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Stockholders' Equity - Changes in Accumulated Other Comprehensive Income by Component, Net of Tax (Details) - USD ($) $ in Millions |  | 12 Months Ended
--- | --- | ---
Mar. 01, 2022 | Jan. 01, 2023 | Jan. 02, 2022 | Jan. 03, 2021
Accumulated Other Comprehensive Income (Loss), Net of Tax [Roll Forward] |  |  |  |  |  |
Balance at beginning of year |  |  | $ 1,336.2 |  | $ 1,203.0 |
Balance at end of year |  |  | 1,254.2 |  | 1,336.2 | $ 1,203.0
Other Expense |  |  |  |  |  |
Accumulated Other Comprehensive Income (Loss), Net of Tax [Roll Forward] |  |  |  |  |  |
Amounts reclassified from accumulated other comprehensive income (loss) |  |  | (1.4) |  |  |
Gain (Loss) on Disposal of Assets |  |  |  |  |  |
Accumulated Other Comprehensive Income (Loss), Net of Tax [Roll Forward] |  |  |  |  |  |
Amounts reclassified from accumulated other comprehensive income (loss) |  |  | 1.4 |  |  |
PersolKelly Pte. Ltd. |  |  |  |  |  |
Accumulated Other Comprehensive Income (Loss), Net of Tax [Roll Forward] |  |  |  |  |  |
Amounts reclassified from accumulated other comprehensive income (loss) |  | $ 1.9 |  |  |  |
Foreign currency translation adjustments: |  |  |  |  |  |
Accumulated Other Comprehensive Income (Loss), Net of Tax [Roll Forward] |  |  |  |  |  |
Balance at beginning of year |  |  | (25.0) |  | (0.8) | (13.2)
Other comprehensive income (loss) before classifications |  |  | (7.5) |  | (24.2) | 13.9
Net current-period other comprehensive income (loss) |  |  | 17.6 |  | (24.2) | 12.4
Balance at end of year |  |  | (7.4) |  | (25.0) | (0.8)
Foreign currency translation adjustments: | Liquidation of Subsidiary |  |  |  |  |  |
Accumulated Other Comprehensive Income (Loss), Net of Tax [Roll Forward] |  |  |  |  |  |
Amounts reclassified from accumulated other comprehensive income (loss) |  |  | 20.4 | [1] | 0.0 | 0.0
Foreign currency translation adjustments: | Equity Method Investment |  |  |  |  |  |
Accumulated Other Comprehensive Income (Loss), Net of Tax [Roll Forward] |  |  |  |  |  |
Amounts reclassified from accumulated other comprehensive income (loss) | [2] |  | 4.7 |  | 0.0 | (1.5)
Foreign currency translation adjustments: | PersolKelly Pte. Ltd. | Other Expense |  |  |  |  |  |
Accumulated Other Comprehensive Income (Loss), Net of Tax [Roll Forward] |  |  |  |  |  |
Amounts reclassified from accumulated other comprehensive income (loss) |  |  | (1.9) |  |  |
Pension liability adjustments: |  |  |  |  |  |
Accumulated Other Comprehensive Income (Loss), Net of Tax [Roll Forward] |  |  |  |  |  |
Balance at beginning of year |  |  | (2.7) |  | (3.4) | (2.6)
Other comprehensive income (loss) before classifications |  |  | 1.5 |  | 0.5 | (0.9)
Amounts reclassified from accumulated other comprehensive income (loss) | [3] |  | 0.1 |  | 0.2 | 0.1
Net current-period other comprehensive income (loss) |  |  | 1.6 |  | 0.7 | (0.8)
Balance at end of year |  |  | (1.1) |  | (2.7) | (3.4)
Accumulated Other Comprehensive Income (Loss) |  |  |  |  |  |
Accumulated Other Comprehensive Income (Loss), Net of Tax [Roll Forward] |  |  |  |  |  |
Balance at beginning of year |  |  | (27.7) |  | (4.2) | (15.8)
Balance at end of year |  |  | $ (8.5) |  | $ (27.7) | $ (4.2)
[1] | Amount was recorded in the loss on currency translation from liquidation of subsidiary in the consolidated statements of earnings.
[2] | Of the amount included in this line item $1.9 million in 2022 was recorded in the other income (expense), net line item in the consolidated statements of earnings related to the investment in PersolKelly Pte. Ltd., (see Investment in PersolKelly Pte. Ltd. footnote for more details). In addition, $1.4 million in 2022 was recorded in the other income (expense), net line item in the consolidated statements of earnings related to other activities and $1.4 million in 2022 was recorded in loss on disposal line item in the consolidated statements of earnings related to the liquidation of the cumulative translation adjustment for the sale of our Russia operations, (see Acquisitions and Dispositions footnote for more details). All amounts in prior years were recorded in the other income (expense), net line item in the consolidated statements of earnings.
[3] | Amount was recorded in the SG&A expenses line item in the consolidated statements of earnings.

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