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Exponential Moving Average Calculator

Calculate an exponential moving average and its smoothing factor.

About Exponential Moving Average Calculator

The exponential moving average never fully discards old data; weights decay geometrically instead. That gives a shorter effective lag than a simple average of the same nominal length. Because the EMA is recursive it needs only the previous value and the current observation, which makes it cheap to maintain on streaming data.

Formula

Exponential Moving Average

EMA = current × α + previous EMA × (1 − α), with α = 2 ÷ (n + 1)

α
Smoothing factor, larger values respond faster
half-life
Periods after which a value’s weight has halved

Worked example

With the default values below, Exponential Moving Average Calculator returns Exponential Moving Average of 119.53846. Change any input above and every figure here is recalculated in your browser.

Inputs used

Current period value
128
Previous EMA
118
EMA periodaccepts 1–200
12

Results

Exponential Moving Average
119.53846
Smoothing Factor
0.153846
Weight on the Current Value
15.3846%
Half-Life of the Weighting
4.149
Equivalent Simple Moving Average Length
12.00

Step by step

  1. 1Values used
  2. 2Exponential Moving Average
  3. 3Exponential Moving Average= 119.53846
  4. 4Smoothing Factor= 0.153846
  5. 5Weight on the Current Value= 15.3846
  6. 6Half-Life of the Weighting= 4.149
  7. 7Equivalent Simple Moving Average Length= 12.00

Assumptions and limits

  • The result is derived only from the 3 inputs listed above. Anything not among them is not part of the calculation.
  • In particular, this calculator does not take inflation, tax or fees or charges into account.
  • Figures are rounded for display to 6 decimal places, so totals built from several rounded parts can differ slightly from the unrounded arithmetic.

How these calculators are built and tested is described on the Methodology page. If a figure looks wrong, please report it.

Frequently Asked Questions

How is Exponential Moving Average calculated?

EMA = current × α + previous EMA × (1 − α), with α = 2 ÷ (n + 1) The exponential moving average never fully discards old data; weights decay geometrically instead. That gives a shorter effective lag than a simple average of the same nominal length.

Why does Exponential Moving Average matter?

Because the EMA is recursive it needs only the previous value and the current observation, which makes it cheap to maintain on streaming data.

What values do I need to enter?

This calculator takes 3 inputs: Current period value, Previous EMA, EMA period. The pre-filled defaults are a realistic starting point — replace them with figures from your own environment for a result you can act on.

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