# Moving Average Calculator

Free moving average calculator. Compute simple (SMA) and exponential (EMA) moving averages from your time series data to identify trends and smooth.

## What this calculates

Calculate simple moving averages (SMA) and exponential moving averages (EMA) from time series data. Moving averages smooth out short-term noise to reveal underlying trends, and are widely used in finance, economics, and quality control.

## Inputs

- **Number of Values** — min 3, max 10 — Number of data points in the series (3-10).
- **Window Size** — min 2, max 10 — Number of periods for the moving average.
- **Type** — options: Simple (SMA), Exponential (EMA) — SMA weights all periods equally; EMA gives more weight to recent values.
- **Value 1 (oldest)** — Data point (chronological order, oldest first).
- **Value 2** — Data point.
- **Value 3** — Data point.
- **Value 4** — Data point.
- **Value 5** — Data point.
- **Value 6** — Data point.
- **Value 7 (newest)** — Data point.
- **Value 8** — Data point.
- **Value 9** — Data point.
- **Value 10** — Data point.

## Outputs

- **Latest SMA** — Most recent simple moving average value.
- **Latest EMA** — Most recent exponential moving average value.
- **All Moving Averages** — formatted as text — Moving average values for each eligible period.
- **Trend Direction** — formatted as text — Whether the series is trending up, down, or flat.

## Details

A simple moving average (SMA) is the unweighted mean of the previous n data points. For each new period, the oldest value drops out and the newest value enters the calculation: SMA = (V1 + V2 + ... + Vn) / n. This gives equal weight to all values in the window.

An exponential moving average (EMA) applies more weight to recent observations using a smoothing factor k = 2 / (n + 1). The formula is EMA_today = Value_today * k + EMA_yesterday * (1 - k). This makes the EMA more responsive to recent changes than the SMA, which is why traders often prefer it for short-term analysis.

Choosing the right window size is a trade-off. Shorter windows (e.g., 3-5 periods) respond quickly to changes but may amplify noise. Longer windows (e.g., 20-50 periods) provide smoother curves but lag behind actual trends. In stock trading, the 50-day and 200-day moving averages are classic benchmarks.

## Frequently Asked Questions

**Q: What is the difference between SMA and EMA?**

A: SMA gives equal weight to all values in the window. EMA gives exponentially more weight to recent values, making it faster to respond to new data. EMA is preferred when recent changes are more important than older observations.

**Q: How do I choose the right window size?**

A: Smaller windows (3-5) capture short-term trends but are noisy. Larger windows (10-50) show long-term trends but respond slowly. In stock trading, 10-day and 20-day windows track short-term moves, while 50-day and 200-day windows reveal major trends.

**Q: Can moving averages predict future values?**

A: Moving averages describe past trends, not future values. However, they are used in forecasting as a baseline. When the short-term moving average crosses above the long-term one (a 'golden cross'), it is often interpreted as a bullish signal, and vice versa.

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Source: https://vastcalc.com/calculators/statistics/moving-average
Category: Statistics
Last updated: 2026-04-21