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

    <schemaVersion>X0306</schemaVersion>

    <documentType>4</documentType>

    <periodOfReport>2022-01-31</periodOfReport>

    <notSubjectToSection16>1</notSubjectToSection16>

    <issuer>
        <issuerCik>0000792966</issuerCik>
        <issuerName>FARMERS &amp; MERCHANTS BANCORP INC</issuerName>
        <issuerTradingSymbol>FMAO</issuerTradingSymbol>
    </issuer>

    <reportingOwner>
        <reportingOwnerId>
            <rptOwnerCik>0001199382</rptOwnerCik>
            <rptOwnerName>SIEBENMORGEN PAUL S</rptOwnerName>
        </reportingOwnerId>
        <reportingOwnerAddress>
            <rptOwnerStreet1>10702 ELDORADO CIRCLE</rptOwnerStreet1>
            <rptOwnerStreet2></rptOwnerStreet2>
            <rptOwnerCity>NOBLESVILLE</rptOwnerCity>
            <rptOwnerState>IN</rptOwnerState>
            <rptOwnerZipCode>46060</rptOwnerZipCode>
            <rptOwnerStateDescription></rptOwnerStateDescription>
        </reportingOwnerAddress>
        <reportingOwnerRelationship>
            <isDirector>1</isDirector>
            <isOfficer>0</isOfficer>
            <isTenPercentOwner>0</isTenPercentOwner>
            <isOther>0</isOther>
        </reportingOwnerRelationship>
    </reportingOwner>

    <footnotes></footnotes>

    <remarks>Effective July 16, 2021, Mr. Siebenmorgen retired from the Board of Directors of the Company and Farmers &amp; Merchants State Bank, in accordance with the mandatory retirement provisions contained in the Company's governing documents</remarks>

    <ownerSignature>
        <signatureName>/s/Lydia Huber</signatureName>
        <signatureDate>2022-03-21</signatureDate>
    </ownerSignature>
</ownershipDocument>
