Entered prices · three smoothing methods

Moving Average Calculator

Paste ordered prices and compare rolling simple, exponential and linear-weighted moving averages on one auditable path. Choose the EMA seed convention explicitly instead of relying on a hidden platform default.

SMA · EMA · LWMA CSV header aware Runs in your browser No trend or crossover signal

Enter the ordered price series

Oldest row first. Keep the symbol, timeframe, feed and applied-price basis consistent.

Entered

A whole number from 2 to 500; at least this many price rows are required.

The seed changes the EMA path; SMA and LWMA are unaffected.

Paste one price per row, optional label + price, or a header containing one price, close, value or applied price column. Comma, semicolon and tab delimiters are accepted.

Calculation boundary: The page preserves entered row order. It does not fetch candles, sort timestamps, fill missing periods, infer an applied price, classify trend or generate a trading signal.

Three-method moving-average audit

Moving Average Comparison 2.0.0.

Derived
No comparison calculated yetEnter at least one complete period or load the audited example.

How the three moving averages are calculated

SMA = Sum of the latest N prices ÷ N
EMA = α × Current price + (1 − α) × Previous EMA
α = 2 ÷ (N + 1)
LWMA = Σ(Price × ascending weight 1…N) ÷ [N × (N + 1) ÷ 2]

SMA gives every value in the latest complete window equal weight. LWMA gives the oldest value weight 1 and the newest value weight N. EMA recursively carries prior history through the selected seed convention.

With a first-entered-price seed, EMA begins at row one and the first N minus 1 values remain warm-up. With a first-complete-window-SMA seed, the first reportable EMA equals the first SMA. Different chart history and initialization rules can therefore produce different EMA values.

Worked example from the audited fixture

Load the example to enter prices 1, 2, 4, 8 and 16 with period 3 and the first-entered-price EMA seed. The latest SMA is 9.33333333, the EMA is 10.6875 and the LWMA is 11.33333333.

The latest three-method range is 2. The price is 6.66666667 above the SMA. These differences show how weighting and initialization affect the same entered sequence; they are not direction or entry labels.

Use and limitations

  • Use one ordered, positive price series from one consistent symbol, timeframe, feed and applied-price basis.
  • CSV headers can identify a label/date column and one price, close, value or applied-price column; other data is ignored.
  • Labels are descriptive. Dates are not parsed, sorted, deduplicated or checked for missing intervals.
  • EMA parity depends on both the chosen seed and the amount of earlier history supplied.
  • The path comparison contains no crossover, trend, momentum, forecast or trading recommendation.

Frequently asked questions

  • Enter one positive price per row, an optional label plus price, or delimited data with a header identifying one price, close, value or applied-price column. Rows remain in the entered order.
  • Each reportable SMA sums the latest N entered prices in a complete rolling window and divides by N.
  • The EMA uses alpha equal to 2 divided by N plus 1 and recursively combines the current entered price with the previous EMA.
  • Choose the convention used by the system you are auditing. First entered price preserves the earlier page convention; first complete-window SMA starts the reportable EMA at that first SMA.
  • Within each complete window, the oldest price receives weight 1 and the newest receives weight N. The weighted total is divided by N times N plus 1 divided by 2.
  • Available history, seed convention, applied price, bar order and implementation details can change the recursive path. Match those inputs before expecting parity.
  • No. Labels are descriptive and the calculator neither parses timestamps nor repairs, sorts or deduplicates the entered sequence.
  • No. The calculator reports numeric paths and differences only. It does not classify a crossover, trend, buy, sell or forecast.

Sources and methodology

Version 2.0.0 performs deterministic local arithmetic and uploads no entered values. SMMA is intentionally outside this three-method comparison.

Bollinger Bands CalculatorPlace an explicit population-deviation envelope around a rolling SMA.Return Volatility CalculatorTransform entered prices into one-period returns and sample dispersion.Adaptive Moving AverageInspect a separately governed efficiency-ratio adaptive recurrence.

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Disclaimer: The results from this tool are estimates for educational and informational purposes only and may differ from your broker's figures. This is not financial or investment advice. Trading forex and CFDs carries a high level of risk and can result in the loss of all your capital. Always verify calculations with your broker and trade within your risk tolerance.