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

    <schemaVersion>X0607</schemaVersion>

    <documentType>3</documentType>

    <periodOfReport>2026-07-13</periodOfReport>

    <noSecuritiesOwned>1</noSecuritiesOwned>

    <issuer>
        <issuerCik>0002083910</issuerCik>
        <issuerName>Archimedes Tech SPAC Partners III Co.</issuerName>
        <issuerTradingSymbol>ARCI</issuerTradingSymbol>
        <issuerForeignTradingSymbol></issuerForeignTradingSymbol>
    </issuer>

    <reportingOwner>
        <reportingOwnerId>
            <rptOwnerCik>0001427316</rptOwnerCik>
            <rptOwnerName>Cannon Stephen N</rptOwnerName>
        </reportingOwnerId>
        <reportingOwnerAddress>
            <rptOwnerNonUSAddressFlag>true</rptOwnerNonUSAddressFlag>
            <rptOwnerStreet1>2093 PHILADELPHIA PIKE #1968</rptOwnerStreet1>
            <rptOwnerStreet2></rptOwnerStreet2>
            <rptOwnerCity>CLAYMONT</rptOwnerCity>
            <rptOwnerNonUSStateTerritory></rptOwnerNonUSStateTerritory>
            <rptOwnerCountry>K3</rptOwnerCountry>
            <rptOwnerZipCode>19703</rptOwnerZipCode>
            <rptOwnerStateDescription>HONG KONG</rptOwnerStateDescription>
        </reportingOwnerAddress>
        <reportingOwnerRelationship>
            <isDirector>1</isDirector>
            <isOfficer>0</isOfficer>
            <isTenPercentOwner>0</isTenPercentOwner>
            <isOther>0</isOther>
            <officerTitle></officerTitle>
            <otherText></otherText>
        </reportingOwnerRelationship>
    </reportingOwner>

    <ownerSignature>
        <signatureName>/s/ Stephen N. Cannon</signatureName>
        <signatureDate>2026-07-17</signatureDate>
    </ownerSignature>
</ownershipDocument>
