<SUBMISSION>
<ACCESSION-NUMBER>0001209191-16-100570
<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>Gonsoulin Alton Anthony Jr
<CIK>0001064045
</OWNER-DATA>
<FILING-VALUES>
<FORM-TYPE>4
<ACT>34
<FILE-NUMBER>000-09827
<FILM-NUMBER>161442439
</FILING-VALUES>
<MAIL-ADDRESS>
<STREET1>P.O. BOX 16757
<CITY>SUGAR LAND
<STATE>TX
<ZIP>77479
</MAIL-ADDRESS>
<FORMER-NAME>
<FORMER-CONFORMED-NAME>GONSOULIN ALTON ANTHONY JR
<DATE-CHANGED>19980615
</FORMER-NAME>
</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>0001064045</rptOwnerCik>
            <rptOwnerName>Gonsoulin Alton Anthony Jr</rptOwnerName>
        </reportingOwnerId>
        <reportingOwnerAddress>
            <rptOwnerStreet1>4655 SWEETWATER BLVD.</rptOwnerStreet1>
            <rptOwnerStreet2>SUITE 300</rptOwnerStreet2>
            <rptOwnerCity>SUGARLAND</rptOwnerCity>
            <rptOwnerState>TX</rptOwnerState>
            <rptOwnerZipCode>77479</rptOwnerZipCode>
            <rptOwnerStateDescription></rptOwnerStateDescription>
        </reportingOwnerAddress>
        <reportingOwnerRelationship>
            <isDirector>1</isDirector>
            <isOfficer>1</isOfficer>
            <isTenPercentOwner>1</isTenPercentOwner>
            <isOther>0</isOther>
            <officerTitle>Chief Executive Officer</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>42567</value>
                </transactionShares>
                <transactionPricePerShare>
                    <value>0.00</value>
                </transactionPricePerShare>
                <transactionAcquiredDisposedCode>
                    <value>A</value>
                </transactionAcquiredDisposedCode>
            </transactionAmounts>
            <postTransactionAmounts>
                <sharesOwnedFollowingTransaction>
                    <value>1045882</value>
                    <footnoteId id="F2"/>
                </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>
        <footnote id="F2">As of the date of this filing, the Reporting Person also owns 2,040,280 shares of the issuer's voting common stock.</footnote>
    </footnotes>

    <remarks></remarks>

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