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

    <schemaVersion>X0609</schemaVersion>

    <documentType>4</documentType>

    <periodOfReport>2026-10-06</periodOfReport>

    <notSubjectToSection16>0</notSubjectToSection16>

    <issuer>
        <issuerCik>0001050441</issuerCik>
        <issuerName>EAGLE BANCORP INC</issuerName>
        <issuerTradingSymbol>EGBN</issuerTradingSymbol>
        <issuerForeignTradingSymbol></issuerForeignTradingSymbol>
    </issuer>

    <reportingOwner>
        <reportingOwnerId>
            <rptOwnerCik>0001523145</rptOwnerCik>
            <rptOwnerName>Newell Eric R</rptOwnerName>
        </reportingOwnerId>
        <reportingOwnerAddress>
            <rptOwnerNonUSAddressFlag>false</rptOwnerNonUSAddressFlag>
            <rptOwnerStreet1>C/O EAGLE BANCORP, INC.</rptOwnerStreet1>
            <rptOwnerStreet2>7500 OLD GEORGETOWN ROAD</rptOwnerStreet2>
            <rptOwnerCity>BETHESDA</rptOwnerCity>
            <rptOwnerState>MD</rptOwnerState>
            <rptOwnerZipCode>20814</rptOwnerZipCode>
            <rptOwnerStateDescription></rptOwnerStateDescription>
        </reportingOwnerAddress>
        <reportingOwnerRelationship>
            <isDirector>0</isDirector>
            <isOfficer>1</isOfficer>
            <isTenPercentOwner>0</isTenPercentOwner>
            <isOther>0</isOther>
            <officerTitle>Senior EVP, CFO</officerTitle>
        </reportingOwnerRelationship>
    </reportingOwner>

    <aff10b5One>0</aff10b5One>

    <nonDerivativeTable>
        <nonDerivativeTransaction>
            <securityTitle>
                <value>Common Stock</value>
            </securityTitle>
            <transactionDate>
                <value>2026-10-06</value>
            </transactionDate>
            <transactionCoding>
                <transactionFormType>5</transactionFormType>
                <transactionCode>J</transactionCode>
                <equitySwapInvolved>0</equitySwapInvolved>
                <footnoteId id="F1"/>
            </transactionCoding>
            <transactionTimeliness>
                <value>E</value>
            </transactionTimeliness>
            <transactionAmounts>
                <transactionShares>
                    <value>7833</value>
                </transactionShares>
                <transactionPricePerShare>
                    <value>0</value>
                </transactionPricePerShare>
                <transactionAcquiredDisposedCode>
                    <value>D</value>
                </transactionAcquiredDisposedCode>
            </transactionAmounts>
            <postTransactionAmounts>
                <sharesOwnedFollowingTransaction>
                    <value>36081</value>
                    <footnoteId id="F2"/>
                </sharesOwnedFollowingTransaction>
            </postTransactionAmounts>
            <ownershipNature>
                <directOrIndirectOwnership>
                    <value>D</value>
                </directOrIndirectOwnership>
            </ownershipNature>
        </nonDerivativeTransaction>
        <nonDerivativeTransaction>
            <securityTitle>
                <value>Common Stock</value>
            </securityTitle>
            <transactionDate>
                <value>2026-10-06</value>
            </transactionDate>
            <transactionCoding>
                <transactionFormType>5</transactionFormType>
                <transactionCode>J</transactionCode>
                <equitySwapInvolved>0</equitySwapInvolved>
                <footnoteId id="F1"/>
            </transactionCoding>
            <transactionTimeliness>
                <value>E</value>
            </transactionTimeliness>
            <transactionAmounts>
                <transactionShares>
                    <value>7833</value>
                </transactionShares>
                <transactionPricePerShare>
                    <value>0</value>
                </transactionPricePerShare>
                <transactionAcquiredDisposedCode>
                    <value>A</value>
                </transactionAcquiredDisposedCode>
            </transactionAmounts>
            <postTransactionAmounts>
                <sharesOwnedFollowingTransaction>
                    <value>7833</value>
                </sharesOwnedFollowingTransaction>
            </postTransactionAmounts>
            <ownershipNature>
                <directOrIndirectOwnership>
                    <value>I</value>
                </directOrIndirectOwnership>
                <natureOfOwnership>
                    <value>By Trust</value>
                    <footnoteId id="F3"/>
                </natureOfOwnership>
            </ownershipNature>
        </nonDerivativeTransaction>
    </nonDerivativeTable>

    <derivativeTable></derivativeTable>

    <footnotes>
        <footnote id="F1">On October 6, 2026, the Reporting Person transferred 7,833 shares of common stock held directly to The Eric Newell Revocable Trust. The transfer reflects a change in the form of beneficial ownership from direct to indirect and is exempt from Section 16 pursuant to Rule 16a-13 under the Securities Exchange Act of 1934, as amended.</footnote>
        <footnote id="F2">The Reporting Person's holdings include 352 shares acquired under the Eagle Bancorp, Inc. 2021 Employee Stock Purchase Plan (the &quot;ESPP&quot;) on March 31, 2026; 290 shares acquired under the ESPP on June 30, 2026; and 265 shares acquired under the ESPP on September 30, 2026.</footnote>
        <footnote id="F3">Shares held by The Eric Newell Revocable Trust, of which the Reporting Person is the sole trustee.</footnote>
    </footnotes>

    <remarks></remarks>

    <ownerSignature>
        <signatureName>Eric R. Newell</signatureName>
        <signatureDate>2026-10-08</signatureDate>
    </ownerSignature>
</ownershipDocument>
