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Moving Average Calculator

Smooth out a series of numbers such as prices, sales or sensor readings. Paste the data, choose the window size and the type of average (simple, exponential, weighted or all three) and get the full averaged series as a table and a line chart, plus the formulas worked through with your values.

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Separate values with commas, spaces or new lines; don't use thousands separators

Between 0 and 1. Empty = 2 ÷ (N + 1)

Enter your values to see the result.
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How to use the Moving Average Calculator

  1. Paste your series in time order, oldest first, separated by commas, spaces or new lines.
  2. Set the window size, e.g. 5 for a 5-day or 3 for a 3-month moving average.
  3. Choose the type: simple, exponential, weighted, or compare all three.
  4. Read the latest average and the trend, and look at the chart.
  5. Download the CSV or copy the whole series.

Moving average formulas

TypeFormula (window N)Behaviour
Simple (SMA)(x_t + x_(t−1) + … + x_(t−N+1)) ÷ NEqual weights, smooth, lags the most
Weighted (WMA)(N·x_t + (N−1)·x_(t−1) + … + 1·x_(t−N+1)) ÷ (N(N+1)/2)Linearly more weight on recent values
Exponential (EMA)α·x_t + (1 − α)·EMA_(t−1), α = 2 ÷ (N + 1)Weights decay geometrically, reacts fastest

Worked example (window 3)

Monthly sales 120, 135, 128, 150, 162:

MonthSalesSMA(3)WMA(3)EMA(3), α = 0.5
1120———
2135———
3128127.67129.00127.67
4150137.67140.17138.83
5162146.67152.33150.42

The EMA starts from the first SMA (127.67), then 0.5 × 150 + 0.5 × 127.67 = 138.83 and 0.5 × 162 + 0.5 × 138.83 = 150.42.

Frequently asked questions

What is a simple moving average?

The simple moving average (SMA) of window N is the plain average of the last N values: (x₁ + x₂ + … + x_N) ÷ N. Each new point drops the oldest value and adds the newest, so the average “moves” along the series.

How is the exponential moving average calculated?

EMA_today = α × value_today + (1 − α) × EMA_yesterday, with α = 2 ÷ (N + 1) by default. This calculator starts the EMA with the SMA of the first N values, the most common convention. Recent values get more weight and older values fade out gradually.

What is a weighted moving average?

A linearly weighted moving average gives the newest value weight N, the one before N − 1, and so on down to 1, then divides by N(N + 1) ÷ 2. For N = 3: (3x₃ + 2x₂ + x₁) ÷ 6.

Which moving average should I use?

SMA is easiest to explain and smooths evenly. EMA and WMA react faster to recent changes, which is why traders often prefer them for prices. For forecasting or noise reduction, try several window sizes and compare.

Why are the first few values blank?

A moving average with window N needs N values, so the first N − 1 points have no complete window. The averaged series therefore starts at point N.

How do I choose the window size?

Larger windows smooth more but lag further behind changes; smaller windows follow the data closely but keep more noise. Match the window to the cycle in your data, e.g. 7 for daily data with a weekly pattern or 12 for monthly data with a yearly one.

Are all the tools on FreeToolCabin tested for quality and accuracy?

Yes! Every tool on our site undergoes automated Q/A testing in real browser environments to ensure high precision, correct output, and zero errors. If you happen to spot a bug or have a suggestion, please contact us at [email protected] and our team will review it right away.

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