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

    <schemaVersion>X0306</schemaVersion>

    <documentType>4</documentType>

    <periodOfReport>2015-05-11</periodOfReport>

    <notSubjectToSection16>0</notSubjectToSection16>

    <issuer>
        <issuerCik>0001180079</issuerCik>
        <issuerName>SILVER SPRING NETWORKS INC</issuerName>
        <issuerTradingSymbol>SSNI</issuerTradingSymbol>
    </issuer>

    <reportingOwner>
        <reportingOwnerId>
            <rptOwnerCik>0001586409</rptOwnerCik>
            <rptOwnerName>Burns James P.</rptOwnerName>
        </reportingOwnerId>
        <reportingOwnerAddress>
            <rptOwnerStreet1>C/O SILVER SPRING NETWORKS, INC.</rptOwnerStreet1>
            <rptOwnerStreet2>555 BROADWAY ST.</rptOwnerStreet2>
            <rptOwnerCity>REDWOOD CITY</rptOwnerCity>
            <rptOwnerState>CA</rptOwnerState>
            <rptOwnerZipCode>94063</rptOwnerZipCode>
            <rptOwnerStateDescription></rptOwnerStateDescription>
        </reportingOwnerAddress>
        <reportingOwnerRelationship>
            <isDirector>0</isDirector>
            <isOfficer>1</isOfficer>
            <isTenPercentOwner>0</isTenPercentOwner>
            <isOther>0</isOther>
            <officerTitle>EVP, Chief Financial Officer</officerTitle>
            <otherText></otherText>
        </reportingOwnerRelationship>
    </reportingOwner>

    <nonDerivativeTable>
        <nonDerivativeTransaction>
            <securityTitle>
                <value>Common Stock</value>
            </securityTitle>
            <transactionDate>
                <value>2015-05-11</value>
            </transactionDate>
            <deemedExecutionDate></deemedExecutionDate>
            <transactionCoding>
                <transactionFormType>4</transactionFormType>
                <transactionCode>A</transactionCode>
                <equitySwapInvolved>0</equitySwapInvolved>
            </transactionCoding>
            <transactionAmounts>
                <transactionShares>
                    <value>3398</value>
                    <footnoteId id="F1"/>
                </transactionShares>
                <transactionPricePerShare>
                    <value>0</value>
                </transactionPricePerShare>
                <transactionAcquiredDisposedCode>
                    <value>A</value>
                </transactionAcquiredDisposedCode>
            </transactionAmounts>
            <postTransactionAmounts>
                <sharesOwnedFollowingTransaction>
                    <value>18295</value>
                </sharesOwnedFollowingTransaction>
            </postTransactionAmounts>
            <ownershipNature>
                <directOrIndirectOwnership>
                    <value>D</value>
                </directOrIndirectOwnership>
            </ownershipNature>
        </nonDerivativeTransaction>
        <nonDerivativeTransaction>
            <securityTitle>
                <value>Common Stock</value>
            </securityTitle>
            <transactionDate>
                <value>2015-05-11</value>
            </transactionDate>
            <deemedExecutionDate></deemedExecutionDate>
            <transactionCoding>
                <transactionFormType>4</transactionFormType>
                <transactionCode>F</transactionCode>
                <equitySwapInvolved>0</equitySwapInvolved>
                <footnoteId id="F2"/>
            </transactionCoding>
            <transactionAmounts>
                <transactionShares>
                    <value>1277</value>
                </transactionShares>
                <transactionPricePerShare>
                    <value>11.77</value>
                </transactionPricePerShare>
                <transactionAcquiredDisposedCode>
                    <value>D</value>
                </transactionAcquiredDisposedCode>
            </transactionAmounts>
            <postTransactionAmounts>
                <sharesOwnedFollowingTransaction>
                    <value>17018</value>
                </sharesOwnedFollowingTransaction>
            </postTransactionAmounts>
            <ownershipNature>
                <directOrIndirectOwnership>
                    <value>D</value>
                </directOrIndirectOwnership>
            </ownershipNature>
        </nonDerivativeTransaction>
        <nonDerivativeTransaction>
            <securityTitle>
                <value>Common Stock</value>
            </securityTitle>
            <transactionDate>
                <value>2015-05-11</value>
            </transactionDate>
            <deemedExecutionDate></deemedExecutionDate>
            <transactionCoding>
                <transactionFormType>4</transactionFormType>
                <transactionCode>M</transactionCode>
                <equitySwapInvolved>0</equitySwapInvolved>
                <footnoteId id="F3"/>
            </transactionCoding>
            <transactionAmounts>
                <transactionShares>
                    <value>4625</value>
                </transactionShares>
                <transactionPricePerShare>
                    <value>0</value>
                </transactionPricePerShare>
                <transactionAcquiredDisposedCode>
                    <value>A</value>
                </transactionAcquiredDisposedCode>
            </transactionAmounts>
            <postTransactionAmounts>
                <sharesOwnedFollowingTransaction>
                    <value>21643</value>
                </sharesOwnedFollowingTransaction>
            </postTransactionAmounts>
            <ownershipNature>
                <directOrIndirectOwnership>
                    <value>D</value>
                </directOrIndirectOwnership>
            </ownershipNature>
        </nonDerivativeTransaction>
        <nonDerivativeTransaction>
            <securityTitle>
                <value>Common Stock</value>
            </securityTitle>
            <transactionDate>
                <value>2015-05-11</value>
            </transactionDate>
            <deemedExecutionDate></deemedExecutionDate>
            <transactionCoding>
                <transactionFormType>4</transactionFormType>
                <transactionCode>F</transactionCode>
                <equitySwapInvolved>0</equitySwapInvolved>
                <footnoteId id="F2"/>
            </transactionCoding>
            <transactionAmounts>
                <transactionShares>
                    <value>1739</value>
                </transactionShares>
                <transactionPricePerShare>
                    <value>11.95</value>
                </transactionPricePerShare>
                <transactionAcquiredDisposedCode>
                    <value>D</value>
                </transactionAcquiredDisposedCode>
            </transactionAmounts>
            <postTransactionAmounts>
                <sharesOwnedFollowingTransaction>
                    <value>19904</value>
                </sharesOwnedFollowingTransaction>
            </postTransactionAmounts>
            <ownershipNature>
                <directOrIndirectOwnership>
                    <value>D</value>
                </directOrIndirectOwnership>
            </ownershipNature>
        </nonDerivativeTransaction>
    </nonDerivativeTable>

    <derivativeTable>
        <derivativeTransaction>
            <securityTitle>
                <value>Performance Stock Units</value>
            </securityTitle>
            <conversionOrExercisePrice>
                <value>0</value>
                <footnoteId id="F4"/>
            </conversionOrExercisePrice>
            <transactionDate>
                <value>2015-05-11</value>
            </transactionDate>
            <deemedExecutionDate></deemedExecutionDate>
            <transactionCoding>
                <transactionFormType>4</transactionFormType>
                <transactionCode>A</transactionCode>
                <equitySwapInvolved>0</equitySwapInvolved>
            </transactionCoding>
            <transactionAmounts>
                <transactionShares>
                    <value>100000</value>
                </transactionShares>
                <transactionPricePerShare>
                    <value>0</value>
                </transactionPricePerShare>
                <transactionAcquiredDisposedCode>
                    <value>A</value>
                </transactionAcquiredDisposedCode>
            </transactionAmounts>
            <exerciseDate>
                <footnoteId id="F5"/>
                <footnoteId id="F6"/>
            </exerciseDate>
            <expirationDate>
                <footnoteId id="F5"/>
                <footnoteId id="F6"/>
            </expirationDate>
            <underlyingSecurity>
                <underlyingSecurityTitle>
                    <value>Common Stock</value>
                </underlyingSecurityTitle>
                <underlyingSecurityShares>
                    <value>100000</value>
                </underlyingSecurityShares>
            </underlyingSecurity>
            <postTransactionAmounts>
                <sharesOwnedFollowingTransaction>
                    <value>100000</value>
                </sharesOwnedFollowingTransaction>
            </postTransactionAmounts>
            <ownershipNature>
                <directOrIndirectOwnership>
                    <value>D</value>
                </directOrIndirectOwnership>
            </ownershipNature>
        </derivativeTransaction>
        <derivativeTransaction>
            <securityTitle>
                <value>Restricted Stock Units</value>
            </securityTitle>
            <conversionOrExercisePrice>
                <value>0</value>
                <footnoteId id="F7"/>
            </conversionOrExercisePrice>
            <transactionDate>
                <value>2015-05-11</value>
            </transactionDate>
            <deemedExecutionDate></deemedExecutionDate>
            <transactionCoding>
                <transactionFormType>4</transactionFormType>
                <transactionCode>M</transactionCode>
                <equitySwapInvolved>0</equitySwapInvolved>
                <footnoteId id="F3"/>
            </transactionCoding>
            <transactionAmounts>
                <transactionShares>
                    <value>4625</value>
                </transactionShares>
                <transactionPricePerShare>
                    <value>0</value>
                </transactionPricePerShare>
                <transactionAcquiredDisposedCode>
                    <value>D</value>
                </transactionAcquiredDisposedCode>
            </transactionAmounts>
            <exerciseDate>
                <footnoteId id="F8"/>
            </exerciseDate>
            <expirationDate>
                <footnoteId id="F8"/>
            </expirationDate>
            <underlyingSecurity>
                <underlyingSecurityTitle>
                    <value>Common Stock</value>
                </underlyingSecurityTitle>
                <underlyingSecurityShares>
                    <value>4625</value>
                </underlyingSecurityShares>
            </underlyingSecurity>
            <postTransactionAmounts>
                <sharesOwnedFollowingTransaction>
                    <value>46250</value>
                </sharesOwnedFollowingTransaction>
            </postTransactionAmounts>
            <ownershipNature>
                <directOrIndirectOwnership>
                    <value>D</value>
                </directOrIndirectOwnership>
            </ownershipNature>
        </derivativeTransaction>
    </derivativeTable>

    <footnotes>
        <footnote id="F1">Represents restricted stock units (&quot;RSUs&quot;) awarded to the Reporting Person on May 11, 2015 that vested in full and settled immediately upon grant.  The shares of Common Stock were delivered to the Reporting Person upon settlement for no consideration.</footnote>
        <footnote id="F2">Exempt transaction pursuant to Section 16b-3(e) for payment of exercise price or tax liability by delivering or withholding securities incident to the receipt, exercise or vesting of a security issued in accordance with Rule 16b-3. All of the shares reported as disposed of in this Form 4 were relinquished to the Issuer by the Reporting Person and cancelled by the Issuer in exchange for the Issuer's agreement to pay federal and state tax withholding obligations of the Reporting Person resulting from the vesting of RSUs. The Reporting Person did not sell or otherwise dispose of any of the shares reported on this Form 4 for any reason other than to cover required taxes.</footnote>
        <footnote id="F3">Release and settlement of RSUs granted to the Reporting Person on November 15, 2013, the grant of which was previously reported on a Form 4 by the Reporting Person.</footnote>
        <footnote id="F4">Each performance stock unit (&quot;PSU&quot;) represents a contingent right to receive 1 share of the Issuer's Common Stock upon settlement for no consideration.</footnote>
        <footnote id="F5">The PSUs shall be eligible to vest as to (i) 60,000 shares if the average trading closing price of the Issuer's Common Stock for 45 consecutive trading days after the grant date and prior to the 3 year anniversary of the grant date (the &quot;Average Price Threshold&quot;) is equal to or greater than $20.00 per share, (ii) an additional 20,000 shares if the Average Price Threshold is equal to or greater than $25.00 per share, and (iii) an additional 20,000 shares if the Average Price Threshold is equal to or greater than $30.00 per share.</footnote>
        <footnote id="F6">The PSUs that become eligible to vest according to the conditions described in note (4) shall vest as to 1/3rd of the total number of such shares on the one-year anniversary of the grant date and as to an additional 1/12th of such shares in equal quarterly installments thereafter. Shares of the Issuer's common stock will be delivered to the Reporting Person following vesting.</footnote>
        <footnote id="F7">Each RSU represents a contingent right to receive 1 share of the Issuer's Common Stock upon settlement for no consideration.</footnote>
        <footnote id="F8">25% of the RSUs vest on November 10, 2014 and thereafter shall vest quarterly as to 6.25% of the total RSUs with the first 6.25% vesting on February 10, 2015. Shares of the Issuer's common stock will be delivered to the Reporting Person following vesting.</footnote>
    </footnotes>

    <remarks></remarks>

    <ownerSignature>
        <signatureName>/s/ James P. Burns by Cecilia Hartwig, Attorney-in-Fact</signatureName>
        <signatureDate>2015-05-13</signatureDate>
    </ownerSignature>
</ownershipDocument>
