<?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>0001369000</rptOwnerCik>
            <rptOwnerName>Klaben Matthew J</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>0</isDirector>
            <isOfficer>1</isOfficer>
            <isTenPercentOwner>0</isTenPercentOwner>
            <isOther>0</isOther>
            <officerTitle>SVP, GC and Secretary</officerTitle>
        </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>31304</value>
                    <footnoteId id="F1"/>
                </transactionShares>
                <transactionPricePerShare>
                    <value>0.00</value>
                </transactionPricePerShare>
                <transactionAcquiredDisposedCode>
                    <value>A</value>
                </transactionAcquiredDisposedCode>
            </transactionAmounts>
            <postTransactionAmounts>
                <sharesOwnedFollowingTransaction>
                    <value>31304</value>
                </sharesOwnedFollowingTransaction>
            </postTransactionAmounts>
            <ownershipNature>
                <directOrIndirectOwnership>
                    <value>D</value>
                </directOrIndirectOwnership>
            </ownershipNature>
        </nonDerivativeTransaction>
        <nonDerivativeTransaction>
            <securityTitle>
                <value>Common Stock</value>
            </securityTitle>
            <transactionDate>
                <value>2020-11-24</value>
            </transactionDate>
            <deemedExecutionDate></deemedExecutionDate>
            <transactionCoding>
                <transactionFormType>4</transactionFormType>
                <transactionCode>D</transactionCode>
                <equitySwapInvolved>0</equitySwapInvolved>
            </transactionCoding>
            <transactionTimeliness>
                <value></value>
            </transactionTimeliness>
            <transactionAmounts>
                <transactionShares>
                    <value>69196</value>
                </transactionShares>
                <transactionPricePerShare>
                    <value>21.68</value>
                    <footnoteId id="F2"/>
                </transactionPricePerShare>
                <transactionAcquiredDisposedCode>
                    <value>D</value>
                </transactionAcquiredDisposedCode>
            </transactionAmounts>
            <postTransactionAmounts>
                <sharesOwnedFollowingTransaction>
                    <value>369238</value>
                    <footnoteId id="F3"/>
                </sharesOwnedFollowingTransaction>
            </postTransactionAmounts>
            <ownershipNature>
                <directOrIndirectOwnership>
                    <value>I</value>
                </directOrIndirectOwnership>
                <natureOfOwnership>
                    <value>By grantor trust</value>
                </natureOfOwnership>
            </ownershipNature>
        </nonDerivativeTransaction>
    </nonDerivativeTable>

    <derivativeTable>
        <derivativeTransaction>
            <securityTitle>
                <value>Stock Options</value>
            </securityTitle>
            <conversionOrExercisePrice>
                <value>23.00</value>
            </conversionOrExercisePrice>
            <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>134161</value>
                </transactionShares>
                <transactionPricePerShare>
                    <value>0.00</value>
                </transactionPricePerShare>
                <transactionAcquiredDisposedCode>
                    <value>A</value>
                </transactionAcquiredDisposedCode>
            </transactionAmounts>
            <exerciseDate>
                <footnoteId id="F4"/>
            </exerciseDate>
            <expirationDate>
                <value>2030-11-20</value>
            </expirationDate>
            <underlyingSecurity>
                <underlyingSecurityTitle>
                    <value>Common Stock</value>
                </underlyingSecurityTitle>
                <underlyingSecurityShares>
                    <value>134161</value>
                </underlyingSecurityShares>
            </underlyingSecurity>
            <postTransactionAmounts>
                <sharesOwnedFollowingTransaction>
                    <value>134161</value>
                </sharesOwnedFollowingTransaction>
            </postTransactionAmounts>
            <ownershipNature>
                <directOrIndirectOwnership>
                    <value>D</value>
                </directOrIndirectOwnership>
            </ownershipNature>
        </derivativeTransaction>
    </derivativeTable>

    <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 (&quot;2020 Incentive Plan&quot;). Each RSU represents the Reporting Person's right to receive one share of common stock, subject to vesting conditions. The RSUs vest in four equal installments on each of the first four anniversaries of the date of grant, subject to the Reporting Person's continued service through each such date.</footnote>
        <footnote id="F2">Reflects a company repurchase price equal to the initial public offering price per share less underwriting discounts and commissions payable thereon, as disclosed in the company's Registration Statement on Form S-1.</footnote>
        <footnote id="F3">Consists of 220,762 shares of vested Common Stock and 148,476 shares of unvested Common Stock. 54,716 of the unvested shares of Common Stock will vest on a daily basis, pro rata through November 15, 2021. 93,760 of the unvested shares of Common Stock will vest as of the first date on which (i) certain investment funds and entities affiliated with Warburg Pincus LLC and GTCR, LLC (the &quot;Sponsors&quot;) have received two and one-half times their invested capital in the company and (ii) the Sponsors' internal rate of return exceeds twenty percent.</footnote>
        <footnote id="F4">These options were granted on November 20, 2020, pursuant to the terms of a stock option agreement under the 2020 Incentive Plan. The options vest in four equal installments on each of the first four anniversaries of the date of grant, subject to the Reporting Person's continued service through each such date.</footnote>
    </footnotes>

    <remarks>The Power of Attorney for Mr. Matthew J. Klaben 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>
