<SUBMISSION>
<ACCESSION-NUMBER>0001209191-16-100578
<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>McConnaughhay Trudy P
<CIK>0001440256
</OWNER-DATA>
<FILING-VALUES>
<FORM-TYPE>4
<ACT>34
<FILE-NUMBER>000-09827
<FILM-NUMBER>161442456
</FILING-VALUES>
<MAIL-ADDRESS>
<STREET1>3584 SIERRA CIRCLE
<CITY>SULPHUR
<STATE>LA
<ZIP>70665
</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>0001440256</rptOwnerCik>
            <rptOwnerName>McConnaughhay Trudy P</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>Chief Financial Officer &amp; Sec.</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>4502</value>
                </transactionShares>
                <transactionPricePerShare>
                    <value>0.00</value>
                </transactionPricePerShare>
                <transactionAcquiredDisposedCode>
                    <value>A</value>
                </transactionAcquiredDisposedCode>
            </transactionAmounts>
            <postTransactionAmounts>
                <sharesOwnedFollowingTransaction>
                    <value>23765</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 Trudy P. McConnaughhay pursuant to a power of attorney</signatureName>
        <signatureDate>2016-02-19</signatureDate>
    </ownerSignature>
</ownershipDocument>
</XML>
</TEXT>
</DOCUMENT>
</SUBMISSION>
