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

    <schemaVersion>X0306</schemaVersion>

    <documentType>4</documentType>

    <periodOfReport>2019-02-28</periodOfReport>

    <notSubjectToSection16>0</notSubjectToSection16>

    <issuer>
        <issuerCik>0000102037</issuerCik>
        <issuerName>UNIVERSAL CORP /VA/</issuerName>
        <issuerTradingSymbol>UVV</issuerTradingSymbol>
    </issuer>

    <reportingOwner>
        <reportingOwnerId>
            <rptOwnerCik>0001263726</rptOwnerCik>
            <rptOwnerName>PEEBLES ROBERT</rptOwnerName>
        </reportingOwnerId>
        <reportingOwnerAddress>
            <rptOwnerStreet1>9201 FOREST HILL AVENUE</rptOwnerStreet1>
            <rptOwnerStreet2></rptOwnerStreet2>
            <rptOwnerCity>RICHMOND</rptOwnerCity>
            <rptOwnerState>VA</rptOwnerState>
            <rptOwnerZipCode>23235</rptOwnerZipCode>
            <rptOwnerStateDescription></rptOwnerStateDescription>
        </reportingOwnerAddress>
        <reportingOwnerRelationship>
            <isDirector>0</isDirector>
            <isOfficer>1</isOfficer>
            <isTenPercentOwner>0</isTenPercentOwner>
            <isOther>0</isOther>
            <officerTitle>VP &amp; Controller</officerTitle>
            <otherText></otherText>
        </reportingOwnerRelationship>
    </reportingOwner>

    <nonDerivativeTable>
        <nonDerivativeTransaction>
            <securityTitle>
                <value>Common Stock</value>
            </securityTitle>
            <transactionDate>
                <value>2019-02-28</value>
            </transactionDate>
            <transactionCoding>
                <transactionFormType>4</transactionFormType>
                <transactionCode>S</transactionCode>
                <equitySwapInvolved>0</equitySwapInvolved>
            </transactionCoding>
            <transactionAmounts>
                <transactionShares>
                    <value>7274</value>
                </transactionShares>
                <transactionPricePerShare>
                    <value>59.5619</value>
                    <footnoteId id="F1"/>
                </transactionPricePerShare>
                <transactionAcquiredDisposedCode>
                    <value>D</value>
                </transactionAcquiredDisposedCode>
            </transactionAmounts>
            <postTransactionAmounts>
                <sharesOwnedFollowingTransaction>
                    <value>27058</value>
                    <footnoteId id="F2"/>
                </sharesOwnedFollowingTransaction>
            </postTransactionAmounts>
            <ownershipNature>
                <directOrIndirectOwnership>
                    <value>D</value>
                </directOrIndirectOwnership>
            </ownershipNature>
        </nonDerivativeTransaction>
    </nonDerivativeTable>

    <derivativeTable></derivativeTable>

    <footnotes>
        <footnote id="F1">The price reported in Column 4 is a weighted average price. These shares were sold in multiple transactions at prices ranging from $59.51 to $59.59 per share, inclusive. The reporting person undertakes to provide the Issuer, any security holder of the Issuer, or the staff of the Securities and Exchange Commission, upon request, full information regarding the number of shares sold at each separate price within the range set forth in this footnote.</footnote>
        <footnote id="F2">Includes 12,350 restricted stock units and 1,514 dividend units on the restricted stock units. The restricted stock units and the dividend units vest on the fifth anniversary of the award date, however, payment will be delayed until termination of service if the individual is a covered employee under Code Section 162(m) on the date of vesting.</footnote>
    </footnotes>

    <remarks></remarks>

    <ownerSignature>
        <signatureName>Robert M. Peebles by Preston D. Wigner, Power of Attorney</signatureName>
        <signatureDate>2019-03-01</signatureDate>
    </ownerSignature>
</ownershipDocument>
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X0306
4
2019-02-28
0
0000102037
UNIVERSAL CORP /VA/
UVV
0001263726
PEEBLES ROBERT
9201 FOREST HILL AVENUE
RICHMOND
VA
23235
0
1
0
0
VP & Controller
Common Stock
2019-02-28
4
S
0
7274
59.5619
D
27058
D
The price reported in Column 4 is a weighted average price. These shares were sold in multiple transactions at prices ranging from $59.51 to $59.59 per share, inclusive. The reporting person undertakes to provide the Issuer, any security holder of the Issuer, or the staff of the Securities and Exchange Commission, upon request, full information regarding the number of shares sold at each separate price within the range set forth in this footnote.
Includes 12,350 restricted stock units and 1,514 dividend units on the restricted stock units. The restricted stock units and the dividend units vest on the fifth anniversary of the award date, however, payment will be delayed until termination of service if the individual is a covered employee under Code Section 162(m) on the date of vesting.
Robert M. Peebles by Preston D. Wigner, Power of Attorney
2019-03-01