Exponential Moving Average (EMA): Definition and Formula

Definitions

In plain terms

An EMA remembers its previous value and moves part of the way toward each new observation, so recent data matters more while older data fades gradually.

Technical

An EMA updates as EMA_t = EMA_(t-1) + alpha times (z_t - EMA_(t-1)), where alpha is a dimensionless smoothing constant between zero and one.

Scope

The recurrence does not by itself choose the seed, missing-data policy, rounding policy, or period label; those must be declared separately.

Formula

EMA_t = EMA_(t-1) + alpha * (z_t - EMA_(t-1))

LaTeX: EMA_t = EMA_{t-1} + \alpha\left(z_t-EMA_{t-1}\right)

Symbol	Meaning	Unit
`EMA_t`	Updated exponential moving average	same as input
`EMA_{t-1}`	Previous exponential moving average	same as input
`z_t`	Current observation	input unit
`\alpha`	Smoothing constant	dimensionless

Output unit: same as input

Examples

With prior EMA 80, new input 100, and alpha 0.10, the updated EMA is 82.

Common misconceptions

Older observations do not fall out of a standard EMA after exactly N periods.

Concept relationships

Prerequisites

Smoothing Constant

Required by

Where this concept is used

Evidence and governance

Calculating the McClellan Oscillator McClellan Financial Publications · first party methodology
Supports: preferred label, short definition, technical definition, formula, units
Limits: Does not prescribe one universal initialization, missing-session, revision-resolution, rounding, or software interface policy.
McClellan Oscillator StockCharts ChartSchool · secondary methodology
Supports: variant distinction
Limits: Platform symbols, displayed thresholds, universe choices, and implementation details are vendor-specific rather than universal methodology requirements.

Reviewed by: fintech-builder-owner-approved
Last reviewed: 2026-07-26
Next review: 2027-07-26
Record status: published

Exponential Moving Average