Contracts with Customers - Additional Information (Details) - USD ($)	3 Months Ended
Mar. 31, 2023	Mar. 31, 2022
Revenue, Remaining Performance Obligation, Expected Timing of Satisfaction [Line Items]
Revenue recognized included contract liability	$ 78,100,000	$ 63,900,000
Impairment of contract assets	0	0
Revisions estimate	0
Impact of changes in estimated claims or incentives on revenue	5,000,000	$ 5,000,000
Remaining unsatisfied performance obligations	$ 6,100,000,000

Contract with customer adjustment to revenue impact of changes in estimated claims or incentives over threshold.

No definition available.

Name:	psn_ContractWithCustomerAdjustmentToRevenueImpactOfChangesInEstimatedClaimsOrIncentivesOverThreshold
Namespace Prefix:	psn_
Data Type:	xbrli:monetaryItemType
Balance Type:	credit
Period Type:	duration

- Definition

Amount of impairment loss for asset recognized from cost incurred to obtain or fulfill contract with customer.

+ References

Reference 1: http://www.xbrl.org/2003/role/disclosureRef
-Publisher FASB
-Name Accounting Standards Codification
-Topic 340
-SubTopic 40
-Section 50
-Paragraph 3
-Subparagraph (b)
-URI https://asc.fasb.org/extlink&oid=126905575&loc=SL49131252-203054

+ Details

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

- Definition

Amount of increase (decrease) in revenue recognized for cumulative catch-up adjustment from change in measure of progress which (increases) decreases obligation to transfer good or service to customer for which consideration from customer has been received or is due.

+ References

Reference 1: http://www.xbrl.org/2003/role/exampleRef
-Publisher FASB
-Name Accounting Standards Codification
-Topic 606
-SubTopic 10
-Section 50
-Paragraph 10
-Subparagraph (b)
-URI https://asc.fasb.org/extlink&oid=126920106&loc=SL49130551-203045

+ Details

Name:	us-gaap_ContractWithCustomerLiabilityCumulativeCatchUpAdjustmentToRevenueChangeInMeasureOfProgress
Namespace Prefix:	us-gaap_
Data Type:	xbrli:monetaryItemType
Balance Type:	credit
Period Type:	duration

- Definition

Amount of revenue recognized that was previously included in balance of obligation to transfer good or service to customer for which consideration from customer has been received or is due.

+ References

Reference 1: http://www.xbrl.org/2003/role/disclosureRef
-Publisher FASB
-Name Accounting Standards Codification
-Topic 606
-SubTopic 10
-Section 50
-Paragraph 8
-Subparagraph (b)
-URI https://asc.fasb.org/extlink&oid=126920106&loc=SL49130549-203045

+ Details

Name:	us-gaap_ContractWithCustomerLiabilityRevenueRecognized
Namespace Prefix:	us-gaap_
Data Type:	xbrli:monetaryItemType
Balance Type:	credit
Period Type:	duration

- Definition

Amount of transaction price allocated to performance obligation that has not been recognized as revenue.

+ References

Reference 1: http://www.xbrl.org/2003/role/disclosureRef
-Publisher FASB
-Name Accounting Standards Codification
-Topic 606
-SubTopic 10
-Section 50
-Paragraph 13
-Subparagraph (a)
-URI https://asc.fasb.org/extlink&oid=126920106&loc=SL49130556-203045

+ Details

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

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