Annual Fund Operating Expenses - First Trust Small Cap Value AlphaDEX Fund - First Trust Small Cap Value AlphaDEX Fund	Dec. 01, 2021
Operating Expenses:
Management Fees	0.70%
Distribution and Service (12b-1) Fees	none
Other Expenses	none
Acquired Fund Fees and Expenses	0.01%
Total Annual Fund Operating Expenses	0.71%

Total Annual Fund Operating Expenses.

Reference 1: http://www.xbrl.org/2003/role/presentationRef
-Publisher SEC
-Name Form
-Number N-1A
-Chapter A
-Section 3
-Subsection table
-Paragraph 1
-Subparagraph 11

+ Details

Name:	rr_AcquiredFundFeesAndExpensesOverAssets
Namespace Prefix:	rr_
Data Type:	rr:NonNegativePure4Type
Balance Type:	na
Period Type:	duration

- Definition

Distribution [and/or Service] (12b-1) Fees" include all distribution or other expenses incurred during the most recent fiscal year under a plan adopted pursuant to rule 12b-1 [17 CFR 270.12b-1]. Under an appropriate caption or a subcaption of "Other Expenses," disclose the amount of any distribution or similar expenses deducted from the Fund's assets other than pursuant to a rule 12b-1 plan.

+ References

Reference 1: http://www.xbrl.org/2003/role/presentationRef
-Publisher SEC
-Name Form
-Number N-1A
-Chapter A
-Section 3
-Subsection table
-Paragraph 1
-Subparagraph 9

+ Details

Name:	rr_DistributionAndService12b1FeesOverAssets
Namespace Prefix:	rr_
Data Type:	rr:NonNegativePure4Type
Balance Type:	na
Period Type:	duration

- Definition

Total Annual Fund Operating Expenses. If the Fund is a Feeder Fund, reflect the aggregate expenses of the Feeder Fund and the Master Fund in a single fee table using the captions provided. In a footnote to the fee table, state that the table and Example reflect the expenses of both the Feeder and Master Funds. If the prospectus offers more than one Class of a Multiple Class Fund or more than one Feeder Fund that invests in the same Master Fund, provide a separate response for each Class or Feeder Fund. Base the percentages of "Annual Fund Operating Expenses" on amounts incurred during the Fund's most recent fiscal year, but include in expenses amounts that would have been incurred absent expense reimbursement or fee waiver arrangements. If the Fund has changed its fiscal year and, as a result, the most recent fiscal year is less than three months, use the fiscal year prior to the most recent fiscal year as the basis for determining "Annual Fund Operating Expenses."

+ References

Reference 1: http://www.xbrl.org/2003/role/presentationRef
-Publisher SEC
-Name Form
-Number N-1A
-Chapter A
-Section 3
-Subsection instructions
-Paragraph 3
-Subparagraph d

+ Details

Name:	rr_ExpensesOverAssets
Namespace Prefix:	rr_
Data Type:	rr:NonNegativePure4Type
Balance Type:	na
Period Type:	duration

- Definition

Management Fees include investment advisory fees (including any fees based on the Fund's performance), any other management fees payable to the investment adviser or its affiliates, and administrative fees payable to the investment adviser or its affiliates that are not included as "Other Expenses."

+ References

Reference 1: http://www.xbrl.org/2003/role/presentationRef
-Publisher SEC
-Name Form
-Number N-1A
-Chapter A
-Section 3
-Subsection instructions
-Paragraph 3
-Subparagraph a

+ Details

Name:	rr_ManagementFeesOverAssets
Namespace Prefix:	rr_
Data Type:	rr:NonNegativePure4Type
Balance Type:	na
Period Type:	duration

- References

No definition available.

+ Details

Name:	rr_OperatingExpensesAbstract
Namespace Prefix:	rr_
Data Type:	xbrli:stringItemType
Balance Type:	na
Period Type:	duration

- Definition

"Other Expenses" include all expenses not otherwise disclosed in the table that are deducted from the Fund's assets or charged to all shareholder accounts. The amount of expenses deducted from the Fund's assets are the amounts shown as expenses in the Fund's statement of operations (including increases resulting from complying with paragraph 2(g) of rule 6-07 of Regulation S-X [17 CFR 210.6-07]). "Other Expenses" do not include extraordinary expenses as determined under generally accepted accounting principles (see Accounting Principles Board Opinion No. 30). If extraordinary expenses were incurred that materially affected the Fund's "Other Expenses," disclose in a footnote to the table what "Other Expenses" would have been had the extraordinary expenses been included.

+ References

Reference 1: http://www.xbrl.org/2003/role/presentationRef
-Publisher SEC
-Name Form
-Number N-1A
-Chapter A
-Section 3
-Subsection instructions
-Paragraph 3
-Subparagraph c
-Clause i

+ Details

Name:	rr_OtherExpensesOverAssets
Namespace Prefix:	rr_
Data Type:	rr:NonNegativePure4Type
Balance Type:	na
Period Type:	duration

- Details

Name:	dei_LegalEntityAxis=ftetaf_S000031807Member
Namespace Prefix:
Data Type:	na
Balance Type:
Period Type:

- Details

Name:	rr_ProspectusShareClassAxis=ftetaf_C000099062Member
Namespace Prefix:
Data Type:	na
Balance Type:
Period Type: