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Balance Sheet Components - Schedule of Other Accrued Liabilities (Details) - USD ($) $ in Millions	Mar. 29, 2025	Jun. 29, 2024
Payables and Accruals [Abstract]
Customer obligations	$ 58.3	$ 58.2
Inventory obligations	6.3	5.6
Operating lease liabilities	11.6	11.5
Income taxes payable	3.4	42.2
Other	31.2	38.8
Other accrued liabilities	$ 110.8	$ 156.3

X

- Definition

Accrued liabilities for inventory purchase.

+ References

No definition available.

+ Details

Name:	syna_AccruedLiabilitiesForInventoryPurchase
Namespace Prefix:	syna_
Data Type:	xbrli:monetaryItemType
Balance Type:	credit
Period Type:	instant

X

- Definition

Customer obligation.

+ References

No definition available.

+ Details

Name:	syna_CustomerObligation
Namespace Prefix:	syna_
Data Type:	xbrli:monetaryItemType
Balance Type:	credit
Period Type:	instant

X

- Definition

Carrying value as of the balance sheet date of obligations incurred and payable, pertaining to costs that are statutory in nature, are incurred on contractual obligations, or accumulate over time and for which invoices have not yet been received or will not be rendered. Examples include taxes, interest, rent and utilities. Used to reflect the current portion of the liabilities (due within one year or within the normal operating cycle if longer).

+ References

Reference 1: http://fasb.org/us-gaap/role/ref/legacyRef
-Topic 210
-SubTopic 10
-Name Accounting Standards Codification
-Section S99
-Paragraph 1
-Subparagraph (SX 210.5-02(20))
-Publisher FASB
-URI https://asc.fasb.org/1943274/2147480566/210-10-S99-1

+ Details

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

X

- Definition

Present value of lessee's discounted obligation for lease payments from operating lease, classified as current.

+ References

Reference 1: http://www.xbrl.org/2003/role/disclosureRef
-Topic 842
-SubTopic 20
-Name Accounting Standards Codification
-Section 45
-Paragraph 1
-Subparagraph (b)
-Publisher FASB
-URI https://asc.fasb.org/1943274/2147479041/842-20-45-1

+ Details

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

X

- Definition

Amount of expenses incurred but not yet paid classified as other, due within one year or the normal operating cycle, if longer.

+ References

Reference 1: http://fasb.org/us-gaap/role/ref/legacyRef
-Topic 210
-SubTopic 10
-Name Accounting Standards Codification
-Section S99
-Paragraph 1
-Subparagraph (SX 210.5-02(20))
-Publisher FASB
-URI https://asc.fasb.org/1943274/2147480566/210-10-S99-1

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

X

- References

No definition available.

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

X

- Definition

Carrying value as of the balance sheet date of obligations incurred and payable for statutory income, sales, use, payroll, excise, real, property and other taxes. Used to reflect the current portion of the liabilities (due within one year or within the normal operating cycle if longer).

+ References

Reference 1: http://fasb.org/us-gaap/role/ref/legacyRef
-Topic 210
-SubTopic 10
-Name Accounting Standards Codification
-Section S99
-Paragraph 1
-Subparagraph (SX 210.5-02(20))
-Publisher FASB
-URI https://asc.fasb.org/1943274/2147480566/210-10-S99-1

Reference 2: http://fasb.org/us-gaap/role/ref/legacyRef
-Topic 210
-SubTopic 10
-Name Accounting Standards Codification
-Section S99
-Paragraph 1
-Subparagraph (SX 210.5-02(19))
-Publisher FASB
-URI https://asc.fasb.org/1943274/2147480566/210-10-S99-1

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Data Type:	xbrli:monetaryItemType
Balance Type:	credit
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