The difference between Changeable and Variable

When used as adjectives, changeable means capable of being changed, whereas variable means able to vary.

Variable is also noun with the meaning: something that is variable.

check bellow for the other definitions of Changeable and Variable

Changeable as an adjective:

Capable of being changed.
Changeable as an adjective:

Subject to sudden or frequent changes.

Examples:

"The weather is very changeable today: we've had bright sunshine, clouds, wind and rain in the same half-hour."

Variable as an adjective:

Able to vary.

Examples:

"variable winds or seasons; a variable quantity"
Variable as an adjective:

Likely to vary.
Variable as an adjective:

Marked by diversity or difference.
Variable as an adjective (mathematics):

Having no fixed quantitative value.
Variable as an adjective (biology):

Tending to deviate from a normal or recognized type.

Variable as a noun:

Something that is variable.
Variable as a noun:

Something whose value may be dictated or discovered.

Examples:

"There are several variables to consider here."
Variable as a noun (mathematics):

A quantity that may assume any one of a set of values.
Variable as a noun (mathematics):

A symbol representing a variable.
Variable as a noun (programming):

A named memory location in which a program can store intermediate results and from which it can read them.
Variable as a noun (astronomy):

A variable star.
Variable as a noun (nautical):

A shifting wind, or one that varies in force.
Variable as a noun (nautical, in the plural):

Those parts of the sea where a steady wind is not expected, especially the parts between the trade-wind belts.