<?xml version="1.0"?>
<ownershipDocument>

    <schemaVersion>X0306</schemaVersion>

    <documentType>4</documentType>

    <periodOfReport>2012-12-28</periodOfReport>

    <notSubjectToSection16>0</notSubjectToSection16>

    <issuer>
        <issuerCik>0000816159</issuerCik>
        <issuerName>AIR METHODS CORP</issuerName>
        <issuerTradingSymbol>AIRM</issuerTradingSymbol>
    </issuer>

    <reportingOwner>
        <reportingOwnerId>
            <rptOwnerCik>0001244803</rptOwnerCik>
            <rptOwnerName>CARMAN TRENT</rptOwnerName>
        </reportingOwnerId>
        <reportingOwnerAddress>
            <rptOwnerStreet1>C/O AIR METHODS CORPORATION</rptOwnerStreet1>
            <rptOwnerStreet2>7301 SOUTH PEORIA STREET</rptOwnerStreet2>
            <rptOwnerCity>ENGLEWOOD</rptOwnerCity>
            <rptOwnerState>CO</rptOwnerState>
            <rptOwnerZipCode>80112</rptOwnerZipCode>
            <rptOwnerStateDescription></rptOwnerStateDescription>
        </reportingOwnerAddress>
        <reportingOwnerRelationship>
            <isDirector>0</isDirector>
            <isOfficer>1</isOfficer>
            <isTenPercentOwner>0</isTenPercentOwner>
            <isOther>0</isOther>
            <officerTitle>Chief Financial Officer</officerTitle>
            <otherText></otherText>
        </reportingOwnerRelationship>
    </reportingOwner>

    <nonDerivativeTable>
        <nonDerivativeTransaction>
            <securityTitle>
                <value>Common Stock</value>
            </securityTitle>
            <transactionDate>
                <value>2012-12-28</value>
            </transactionDate>
            <deemedExecutionDate></deemedExecutionDate>
            <transactionCoding>
                <transactionFormType>4</transactionFormType>
                <transactionCode>P</transactionCode>
                <equitySwapInvolved>0</equitySwapInvolved>
                <footnoteId id="F1"/>
            </transactionCoding>
            <transactionAmounts>
                <transactionShares>
                    <value>3903.411</value>
                </transactionShares>
                <transactionPricePerShare>
                    <value>37.6594</value>
                </transactionPricePerShare>
                <transactionAcquiredDisposedCode>
                    <value>A</value>
                </transactionAcquiredDisposedCode>
            </transactionAmounts>
            <postTransactionAmounts>
                <sharesOwnedFollowingTransaction>
                    <value>96403.411</value>
                    <footnoteId id="F3"/>
                    <footnoteId id="F2"/>
                </sharesOwnedFollowingTransaction>
            </postTransactionAmounts>
            <ownershipNature>
                <directOrIndirectOwnership>
                    <value>D</value>
                </directOrIndirectOwnership>
            </ownershipNature>
        </nonDerivativeTransaction>
    </nonDerivativeTable>

    <derivativeTable></derivativeTable>

    <footnotes>
        <footnote id="F1">The reporting person's purchase of Air Methods Corporation's (the &quot;Issuer's&quot;) common stock reported herein was matchable under Section 16(b) of the Securities Exchange Act of 1934, to the extent of 3,903.411 (post-split) shares, as a result of the reporting person's purchase of 3,903.411 (post-split) shares of the Issuer's common stock at a price of $37.6594 (post-split) per share on December 28, 2012.  The reporting person has paid to the Issuer $2,624.26 representing the full amount of the profit realized in connection with the short-swing transaction.</footnote>
        <footnote id="F2">Total beneficial ownership includes 9,997 shares of restricted stock subject to future vesting provisions.</footnote>
        <footnote id="F3">Actual shares purchased on December 28, 2012 were 1,301.137 shares at $112.9781 per share on a pre-split basis.  The purchase by the reporting person was triggered by the Issuer's year-end dividend distribution; the proceeds of which were governed by an automatic dividend reinvestment program established by the reporting person with his investment advisor.  Amounts reflected in Table I reflect amounts after giving effect to the Issuer's 3-for-1 stock split effected at the close of business on December 28, 2012.</footnote>
    </footnotes>

    <remarks></remarks>

    <ownerSignature>
        <signatureName>/s/ Trent J. Carman</signatureName>
        <signatureDate>2013-05-07</signatureDate>
    </ownerSignature>
</ownershipDocument>
