Quorum requirements for a referendum to be valid

For optional referendums:

Denmark, Constitution 1953, accessed 24 September 2019

Section 42:

(1) Whereas Bill has been passed by the Folketing, one-third of the members of the Folketing may, within three weekdays from the final passing of the Bill, request of the President that the Bill be submitted to a referendum. Such request shall be made in writing and signed by the members making the request. […]

(5) At the referendum votes shall be cast for or against the Bill. For the Bill to be rejected, a majority of the electors who vote and not less than thirty per cent of all persons who are entitled to vote shall have voted against the Bill.

For mandatory referendums:

Denmark, Constitution 1953, accessed 24 September 2019

Section 20:

(1) Powers vested in the authorities of the Realm under this Constitutional Act may, to such extent as shall be provided by statute, be delegated to international authorities set up by mutual agreement with other states for the promotion of international rules of law and cooperation.

(2) For the enactment of a Bill dealing with the above, a majority of five-sixths of the members of the Folketing shall be required. If this majority is not obtained, whereas the majority required for the passing of ordinary Bills is obtained, and if the Government maintains it, the Bill shall be submitted to the electorate for approval or rejection in accordance with the rules for referenda laid down in section 42.

Section 29(2): The age qualification for suffrage shall be as determined by the referendum held under the Act dated March 25, 1953. Such age qualification for suffrage may be altered at any time by statute. A Bill passed by the Folketing for the purpose of such enactment shall receive the Royal Assent only when the provision for altering the age qualification for suffrage has been submitted to a referendum in accordance with sub-section (5) of section 42, and which has not resulted in the rejection of the provision.

Section 88: Should the Folketing pass a Bill for the purposes of a new constitutional provision, and the Government wish to proceed with the matter, writs shall be issued for the election of members of a new Folketing. If the Bill is passed unamended by the Folketing assembling after the election, the Bill shall, within six months after its final passage, be submitted to the electors for approval or rejection by direct voting. Rules for this voting shall be laid down by statute. If a majority of the persons taking part in the voting, and at least 40 per cent of the electorate, have voted in favour of the Bill as passed by the Folketing, and if the Bill receives the Royal Assent, it shall form an integral part of the Constitutional Act.

30% of eligible voters for both optional and mandatory referendums; the only exception is the issue of amending the Constitution - it requires 40% of eligible voters.