Share Transactions - Share repurchases (Details) - Common shares shares in Millions, $ in Millions	3 Months Ended
Mar. 31, 2022 USD ($) shares
Class of Stock [Line Items]
Cumulative number of shares acquired since inception of share repurchase program \| shares	426.2
Aggregate purchase price of shares acquired since inception of share repurchase program	$ 5,540.0
Treasury stock, shares acquired (shares) \| shares	5.6
Shares repurchased for treasury	$ 255.0
Remaining authorized repurchase amount	$ 927.2

Cumulative number of shares that have been repurchased since the inception of the share repurchase program.

No definition available.

Name:	acgl_TreasuryStockSharesAcquiredCumulativeSinceInception
Namespace Prefix:	acgl_
Data Type:	xbrli:sharesItemType
Balance Type:	na
Period Type:	duration

- Definition

Aggregate cumulative purchase price of common and preferred stock that have been repurchased since the inception of the share repurchase program.

+ References

No definition available.

+ Details

Name:	acgl_TreasuryStockValueAcquiredCumulativeSinceInception
Namespace Prefix:	acgl_
Data Type:	xbrli:monetaryItemType
Balance Type:	debit
Period Type:	duration

- Definition

Line items represent financial concepts included in a table. These concepts are used to disclose reportable information associated with domain members defined in one or many axes to the table.

+ References

No definition available.

+ Details

Name:	us-gaap_ClassOfStockLineItems
Namespace Prefix:	us-gaap_
Data Type:	xbrli:stringItemType
Balance Type:	na
Period Type:	duration

- Definition

Amount remaining of a stock repurchase plan authorized.

+ References

No definition available.

+ Details

Name:	us-gaap_StockRepurchaseProgramRemainingAuthorizedRepurchaseAmount1
Namespace Prefix:	us-gaap_
Data Type:	xbrli:monetaryItemType
Balance Type:	credit
Period Type:	instant

- Definition

Number of shares that have been repurchased during the period and are being held in treasury.

+ References

Reference 1: http://fasb.org/us-gaap/role/ref/legacyRef
-Publisher FASB
-Name Accounting Standards Codification
-Topic 505
-SubTopic 10
-Section 50
-Paragraph 2
-URI http://asc.fasb.org/extlink&oid=123467817&loc=d3e21463-112644

Reference 2: http://fasb.org/us-gaap/role/ref/legacyRef
-Publisher FASB
-Name Accounting Standards Codification
-Topic 505
-SubTopic 10
-Section S99
-Paragraph 1
-Subparagraph (SX 210.3-04)
-URI http://asc.fasb.org/extlink&oid=120397183&loc=d3e187085-122770

Reference 3: http://fasb.org/us-gaap/role/ref/legacyRef
-Publisher FASB
-Name Accounting Standards Codification
-Topic 210
-SubTopic 10
-Section S99
-Paragraph 1
-Subparagraph (SX 210.5-02(29))
-URI http://asc.fasb.org/extlink&oid=120391452&loc=d3e13212-122682

+ Details

Name:	us-gaap_TreasuryStockSharesAcquired
Namespace Prefix:	us-gaap_
Data Type:	xbrli:sharesItemType
Balance Type:	na
Period Type:	duration

- Definition

Equity impact of the cost of common and preferred stock that were repurchased during the period. Recorded using the cost method.

+ References

Reference 1: http://fasb.org/us-gaap/role/ref/legacyRef
-Publisher FASB
-Name Accounting Standards Codification
-Topic 505
-SubTopic 10
-Section 50
-Paragraph 2
-URI http://asc.fasb.org/extlink&oid=123467817&loc=d3e21463-112644

Reference 2: http://fasb.org/us-gaap/role/ref/legacyRef
-Publisher FASB
-Name Accounting Standards Codification
-Topic 505
-SubTopic 30
-Section 45
-Paragraph 1
-URI http://asc.fasb.org/extlink&oid=6405813&loc=d3e23239-112655

Reference 3: http://fasb.org/us-gaap/role/ref/legacyRef
-Publisher FASB
-Name Accounting Standards Codification
-Topic 505
-SubTopic 10
-Section S99
-Paragraph 1
-Subparagraph (SX 210.3-04)
-URI http://asc.fasb.org/extlink&oid=120397183&loc=d3e187085-122770

+ Details

Name:	us-gaap_TreasuryStockValueAcquiredCostMethod
Namespace Prefix:	us-gaap_
Data Type:	xbrli:monetaryItemType
Balance Type:	debit
Period Type:	duration

- Details

Name:	us-gaap_StatementClassOfStockAxis=us-gaap_CommonStockMember
Namespace Prefix:
Data Type:	na
Balance Type:
Period Type: