Leases - Balance Sheet Location (Details) - USD ($) $ in Millions	Jan. 02, 2021	Dec. 28, 2019
Operating leases
Right-of-use assets	$ 120.9	$ 123.0
Short-term lease liabilities (included in “Accrued expenses and other current liabilities”)	$ 21.8	$ 19.5
Operating Lease, Liability, Current, Statement of Financial Position	us-gaap:AccruedLiabilitiesCurrent	us-gaap:AccruedLiabilitiesCurrent
Long-term lease liabilities	$ 111.4	$ 114.8
Operating Lease, Liability, Noncurrent, Statement of Financial Position	gtes:LeaseLiabilityNoncurrent	gtes:LeaseLiabilityNoncurrent
Operating Lease, Liability	$ 133.2	$ 134.3
Finance leases
Right-of-use assets	$ 4.1	$ 2.8
Finance Lease, Right-of-Use Asset, Statement of Financial Position	us-gaap:PropertyPlantAndEquipmentAndFinanceLeaseRightOfUseAssetAfterAccumulatedDepreciationAndAmortization	us-gaap:PropertyPlantAndEquipmentAndFinanceLeaseRightOfUseAssetAfterAccumulatedDepreciationAndAmortization
Short-term lease liabilities (included in “Accrued expenses and other current liabilities”)	$ 0.8	$ 0.3
Finance Lease, Liability, Current, Statement of Financial Position	us-gaap:AccruedLiabilitiesCurrent	us-gaap:AccruedLiabilitiesCurrent
Long-term lease liabilities	$ 2.2	$ 1.4
Finance Lease, Liability, Noncurrent, Statement of Financial Position	gtes:LeaseLiabilityNoncurrent	gtes:LeaseLiabilityNoncurrent
Total lease liabilities	$ 3.0	$ 1.7