Moving Average Calculator

Calculate from a Consistent Data Series

1. Enter numeric observations from oldest to newest. Commas, spaces and line breaks are separators; do not include CSV headers, dates or thousands-separator commas.
2. Choose a whole period from 1 to the number of observations. Keep a consistent interval and price definition; adjusted and unadjusted prices can produce different averages.
3. Select SMA or EMA, then Calculate. The chart uses observation index rather than dates. Editing an input clears the previous result.
4. Load Example fills and calculates a clearly synthetic series using a 5-period SMA. It is not market data or a trading result.

Formulas and Initialization

SMA gives equal weight to the latest n observations. EMA uses alpha = 2 / (n + 1); this calculator seeds it with the first n-observation SMA. Later EMA values retain a declining contribution from older data beyond the latest n observations. Results are displayed to four decimal places; the EMA recursion uses unrounded values.

For a hypothetical series 10, 12, 14, 20 and period 3, the first SMA and EMA are 12 at observation 3. The next SMA is 15.3333, while the EMA is 0.5 × 20 + 0.5 × 12 = 16.

What an Average Does Not Establish

Both averages summarize previous observations and lag new prices. An upward slope or a price crossing does not by itself demonstrate a profitable rule. This page calculates one average and does not detect a golden cross, fetch quotes, send alerts or place trades.

When comparing with a charting platform, match source prices, observation interval, period, warm-up history and EMA seed. A different initialization can explain early discrepancies without an arithmetic error.

Formula references: Fidelity SMA guide and Fidelity EMA guide.

Frequently Asked Questions