Accumulated Other Comprehensive Loss - Reclassifications (Details) - USD ($) $ in Thousands	3 Months Ended	6 Months Ended
Dec. 31, 2019	Dec. 31, 2018	Dec. 31, 2019	Dec. 31, 2018
Reclassification Adjustment out of Accumulated Other Comprehensive Loss [Line Items]
Currency exchange contracts	$ 4,211	$ 4,022	$ 6,891	$ 6,782
Reclassification of unrealized (gain) loss on derivatives designated and qualified as cash flow hedges, tax	128	(85)	69	(278)
Recognition of actuarial losses	2,615	1,737	5,239	3,488
(Benefit) provision for income taxes	(45,253)	18,529	(41,487)	37,921
Reclassification out of Accumulated Other Comprehensive Loss [Member] \| Accumulated Net (Loss) Gain from Designated or Qualifying Cash Flow Hedges [Member]
Reclassification Adjustment out of Accumulated Other Comprehensive Loss [Line Items]
Reclassification of unrealized (gain) loss on derivatives designated and qualified as cash flow hedges, tax	128	(85)	69	(278)
Total before tax	521	(347)	281	(1,135)
Net of tax	(393)	262	(212)	857
Reclassification out of Accumulated Other Comprehensive Loss [Member] \| Accumulated Defined Benefit Plans Adjustment [Member]
Reclassification Adjustment out of Accumulated Other Comprehensive Loss [Line Items]
Amortization of transition obligations	22	23	44	45
Amortization of prior service credit	(56)	(27)	(113)	(55)
Recognition of actuarial losses	2,649	1,741	5,308	3,498
Total before tax	2,615	1,737	5,239	3,488
(Benefit) provision for income taxes	(625)	(439)	(1,289)	(882)
Net of tax	(1,990)	(1,298)	(3,950)	(2,606)
Reclassification out of Accumulated Other Comprehensive Loss [Member] \| Forward Starting Interest Rate Swap Contracts [Member] \| Accumulated Net (Loss) Gain from Designated or Qualifying Cash Flow Hedges [Member]
Reclassification Adjustment out of Accumulated Other Comprehensive Loss [Line Items]
Forward starting interest rate swaps	611	588	1,222	1,176
Reclassification out of Accumulated Other Comprehensive Loss [Member] \| Currency Forward Contracts [Member] \| Accumulated Net (Loss) Gain from Designated or Qualifying Cash Flow Hedges [Member]
Reclassification Adjustment out of Accumulated Other Comprehensive Loss [Line Items]
Currency exchange contracts	$ (1,132)	$ (241)	$ (1,503)	$ (41)

Amount after tax of income (loss) from continuing operations including portion attributable to the noncontrolling interest.

Reference 1: http://fasb.org/us-gaap/role/ref/legacyRef
-Publisher FASB
-Name Accounting Standards Codification
-Topic 810
-SubTopic 10
-Section 45
-Paragraph 19
-URI http://asc.fasb.org/extlink&oid=108774443&loc=SL4569616-111683

+ Details

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

- Definition

Amount of current income tax expense (benefit) and deferred income tax expense (benefit) pertaining to continuing operations.

+ References

Reference 1: http://www.xbrl.org/2003/role/disclosureRef
-Publisher FASB
-Name Accounting Standards Codification
-Topic 280
-SubTopic 10
-Section 50
-Paragraph 22
-Subparagraph (h)
-URI http://asc.fasb.org/extlink&oid=115929826&loc=d3e8736-108599

Reference 2: http://www.xbrl.org/2003/role/disclosureRef
-Publisher FASB
-Name Accounting Standards Codification
-Topic 235
-SubTopic 10
-Section S99
-Paragraph 1
-Subparagraph (SX 210.4-08(h))
-URI http://asc.fasb.org/extlink&oid=26873400&loc=d3e23780-122690

Reference 3: http://www.xbrl.org/2003/role/disclosureRef
-Publisher FASB
-Name Accounting Standards Codification
-Topic 740
-SubTopic 20
-Section 45
-Paragraph 2
-Subparagraph (a)
-URI http://asc.fasb.org/extlink&oid=109238882&loc=d3e38679-109324

+ Details

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

- Definition

The net amount of operating interest income (expense).

+ References

Reference 1: http://fasb.org/us-gaap/role/ref/legacyRef
-Publisher FASB
-Name Accounting Standards Codification
-Topic 942
-SubTopic 220
-Section S99
-Paragraph 1
-Subparagraph (SX 210.9-04.10)
-URI http://asc.fasb.org/extlink&oid=116637391&loc=SL114874048-224260

+ Details

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

- Definition

Amount, after deduction of tax, noncontrolling interests, dividends on preferred stock and participating securities; of income (loss) available to common shareholders.

+ References

Reference 1: http://www.xbrl.org/2003/role/disclosureRef
-Publisher FASB
-Name Accounting Standards Codification
-Topic 250
-SubTopic 10
-Section 50
-Paragraph 11
-URI http://asc.fasb.org/extlink&oid=109234566&loc=d3e22694-107794

Reference 2: http://fasb.org/us-gaap/role/ref/legacyRef
-Publisher FASB
-Name Accounting Standards Codification
-Topic 260
-SubTopic 10
-Section 45
-Paragraph 11
-URI http://asc.fasb.org/extlink&oid=117326831&loc=d3e1377-109256

+ Details

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

- Definition

Amount, before tax, of reclassification adjustment from accumulated other comprehensive (income) loss for prior service cost (credit) of defined benefit plan.

+ References

Reference 1: http://fasb.org/us-gaap/role/ref/legacyRef
-Publisher FASB
-Name Accounting Standards Codification
-Topic 715
-SubTopic 20
-Section 50
-Paragraph 1
-Subparagraph (i)
-URI http://asc.fasb.org/extlink&oid=118255775&loc=d3e1928-114920

Reference 2: http://www.xbrl.org/2003/role/disclosureRef
-Publisher FASB
-Name Accounting Standards Codification
-Topic 220
-SubTopic 10
-Section 45
-Paragraph 17A
-URI http://asc.fasb.org/extlink&oid=118930883&loc=SL34724391-108580

Reference 3: http://fasb.org/us-gaap/role/ref/legacyRef
-Publisher FASB
-Name Accounting Standards Codification
-Topic 220
-SubTopic 10
-Section 45
-Paragraph 15
-URI http://asc.fasb.org/extlink&oid=118930883&loc=d3e689-108580

Reference 4: http://fasb.org/us-gaap/role/ref/legacyRef
-Publisher FASB
-Name Accounting Standards Codification
-Topic 220
-SubTopic 10
-Section 45
-Paragraph 11
-URI http://asc.fasb.org/extlink&oid=118930883&loc=d3e637-108580

+ Details

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

- Definition

Amount of tax expense (benefit) of reclassification adjustment from accumulated other comprehensive income of accumulated gain (loss) realized from derivative instruments designated and qualifying as the effective portion of cash flow hedges and an entity's share of an equity investee's deferred hedging gain (loss).

+ References

Reference 1: http://fasb.org/us-gaap/role/ref/legacyRef
-Publisher FASB
-Name Accounting Standards Codification
-Topic 220
-SubTopic 10
-Section 45
-Paragraph 12
-URI http://asc.fasb.org/extlink&oid=118930883&loc=d3e640-108580

+ Details

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

- Definition

Amount, before tax, of reclassification adjustment from accumulated other comprehensive income (loss) for gain (loss) of defined benefit plan.

+ References

Reference 1: http://fasb.org/us-gaap/role/ref/legacyRef
-Publisher FASB
-Name Accounting Standards Codification
-Topic 220
-SubTopic 10
-Section 45
-Paragraph 11
-URI http://asc.fasb.org/extlink&oid=118930883&loc=d3e637-108580

Reference 2: http://fasb.org/us-gaap/role/ref/legacyRef
-Publisher FASB
-Name Accounting Standards Codification
-Topic 220
-SubTopic 10
-Section 45
-Paragraph 15
-URI http://asc.fasb.org/extlink&oid=118930883&loc=d3e689-108580

Reference 3: http://fasb.org/us-gaap/role/ref/legacyRef
-Publisher FASB
-Name Accounting Standards Codification
-Topic 715
-SubTopic 20
-Section 50
-Paragraph 1
-Subparagraph (i)
-URI http://asc.fasb.org/extlink&oid=118255775&loc=d3e1928-114920

Reference 4: http://www.xbrl.org/2003/role/disclosureRef
-Publisher FASB
-Name Accounting Standards Codification
-Topic 220
-SubTopic 10
-Section 45
-Paragraph 17A
-URI http://asc.fasb.org/extlink&oid=118930883&loc=SL34724391-108580

+ Details

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

- Definition

Amount, before tax, of reclassification adjustment from accumulated other comprehensive income (loss) for transition asset (obligation) of defined benefit plan.

+ References

Reference 1: http://fasb.org/us-gaap/role/ref/legacyRef
-Publisher FASB
-Name Accounting Standards Codification
-Topic 220
-SubTopic 10
-Section 45
-Paragraph 15
-URI http://asc.fasb.org/extlink&oid=118930883&loc=d3e689-108580

Reference 2: http://fasb.org/us-gaap/role/ref/legacyRef
-Publisher FASB
-Name Accounting Standards Codification
-Topic 220
-SubTopic 10
-Section 45
-Paragraph 11
-URI http://asc.fasb.org/extlink&oid=118930883&loc=d3e637-108580

Reference 3: http://www.xbrl.org/2003/role/disclosureRef
-Publisher FASB
-Name Accounting Standards Codification
-Topic 220
-SubTopic 10
-Section 45
-Paragraph 17A
-URI http://asc.fasb.org/extlink&oid=118930883&loc=SL34724391-108580

Reference 4: http://fasb.org/us-gaap/role/ref/legacyRef
-Publisher FASB
-Name Accounting Standards Codification
-Topic 715
-SubTopic 20
-Section 50
-Paragraph 1
-Subparagraph (i)
-URI http://asc.fasb.org/extlink&oid=118255775&loc=d3e1928-114920

+ Details

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

- Definition

Amount of income (expense) related to nonoperating activities, classified as other.

+ References

Reference 1: http://fasb.org/us-gaap/role/ref/legacyRef
-Publisher FASB
-Name Accounting Standards Codification
-Topic 220
-SubTopic 10
-Section S99
-Paragraph 2
-Subparagraph (SX 210.5-03.9)
-URI http://asc.fasb.org/extlink&oid=116634182&loc=SL114868664-224227

+ Details

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

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

- Details

Name:	us-gaap_ReclassificationOutOfAccumulatedOtherComprehensiveIncomeAxis=us-gaap_ReclassificationOutOfAccumulatedOtherComprehensiveIncomeMember
Namespace Prefix:
Data Type:	na
Balance Type:
Period Type:

- Details

Name:	us-gaap_StatementEquityComponentsAxis=us-gaap_AccumulatedNetGainLossFromDesignatedOrQualifyingCashFlowHedgesMember
Namespace Prefix:
Data Type:	na
Balance Type:
Period Type:

- Details

Name:	us-gaap_StatementEquityComponentsAxis=us-gaap_AccumulatedDefinedBenefitPlansAdjustmentMember
Namespace Prefix:
Data Type:	na
Balance Type:
Period Type:

- Details

Name:	us-gaap_DerivativeInstrumentRiskAxis=kmt_ForwardStartingInterestRateSwapContractsMember
Namespace Prefix:
Data Type:	na
Balance Type:
Period Type:

- Details

Name:	us-gaap_DerivativeInstrumentRiskAxis=kmt_CurrencyForwardContractsMember
Namespace Prefix:
Data Type:	na
Balance Type:
Period Type: