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

    <schemaVersion>X0306</schemaVersion>

    <documentType>4</documentType>

    <periodOfReport>2018-06-05</periodOfReport>

    <notSubjectToSection16>0</notSubjectToSection16>

    <issuer>
        <issuerCik>0001301501</issuerCik>
        <issuerName>Achaogen Inc</issuerName>
        <issuerTradingSymbol>AKAO</issuerTradingSymbol>
    </issuer>

    <reportingOwner>
        <reportingOwnerId>
            <rptOwnerCik>0001239242</rptOwnerCik>
            <rptOwnerName>ROBERTS BRYAN E</rptOwnerName>
        </reportingOwnerId>
        <reportingOwnerAddress>
            <rptOwnerStreet1>C/O VENROCK</rptOwnerStreet1>
            <rptOwnerStreet2>3340 HILLVIEW AVENUE</rptOwnerStreet2>
            <rptOwnerCity>PALO ALTO</rptOwnerCity>
            <rptOwnerState>CA</rptOwnerState>
            <rptOwnerZipCode>94304</rptOwnerZipCode>
            <rptOwnerStateDescription></rptOwnerStateDescription>
        </reportingOwnerAddress>
        <reportingOwnerRelationship>
            <isDirector>1</isDirector>
            <isOfficer>0</isOfficer>
            <isTenPercentOwner>0</isTenPercentOwner>
            <isOther>0</isOther>
            <officerTitle></officerTitle>
            <otherText></otherText>
        </reportingOwnerRelationship>
    </reportingOwner>

    <nonDerivativeTable></nonDerivativeTable>

    <derivativeTable>
        <derivativeTransaction>
            <securityTitle>
                <value>Stock Option (Right to Buy)</value>
            </securityTitle>
            <conversionOrExercisePrice>
                <value>12.07</value>
            </conversionOrExercisePrice>
            <transactionDate>
                <value>2018-06-05</value>
            </transactionDate>
            <deemedExecutionDate></deemedExecutionDate>
            <transactionCoding>
                <transactionFormType>4</transactionFormType>
                <transactionCode>A</transactionCode>
                <equitySwapInvolved>0</equitySwapInvolved>
            </transactionCoding>
            <transactionAmounts>
                <transactionShares>
                    <value>15000</value>
                </transactionShares>
                <transactionPricePerShare>
                    <value>0</value>
                </transactionPricePerShare>
                <transactionAcquiredDisposedCode>
                    <value>A</value>
                </transactionAcquiredDisposedCode>
            </transactionAmounts>
            <exerciseDate>
                <footnoteId id="F1"/>
            </exerciseDate>
            <expirationDate>
                <value>2028-06-05</value>
            </expirationDate>
            <underlyingSecurity>
                <underlyingSecurityTitle>
                    <value>Common Stock</value>
                </underlyingSecurityTitle>
                <underlyingSecurityShares>
                    <value>15000</value>
                </underlyingSecurityShares>
            </underlyingSecurity>
            <postTransactionAmounts>
                <sharesOwnedFollowingTransaction>
                    <value>15000</value>
                </sharesOwnedFollowingTransaction>
            </postTransactionAmounts>
            <ownershipNature>
                <directOrIndirectOwnership>
                    <value>D</value>
                    <footnoteId id="F2"/>
                </directOrIndirectOwnership>
            </ownershipNature>
        </derivativeTransaction>
    </derivativeTable>

    <footnotes>
        <footnote id="F1">The option vests with respect to 1/12th of the shares subject thereto on each monthly anniversary of the grant date, which vesting will accelerate in full on the date of the next annual stockholder's meeting to the extent unvested as of such date, subject to continued service through each applicable vesting date.</footnote>
        <footnote id="F2">The reporting person is a member of VR Management, LLC (the &quot;Management Company&quot;). Under an agreement between the reporting person and the Management Company, the reporting person is deemed to hold the reported option and the shares underlying the option for the sole benefit of the Management Company and must exercise the reported option solely upon the direction of the Management Company, which is entitled to the shares upon exercise. The Management Company may be deemed the indirect beneficial owner of the reported option and the shares underlying the option, and the reporting person may be deemed the indirect beneficial owner of the reported option and the shares underlying the option through his interest in the Management Company. The reporting person disclaims beneficial ownership of the reported shares except to the extent of his pecuniary interest therein.</footnote>
    </footnotes>

    <ownerSignature>
        <signatureName>/s/ David L. Stepp, as attorney in fact for Bryan E. Roberts</signatureName>
        <signatureDate>2018-06-07</signatureDate>
    </ownerSignature>
</ownershipDocument>
