EXHIBIT A

JOINT FILING AGREEMENT

This will confirm the agreement by and among the undersigned that the Schedule 13G filed with the Securities and Exchange Commission on or about the date hereof with respect to the beneficial ownership by the undersigned of the common Stock, par value $0.01 per share, of Sotera Health Co. (this “Agreement”), is being filed, and all amendments thereto will be filed, by GTCR Investment XI LLC as the designated filer on behalf of each of the persons and entities named below that is named as a reporting person in such filing in accordance with Rule 13d-1(k) under the Securities Exchange Act of 1934, as amended. This Agreement may be executed in two or more counterparts, each of which shall be deemed an original, but all of which together shall constitute one and the same instrument.

Dated: February 11, 2022

GTCR INVESTMENT XI LLC

/s/ Jeffrey Wright

Name: Jeffrey Wright

Title: Chief Legal Officer

GTCR FUND XI/A LP

/s/ Jeffrey Wright

Name: Jeffrey Wright

Title: Chief Legal Officer of GTCR Investment XI LLC, the general partner of GTCR Partners XI/A&C LP, the general partner of GTCR FUND XI/A LP

GTCR FUND XI/C LP

/s/ Jeffrey Wright

Name: Jeffrey Wright

Title: Chief Legal Officer of GTCR Investment XI LLC, the general partner of GTCR Partners XI/A&C LP, the general partner of GTCR FUND XI/C LP

GTCR CO-INVEST XI LP

/s/ Jeffrey Wright

Name: Jeffrey Wright

Title: Chief Legal Officer of GTCR Investment XI LLC, the general partner of GTCR CO-INVEST XI LP

GTCR PARTNERS XI/A&C LP

/s/ Jeffrey Wright

Name: Jeffrey Wright

Title: Chief Legal Officer of GTCR Investment XI LLC, the general partner of GTCR PARTNERS XI/A&C LP