Derivative financial instruments - Fair Values of Derivative Instruments (Details) - USD ($) $ in Millions	Mar. 28, 2020	Dec. 28, 2019
Derivatives, Fair Value
Net	$ (68.3)	$ (55.5)
Prepaid expenses and other assets
Derivatives, Fair Value
Derivative assets	2.9	5.4
Other non- current assets
Derivatives, Fair Value
Derivative assets	0.0	0.0
Accrued expenses and other current liabilities
Derivatives, Fair Value
Derivative liabilities	(15.3)	(9.6)
Other non- current liabilities
Derivatives, Fair Value
Derivative liabilities	(55.9)	(51.3)
Derivatives designated as hedging instruments: \| —Currency swaps
Derivatives, Fair Value
Net	(12.6)	(15.1)
Derivatives designated as hedging instruments: \| —Currency swaps \| Prepaid expenses and other assets
Derivatives, Fair Value
Derivative assets	2.2	4.2
Derivatives designated as hedging instruments: \| —Currency swaps \| Other non- current liabilities
Derivatives, Fair Value
Derivative liabilities	(14.8)	(19.3)
Derivatives designated as hedging instruments: \| —Interest rate caps
Derivatives, Fair Value
Net	(5.1)	(7.0)
Derivatives designated as hedging instruments: \| —Interest rate caps \| Accrued expenses and other current liabilities
Derivatives, Fair Value
Derivative liabilities	(2.5)	(4.0)
Derivatives designated as hedging instruments: \| —Interest rate caps \| Other non- current liabilities
Derivatives, Fair Value
Derivative liabilities	(2.6)	(3.0)
Derivatives designated as hedging instruments: \| —Interest rate swaps
Derivatives, Fair Value
Net	(50.3)	(34.3)
Derivatives designated as hedging instruments: \| —Interest rate swaps \| Accrued expenses and other current liabilities
Derivatives, Fair Value
Derivative liabilities	(11.8)	(5.3)
Derivatives designated as hedging instruments: \| —Interest rate swaps \| Other non- current liabilities
Derivatives, Fair Value
Derivative liabilities	(38.5)	(29.0)
Derivatives not designated as hedging instruments: \| —Currency swaps
Derivatives, Fair Value
Net	(0.6)	(0.1)
Derivatives not designated as hedging instruments: \| —Currency swaps \| Prepaid expenses and other assets
Derivatives, Fair Value
Derivative assets	0.1
Derivatives not designated as hedging instruments: \| —Currency swaps \| Accrued expenses and other current liabilities
Derivatives, Fair Value
Derivative liabilities	(0.7)	(0.1)
Derivatives not designated as hedging instruments: \| —Currency forward contracts
Derivatives, Fair Value
Net	0.3	1.0
Derivatives not designated as hedging instruments: \| —Currency forward contracts \| Prepaid expenses and other assets
Derivatives, Fair Value
Derivative assets	0.6	1.2
Derivatives not designated as hedging instruments: \| —Currency forward contracts \| Accrued expenses and other current liabilities
Derivatives, Fair Value
Derivative liabilities	$ (0.3)	$ (0.2)

Fair value, after the effects of master netting arrangements, of a financial asset or other contract with one or more underlyings, notional amount or payment provision or both, and the contract can be net settled by means outside the contract or delivery of an asset. Includes assets not subject to a master netting arrangement and not elected to be offset.

Reference 1: http://fasb.org/us-gaap/role/ref/legacyRef
-Publisher FASB
-Name Accounting Standards Codification
-Topic 210
-SubTopic 20
-Section 55
-Paragraph 10
-URI http://asc.fasb.org/extlink&oid=99393222&loc=SL20226008-175313

Reference 2: http://www.xbrl.org/2003/role/disclosureRef
-Publisher FASB
-Name Accounting Standards Codification
-Topic 825
-SubTopic 10
-Section 50
-Paragraph 10
-URI http://asc.fasb.org/extlink&oid=118260190&loc=d3e13433-108611

Reference 3: http://fasb.org/us-gaap/role/ref/legacyRef
-Publisher FASB
-Name Accounting Standards Codification
-Topic 210
-SubTopic 20
-Section 50
-Paragraph 3
-Subparagraph (c)
-URI http://asc.fasb.org/extlink&oid=51824906&loc=SL20225862-175312

+ Details

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

- Definition

Fair values as of the balance sheet date of the net amount of all assets and liabilities resulting from contracts that meet the criteria of being accounted for as derivative instruments.

+ References

Reference 1: http://fasb.org/us-gaap/role/ref/legacyRef
-Publisher FASB
-Name Accounting Standards Codification
-Topic 815
-SubTopic 10
-Section 45
-Paragraph 5
-URI http://asc.fasb.org/extlink&oid=117331979&loc=d3e41228-113958

+ Details

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

- Definition

Fair value, after the effects of master netting arrangements, of a financial liability or contract with one or more underlyings, notional amount or payment provision or both, and the contract can be net settled by means outside the contract or delivery of an asset. Includes liabilities not subject to a master netting arrangement and not elected to be offset.

+ References

Reference 1: http://fasb.org/us-gaap/role/ref/legacyRef
-Publisher FASB
-Name Accounting Standards Codification
-Topic 210
-SubTopic 20
-Section 50
-Paragraph 3
-Subparagraph (c)
-URI http://asc.fasb.org/extlink&oid=51824906&loc=SL20225862-175312

Reference 2: http://www.xbrl.org/2003/role/disclosureRef
-Publisher FASB
-Name Accounting Standards Codification
-Topic 825
-SubTopic 10
-Section 50
-Paragraph 10
-URI http://asc.fasb.org/extlink&oid=118260190&loc=d3e13433-108611

Reference 3: http://fasb.org/us-gaap/role/ref/legacyRef
-Publisher FASB
-Name Accounting Standards Codification
-Topic 210
-SubTopic 20
-Section 55
-Paragraph 10
-URI http://asc.fasb.org/extlink&oid=99393222&loc=SL20226008-175313

+ Details

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

- Details

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

- Details

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

- Details

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

- Details

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

- Details

Name:	us-gaap_HedgingDesignationAxis=us-gaap_DesignatedAsHedgingInstrumentMember
Namespace Prefix:
Data Type:	na
Balance Type:
Period Type:

- Details

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

- Details

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

- Details

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

- Details

Name:	us-gaap_HedgingDesignationAxis=us-gaap_NondesignatedMember
Namespace Prefix:
Data Type:	na
Balance Type:
Period Type:

- Details

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