<SUBMISSION>
<ACCESSION-NUMBER>0001209191-16-100575
<TYPE>4
<PUBLIC-DOCUMENT-COUNT>1
<PERIOD>20160217
<FILING-DATE>20160219
<DATE-OF-FILING-DATE-CHANGE>20160219
<ISSUER>
<COMPANY-DATA>
<CONFORMED-NAME>PHI INC
<CIK>0000350403
<ASSIGNED-SIC>4522
<IRS-NUMBER>720395707
<STATE-OF-INCORPORATION>LA
<FISCAL-YEAR-END>1231
</COMPANY-DATA>
<BUSINESS-ADDRESS>
<STREET1>2001 SE EVANGELINE THRUWAY
<STREET2>-
<CITY>LAFAYETTE
<STATE>LA
<ZIP>70508
<PHONE>(337) 235-2452
</BUSINESS-ADDRESS>
<MAIL-ADDRESS>
<STREET1>PO BOX 90808
<CITY>LAFAYETTE
<STATE>LA
<ZIP>70509
</MAIL-ADDRESS>
<FORMER-COMPANY>
<FORMER-CONFORMED-NAME>PETROLEUM HELICOPTERS INC
<DATE-CHANGED>19920703
</FORMER-COMPANY>
</ISSUER>
<REPORTING-OWNER>
<OWNER-DATA>
<CONFORMED-NAME>ROVINELLI RICHARD A
<CIK>0001184617
</OWNER-DATA>
<FILING-VALUES>
<FORM-TYPE>4
<ACT>34
<FILE-NUMBER>000-09827
<FILM-NUMBER>161442446
</FILING-VALUES>
<MAIL-ADDRESS>
<STREET1>2001 SE EVANGELINE THRUWAY
<CITY>LAFAYETTE
<STATE>LA
<ZIP>70508
</MAIL-ADDRESS>
</REPORTING-OWNER>
<DOCUMENT>
<TYPE>4
<SEQUENCE>1
<FILENAME>doc4.xml
<DESCRIPTION>FORM 4 SUBMISSION
<TEXT>
<XML>
<?xml version="1.0"?>
<ownershipDocument>

    <schemaVersion>X0306</schemaVersion>

    <documentType>4</documentType>

    <periodOfReport>2016-02-17</periodOfReport>

    <notSubjectToSection16>0</notSubjectToSection16>

    <issuer>
        <issuerCik>0000350403</issuerCik>
        <issuerName>PHI INC</issuerName>
        <issuerTradingSymbol>PHIIK</issuerTradingSymbol>
    </issuer>

    <reportingOwner>
        <reportingOwnerId>
            <rptOwnerCik>0001184617</rptOwnerCik>
            <rptOwnerName>ROVINELLI RICHARD A</rptOwnerName>
        </reportingOwnerId>
        <reportingOwnerAddress>
            <rptOwnerStreet1>2001 SE EVANGELINE THRUWAY</rptOwnerStreet1>
            <rptOwnerStreet2></rptOwnerStreet2>
            <rptOwnerCity>LAFAYETTE</rptOwnerCity>
            <rptOwnerState>LA</rptOwnerState>
            <rptOwnerZipCode>70508</rptOwnerZipCode>
            <rptOwnerStateDescription></rptOwnerStateDescription>
        </reportingOwnerAddress>
        <reportingOwnerRelationship>
            <isDirector>0</isDirector>
            <isOfficer>1</isOfficer>
            <isTenPercentOwner>0</isTenPercentOwner>
            <isOther>0</isOther>
            <officerTitle>CAO, DIRECTOR HUMAN RESOURCES</officerTitle>
        </reportingOwnerRelationship>
    </reportingOwner>

    <nonDerivativeTable>
        <nonDerivativeTransaction>
            <securityTitle>
                <value>Non-Voting Common Stock</value>
            </securityTitle>
            <transactionDate>
                <value>2016-02-17</value>
            </transactionDate>
            <deemedExecutionDate></deemedExecutionDate>
            <transactionCoding>
                <transactionFormType>4</transactionFormType>
                <transactionCode>A</transactionCode>
                <equitySwapInvolved>0</equitySwapInvolved>
                <footnoteId id="F1"/>
            </transactionCoding>
            <transactionTimeliness>
                <value></value>
            </transactionTimeliness>
            <transactionAmounts>
                <transactionShares>
                    <value>4768</value>
                </transactionShares>
                <transactionPricePerShare>
                    <value>0.00</value>
                </transactionPricePerShare>
                <transactionAcquiredDisposedCode>
                    <value>A</value>
                </transactionAcquiredDisposedCode>
            </transactionAmounts>
            <postTransactionAmounts>
                <sharesOwnedFollowingTransaction>
                    <value>23911</value>
                </sharesOwnedFollowingTransaction>
            </postTransactionAmounts>
            <ownershipNature>
                <directOrIndirectOwnership>
                    <value>D</value>
                </directOrIndirectOwnership>
            </ownershipNature>
        </nonDerivativeTransaction>
    </nonDerivativeTable>

    <footnotes>
        <footnote id="F1">Represents the number of shares of non-voting stock issuable under performance-based RSUs originally granted to the Reporting Person on May 2, 2013. On February 17, 2016, the Compensation Committee of the Issuer's Board of Directors certified that the applicable performance metric was met. These RSUs are scheduled to vest on March 15, 2016.</footnote>
    </footnotes>

    <remarks></remarks>

    <ownerSignature>
        <signatureName>/s/ Kenneth J. Najder, on behalf of Richard A. Rovinelli pursuant to a power of attorney</signatureName>
        <signatureDate>2016-02-19</signatureDate>
    </ownerSignature>
</ownershipDocument>
</XML>
</TEXT>
</DOCUMENT>
</SUBMISSION>
