Stock and Stock-Based Compensation Plans - Narrative (Details)	12 Months Ended
	Jan. 01, 2023 USD ($) installment $ / shares shares	Jan. 02, 2022 USD ($)	Dec. 27, 2020 USD ($)
Share-based Compensation Arrangement by Share-based Payment Award [Line Items]
Aggregate awards granted limit, options (in shares) \| shares	1,000,000
Aggregate awards granted limit, restricted shares (in shares) \| shares	500,000
Cash-based award limit \| $	$ 5,000,000
Cash fees received limit \| $	750,000
Stock-based compensation \| $	13,000,000	$ 11,400,000	$ 8,500,000
Unrecognized expense \| $	$ 14,400,000
Weighted average term of unrecognized expense	1 year 7 months 6 days
Grant date fair value of shares \| $	$ 13,300,000
Fair value of shares vested during year \| $	900,000
Total intrinsic value of service options \| $	$ 600,000
2019 Omnibus Stock and Incentive Plan
Share-based Compensation Arrangement by Share-based Payment Award [Line Items]
Number of common shares reserved and available for awards (in shares) \| shares	4,354,169
Performance-based Restricted Stock Units
Share-based Compensation Arrangement by Share-based Payment Award [Line Items]
Granted (in shares) \| shares	150,937
Granted (in dollars per share) \| $ / shares	$ 38.79
Grant date stock price (in dollars per share) \| $ / shares	$ 38.37
Term of compensation award	2 years 9 months 3 days
Risk-free interest rate	2.49%
Volatility based on peer public companies	45.48%
Peer group's average	45.18%
Correlation coefficients	60.00%
Peer group average	0.72
Dividend yield	0.00%
Performance-based Restricted Stock Units \| Award Date, First Grant
Share-based Compensation Arrangement by Share-based Payment Award [Line Items]
Vesting period	3 years
Performance-based Restricted Stock Units \| Certain Executive Officers and Certain Other Employees
Share-based Compensation Arrangement by Share-based Payment Award [Line Items]
Granted (in dollars per share) \| $ / shares	$ 42.18
Performance-based Restricted Stock Units \| Certain Executive Officers and Certain Other Employees \| Award Date, First Grant
Share-based Compensation Arrangement by Share-based Payment Award [Line Items]
Granted (in shares) \| shares	117,832
Performance-based Restricted Stock Units \| Certain Executive Officers and Certain Other Employees \| Grant Date, Second Grant
Share-based Compensation Arrangement by Share-based Payment Award [Line Items]
Granted (in shares) \| shares	33,105
Vesting period	3 years
Restricted Stock Units (RSUs)
Share-based Compensation Arrangement by Share-based Payment Award [Line Items]
Granted (in shares) \| shares	235,933
Granted (in dollars per share) \| $ / shares	$ 38.18
Number of equal annual installments \| installment	3
Restricted Stock Awards
Share-based Compensation Arrangement by Share-based Payment Award [Line Items]
Granted (in shares) \| shares	30,826
Vesting period	1 year
Granted (in dollars per share) \| $ / shares	$ 35.00
Number of equal annual installments \| installment	4
Restricted Stock Awards \| Non-Employee Directors
Share-based Compensation Arrangement by Share-based Payment Award [Line Items]
Vesting period	1 year
Number of equal annual installments \| installment	1
ESPP
Share-based Compensation Arrangement by Share-based Payment Award [Line Items]
Offering periods for ESPP	1 month
Discount from fair value	15.00%
Participant's annual contribution limit \| $	$ 25,000

IAA, Inc. 10-K