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Fair Value Measurements (Additional Information) (Details) - USD ($) $ in Millions	12 Months Ended
	Jun. 29, 2024	Jun. 24, 2023	Jun. 29, 2023
Defined Benefit Plan Disclosure [Line Items]
Cash held in bank	$ 238.4		$ 853.9
Level 1, 2 or 3 Member
Defined Benefit Plan Disclosure [Line Items]
Asset transfer	$ 0.0	$ 0.0

X

- Definition

Cash held in bank

+ References

No definition available.

+ Details

Name:	syna_CashHeldInBank
Namespace Prefix:	syna_
Data Type:	xbrli:monetaryItemType
Balance Type:	debit
Period Type:	instant

X

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

X

- Definition

Amount of transfer of financial instrument classified as an asset into (out of) level 3 of the fair value hierarchy.

+ References

No definition available.

+ Details

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

X

- Details

Name:	us-gaap_FairValueByFairValueHierarchyLevelAxis=us-gaap_FairValueInputsLevel12And3Member
Namespace Prefix:
Data Type:	na
Balance Type:
Period Type: