<?xml version="1.0"?>
<ownershipDocument>

    <schemaVersion>X0306</schemaVersion>

    <documentType>4</documentType>

    <periodOfReport>2020-11-20</periodOfReport>

    <notSubjectToSection16>0</notSubjectToSection16>

    <issuer>
        <issuerCik>0001822479</issuerCik>
        <issuerName>Sotera Health Co</issuerName>
        <issuerTradingSymbol>SHC</issuerTradingSymbol>
    </issuer>

    <reportingOwner>
        <reportingOwnerId>
            <rptOwnerCik>0001796076</rptOwnerCik>
            <rptOwnerName>Klee Ann R.</rptOwnerName>
        </reportingOwnerId>
        <reportingOwnerAddress>
            <rptOwnerStreet1>C/O SOTERA HEALTH COMPANY</rptOwnerStreet1>
            <rptOwnerStreet2>9100 SOUTH HILLS BLVD, SUITE 300</rptOwnerStreet2>
            <rptOwnerCity>BROADVIEW HEIGHTS</rptOwnerCity>
            <rptOwnerState>OH</rptOwnerState>
            <rptOwnerZipCode>44147</rptOwnerZipCode>
            <rptOwnerStateDescription></rptOwnerStateDescription>
        </reportingOwnerAddress>
        <reportingOwnerRelationship>
            <isDirector>1</isDirector>
            <isOfficer>0</isOfficer>
            <isTenPercentOwner>0</isTenPercentOwner>
            <isOther>0</isOther>
        </reportingOwnerRelationship>
    </reportingOwner>

    <nonDerivativeTable>
        <nonDerivativeTransaction>
            <securityTitle>
                <value>Common Stock, $0.01 par value per share (&quot;Common Stock&quot;)</value>
            </securityTitle>
            <transactionDate>
                <value>2020-11-20</value>
            </transactionDate>
            <deemedExecutionDate></deemedExecutionDate>
            <transactionCoding>
                <transactionFormType>4</transactionFormType>
                <transactionCode>A</transactionCode>
                <equitySwapInvolved>0</equitySwapInvolved>
            </transactionCoding>
            <transactionTimeliness>
                <value></value>
            </transactionTimeliness>
            <transactionAmounts>
                <transactionShares>
                    <value>5869</value>
                    <footnoteId id="F1"/>
                </transactionShares>
                <transactionPricePerShare>
                    <value>0.00</value>
                </transactionPricePerShare>
                <transactionAcquiredDisposedCode>
                    <value>A</value>
                </transactionAcquiredDisposedCode>
            </transactionAmounts>
            <postTransactionAmounts>
                <sharesOwnedFollowingTransaction>
                    <value>56794</value>
                    <footnoteId id="F2"/>
                </sharesOwnedFollowingTransaction>
            </postTransactionAmounts>
            <ownershipNature>
                <directOrIndirectOwnership>
                    <value>D</value>
                </directOrIndirectOwnership>
            </ownershipNature>
        </nonDerivativeTransaction>
    </nonDerivativeTable>

    <footnotes>
        <footnote id="F1">These securities consist of Restricted Stock Units (&quot;RSUs&quot;) that were granted on November 20, 2020, pursuant to the terms of an RSU agreement under the Sotera Health Company 2020 Omnibus Incentive Plan. Each RSU represents the Reporting Person's right to receive one share of Common Stock, subject to vesting conditions. The RSUs will vest in full on the date immediately prior to the Issuer's next regular annual shareholders meeting, subject to the Reporting Person's continued service as a non-employee director of the Issuer through such date.</footnote>
        <footnote id="F2">Consists of 5,869 RSUs and 50,925 shares of Common Stock, including 16,199 shares of vested Common Stock and 34,726 shares of unvested Common Stock. 20% of the unvested shares of Common Stock will vest on May 27, 2021 (the one year anniversary of the date of grant), and the remaining unvested shares will vest on a daily basis pro rata thereafter, through May 27, 2025.</footnote>
    </footnotes>

    <remarks>The Power of Attorney for Ms. Ann R. Klee is filed as an exhibit to the Form 3 filed on November 20, 2020, which is hereby incorporated by reference.</remarks>

    <ownerSignature>
        <signatureName>/s/ Jessica L. M. H. Epp, Attorney-in-Fact</signatureName>
        <signatureDate>2020-11-24</signatureDate>
    </ownerSignature>
</ownershipDocument>
