Goodwill and Other Intangible Assets - Components of Other Intangible Assets (Details) - USD ($) $ in Thousands	6 Months Ended
Dec. 31, 2021	Jun. 30, 2021
The components of intangible assets
Accumulated amortization	$ (159,163)	$ (153,972)
Intangible Assets, Gross (Excluding Goodwill)	272,172	274,013
Trademarks [Member]
The components of intangible assets
Gross carrying amount, Indefinite	11,257	11,818
Technology-based and other [Member]
The components of intangible assets
Gross carrying amount, finite	33,180	33,632
Accumulated amortization	(24,360)	(24,413)
Customer-related [Member]
The components of intangible assets
Gross carrying amount, finite	182,559	183,338
Accumulated amortization	(102,425)	(98,901)
Unpatented technology [Member]
The components of intangible assets
Gross carrying amount, finite	32,013	31,957
Accumulated amortization	(21,851)	(20,575)
Trademarks [Member]
The components of intangible assets
Gross carrying amount, finite	13,163	13,268
Accumulated amortization	$ (10,527)	$ (10,083)
Minimum [Member] \| Technology-based and other [Member]
The components of intangible assets
Useful life related to technology-based intangible assets	4 years
Minimum [Member] \| Customer-related [Member]
The components of intangible assets
Useful life related to technology-based intangible assets	10 years
Minimum [Member] \| Unpatented technology [Member]
The components of intangible assets
Useful life related to technology-based intangible assets	10 years
Minimum [Member] \| Trademarks [Member]
The components of intangible assets
Useful life related to technology-based intangible assets	5 years
Maximum [Member] \| Technology-based and other [Member]
The components of intangible assets
Useful life related to technology-based intangible assets	20 years
Maximum [Member] \| Customer-related [Member]
The components of intangible assets
Useful life related to technology-based intangible assets	21 years
Maximum [Member] \| Unpatented technology [Member]
The components of intangible assets
Useful life related to technology-based intangible assets	30 years
Maximum [Member] \| Trademarks [Member]
The components of intangible assets
Useful life related to technology-based intangible assets	20 years

The components of intangible assets.

No definition available.

Name:	kmt_ComponentsOfIntangibleAssetsAbstract
Namespace Prefix:	kmt_
Data Type:	xbrli:stringItemType
Balance Type:	na
Period Type:	duration

- Definition

Useful life of finite-lived intangible assets, in 'PnYnMnDTnHnMnS' format, for example, 'P1Y5M13D' represents the reported fact of one year, five months, and thirteen days.

+ References

No definition available.

+ Details

Name:	us-gaap_FiniteLivedIntangibleAssetUsefulLife
Namespace Prefix:	us-gaap_
Data Type:	xbrli:durationItemType
Balance Type:	na
Period Type:	duration

- Definition

Accumulated amount of amortization of assets, excluding financial assets and goodwill, lacking physical substance with a finite life.

+ References

Reference 1: http://www.xbrl.org/2003/role/disclosureRef
-Publisher FASB
-Name Accounting Standards Codification
-Topic 350
-SubTopic 30
-Section 50
-Paragraph 2
-Subparagraph (a)(1)
-URI http://asc.fasb.org/extlink&oid=66006027&loc=d3e16323-109275

+ Details

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

- Definition

Amount before amortization of assets, excluding financial assets and goodwill, lacking physical substance with a finite life.

+ References

Reference 1: http://www.xbrl.org/2003/role/disclosureRef
-Publisher FASB
-Name Accounting Standards Codification
-Topic 928
-SubTopic 340
-Section 50
-Paragraph 1
-URI http://asc.fasb.org/extlink&oid=6473545&loc=d3e61844-108004

Reference 2: http://fasb.org/us-gaap/role/ref/legacyRef
-Publisher FASB
-Name Accounting Standards Codification
-Topic 350
-SubTopic 30
-Section 50
-Paragraph 2
-Subparagraph (a)(1)
-URI http://asc.fasb.org/extlink&oid=66006027&loc=d3e16323-109275

+ Details

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

- Definition

Amount of assets, excluding financial assets and goodwill, lacking physical substance and having a projected indefinite period of benefit.

+ References

Reference 1: http://fasb.org/us-gaap/role/ref/legacyRef
-Publisher FASB
-Name Accounting Standards Codification
-Topic 350
-SubTopic 30
-Section 50
-Paragraph 2
-Subparagraph (b)
-URI http://asc.fasb.org/extlink&oid=66006027&loc=d3e16323-109275

+ Details

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

- Definition

Amount before accumulated amortization of intangible assets, excluding goodwill.

+ References

No definition available.

+ Details

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

- Details

Name:	us-gaap_IndefiniteLivedIntangibleAssetsByMajorClassAxis=us-gaap_TrademarksMember
Namespace Prefix:
Data Type:	na
Balance Type:
Period Type:

- Details

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

- Details

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

- Details

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

- Details

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

- Details

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

- Details

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