Commitments and contingencies disclosure.

No definition available.

Name:	kod_CommitmentsAndContingenciesDisclosureLineItems
Namespace Prefix:	kod_
Data Type:	xbrli:stringItemType
Balance Type:	na
Period Type:	duration

- Definition

Estimated capital contributions.

+ References

No definition available.

+ Details

Name:	kod_EstimatedCapitalContributions
Namespace Prefix:	kod_
Data Type:	xbrli:monetaryItemType
Balance Type:	debit
Period Type:	instant

- Definition

Manufacturing Agreement Expense

+ References

No definition available.

+ Details

Name:	kod_ManufacturingAgreementExpense
Namespace Prefix:	kod_
Data Type:	xbrli:monetaryItemType
Balance Type:	debit
Period Type:	duration

- Definition

Manufacturing agreement initial term.

+ References

No definition available.

+ Details

Name:	kod_ManufacturingAgreementInitialTerm
Namespace Prefix:	kod_
Data Type:	xbrli:durationItemType
Balance Type:	na
Period Type:	duration

- Definition

Manufacturing agreement term that can be extended.

+ References

No definition available.

+ Details

Name:	kod_ManufacturingAgreementTermThatCanBeExtended
Namespace Prefix:	kod_
Data Type:	xbrli:durationItemType
Balance Type:	na
Period Type:	duration

- Definition

Amount of contractual obligation, including but not limited to, long-term debt, capital lease obligations, operating lease obligations, purchase obligations, and other commitments.

+ References

No definition available.

+ Details

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

- Definition

Present value of lessee's discounted obligation for lease payments from operating lease.

+ References

Reference 1: http://www.xbrl.org/2003/role/disclosureRef
-Publisher FASB
-Name Accounting Standards Codification
-Topic 842
-SubTopic 20
-Section 45
-Paragraph 1
-Subparagraph (b)
-URI https://asc.fasb.org/extlink&oid=123391704&loc=SL77918627-209977

+ Details

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

- Definition

Amount of lessee's right to use underlying asset under operating lease.

+ References

Reference 1: http://www.xbrl.org/2003/role/disclosureRef
-Publisher FASB
-Name Accounting Standards Codification
-Topic 842
-SubTopic 20
-Section 45
-Paragraph 1
-Subparagraph (a)
-URI https://asc.fasb.org/extlink&oid=123391704&loc=SL77918627-209977

+ Details

Name:	us-gaap_OperatingLeaseRightOfUseAsset
Namespace Prefix:	us-gaap_
Data Type:	xbrli:monetaryItemType
Balance Type:	debit
Period Type:	instant

- Details

Name:	us-gaap_FiniteLivedIntangibleAssetsByMajorClassAxis=us-gaap_LeaseAgreementsMember
Namespace Prefix:
Data Type:	na
Balance Type:
Period Type:

- Details

Name:	us-gaap_PropertyPlantAndEquipmentByTypeAxis=kod_ClinicalAndCommercialSupplyMember
Namespace Prefix:
Data Type:	na
Balance Type:
Period Type:

- Details

Name:	us-gaap_TypeOfArrangementAxis=kod_ManufacturingAgreementMember
Namespace Prefix:
Data Type:	na
Balance Type:
Period Type:

- Details

Name:	srt_CounterpartyNameAxis=kod_LonzaMember
Namespace Prefix:
Data Type:	na
Balance Type:
Period Type:

- Details

Name:	srt_RangeAxis=srt_MaximumMember
Namespace Prefix:
Data Type:	na
Balance Type:
Period Type:

- Details

Name:	us-gaap_BalanceSheetLocationAxis=us-gaap_OtherAssetsMember
Namespace Prefix:
Data Type:	na
Balance Type:
Period Type:

Commitments and Contingencies - Additional Information (Details) $ in Thousands, SFr in Millions	1 Months Ended	6 Months Ended
	Aug. 31, 2020	Jun. 30, 2022 USD ($)	Jun. 30, 2022 CHF (SFr)	Dec. 31, 2021 USD ($)	Apr. 30, 2021 CHF (SFr)
Commitments And Contingencies Disclosure [Line Items]
Operating lease right-of-use asset		$ 63,076		$ 66,744
Lease Agreement
Commitments And Contingencies Disclosure [Line Items]
Operating lease right-of-use asset		0
Lease liabilities		0
Clinical and Commercial Supply of Drug Substance \| Manufacturing Agreement \| Lonza
Commitments And Contingencies Disclosure [Line Items]
Annual suite fees payment \| SFr					SFr 150.0
Revised estimated capital contribution \| SFr					SFr 75.0
Manufacturing agreement initial term	8 years
Clinical and Commercial Supply of Drug Substance \| Maximum \| Manufacturing Agreement \| Lonza
Commitments And Contingencies Disclosure [Line Items]
Manufacturing agreement term that can be extended	16 years
Other Assets [Member] \| Manufacturing Agreement
Commitments And Contingencies Disclosure [Line Items]
Manufacturing Agreement Expense		$ 44,100	SFr 40.0