages are not drawn. The table exposes every point, 200 rows per page; overlapping lines may coincide. CSV includes every point, not just the displayed page: index,value,sma,ema. UTF-8, comma separators, CRLF, decimal point and full serialized numeric precision. Missing averages are empty fields; index starts at 1.
Calculations in Simple & Exponential Moving Average (SMA/EMA) use standard IEEE 754 precision or exact rational models. Verify significant accounting or tax figures with authoritative references.
In-browser calculation boundary
Formula calculations and numeric evaluations in Simple & Exponential Moving Average (SMA/EMA) run synchronously in the browser JavaScript engine with zero server telemetry.
Mathematical formulas & precision standards
Mathematical constants, IEEE 754 floating-point standards, and numerical analysis specifications:
Simple & Exponential Moving Average (SMA/EMA) verification · Audit standards
How to use it
- Enter, paste, or select your input data into the Simple & Exponential Moving Average (SMA/EMA) workspace controls.
- Review parameter fields, units, or options configured for Simple & Exponential Moving Average (SMA/EMA).
- Click the action button or observe immediate live calculations rendered by Simple & Exponential Moving Average (SMA/EMA).
Frequently asked questions
How are SMA and EMA defined?+
Trailing SMA[i] = sum(values[i−N+1…i])/N.
What does the chart show?+
Boundary constraints concerning "What does the chart show?" prevent invalid parameter state mutations client-side.
What precision and limits apply?+
No file or usage quota.
What should the example produce?+
CSV has five data rows.