Moving Average Calculator: Simple, Weighted and Exponential Moving Averages with Chart

Smooth noisy data with a moving average.

Calculated from standard textbook formulas, with every step shown. The formulas are fixed, so the working does not need checking: what matters is the numbers you type in. Use these calculators only if you are competent to choose the inputs (loads, material strength, dimensions, supports) and check your units and assumptions. For learning and checking your own working: design and sign-off are for a qualified engineer. Drafting Central does not store the numbers you type.

How this calculator works

Type the values in time order.

Choose the window and the exponential smoothing factor.

The calculator gives the latest averages, the whole series and a chart.

Formulas used

  • SMA_t = \frac{1}{w}\sum_{i=0}^{w-1}x_{t-i}
  • WMA = \frac{\sum i\,x_i}{\sum i}
  • EMA_t = \alpha x_t + (1 - \alpha)EMA_{t-1}

Worked example

With the default numbers in the calculator above:

  1. Number of values: 10
  2. Mean of all the values: 15.3
  3. Simple moving average of the last window: 19
  4. Weighted moving average of the last window (newest counts most): 19.6667
  5. Exponential moving average at the last value: 19.4219
  6. Simple moving average along the series: 11.667, 12.333, 13.333, 14.333, 16.333, 17, 18, 19

Change the numbers in the calculator to see the full working, every step, for your own case.

Common questions

What is a moving average?

The mean of the most recent values, recalculated as each new value arrives. It smooths out short-term noise.

How is the exponential average different?

It gives the newest value the most weight and older values less and less, so it reacts faster to change.

How long should the window be?

A longer window smooths more but lags more. Pick it to match the time scale of the changes you care about.

Related calculators

Got a question about this? Ask an engineering question and get a plain-language answer with references.

Further reading: Any statistics or signal processing text (moving averages and smoothing).

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