<?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>0001832406</rptOwnerCik>
            <rptOwnerName>Leffler Scott 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>CFO and Treasurer</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>52173</value>
                    <footnoteId id="F1"/>
                </transactionShares>
                <transactionPricePerShare>
                    <value>0.00</value>
                </transactionPricePerShare>
                <transactionAcquiredDisposedCode>
                    <value>A</value>
                </transactionAcquiredDisposedCode>
            </transactionAmounts>
            <postTransactionAmounts>
                <sharesOwnedFollowingTransaction>
                    <value>820426</value>
                    <footnoteId id="F2"/>
                </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>115326</value>
                </transactionShares>
                <transactionPricePerShare>
                    <value>21.68</value>
                    <footnoteId id="F3"/>
                </transactionPricePerShare>
                <transactionAcquiredDisposedCode>
                    <value>D</value>
                </transactionAcquiredDisposedCode>
            </transactionAmounts>
            <postTransactionAmounts>
                <sharesOwnedFollowingTransaction>
                    <value>705100</value>
                    <footnoteId id="F4"/>
                </sharesOwnedFollowingTransaction>
            </postTransactionAmounts>
            <ownershipNature>
                <directOrIndirectOwnership>
                    <value>D</value>
                </directOrIndirectOwnership>
            </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>223602</value>
                </transactionShares>
                <transactionPricePerShare>
                    <value>0.00</value>
                </transactionPricePerShare>
                <transactionAcquiredDisposedCode>
                    <value>A</value>
                </transactionAcquiredDisposedCode>
            </transactionAmounts>
            <exerciseDate>
                <footnoteId id="F5"/>
            </exerciseDate>
            <expirationDate>
                <value>2030-11-20</value>
            </expirationDate>
            <underlyingSecurity>
                <underlyingSecurityTitle>
                    <value>Common Stock</value>
                </underlyingSecurityTitle>
                <underlyingSecurityShares>
                    <value>223602</value>
                </underlyingSecurityShares>
            </underlyingSecurity>
            <postTransactionAmounts>
                <sharesOwnedFollowingTransaction>
                    <value>223602</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">Consists of 768,253 shares of Common Stock (see Footnote #4 for information regarding the vesting of the Common Stock) and 52,173 RSUs.</footnote>
        <footnote id="F3">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="F4">Consists of 347,109 shares of vested Common Stock, 305,818 shares of unvested Common Stock and 52,173 RSUs. 137,049 of the unvested shares of Common Stock will vest on a daily basis, pro rata through April 3, 2022. 168,769 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. See Footnote #1 for information regarding the vesting of the RSUs.</footnote>
        <footnote id="F5">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. Scott J. Leffler 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>
