In the 1998 Bundestag election, six parties, namely the SPD, the CDU and its Bavarian counterpart, the CSU (which forms a joint parliamentary group with the CDU but runs as a separate party), Alliance 90/The Greens, the F.D.P. and the PDS received at least five percent of all valid second votes cast, and were thus entitled to participate in the proportional allocation of seats at the federal level; between themselves, these parties accumulated a total of 46,408,690 second votes. None of the other parties that participated in the election reached the five percent threshold nor received any constituency mandates; therefore, these were excluded from the apportionment process.
The next step was to calculate the number of seats each one of the six qualifying parties was entitled to receive. The results were as follows:
| 20,181,269 46,408,690 |
x | 656 | = | 285.267963 | for the SPD | |
| 14,004,908 46,408,690 |
x | 656 | = | 197.963348 | for the CDU | |
| 3,324,480 46,408,690 |
x | 656 | = | 46.992468 | for the CSU | |
| 3,301,624 46,408,690 |
x | 656 | = | 46.669392 | for Alliance 90/The Greens | |
| 3,080,955 46,408,690 |
x | 656 | = | 43.550173 | for the F.D.P. | |
| and | ||||||
| 2,515,454 46,408,690 |
x | 656 | = | 35.556656 | for the PDS | |
At this point, the allocation of Bundestag seats stood as follows:
| SPD | 285 |
| CDU | 197 |
| CSU | 46 |
| Alliance 90/The Greens | 46 |
| F.D.P. | 43 |
| PDS | 35 |
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| Total | 652 |
However, four of the 656 seats remained to be allocated. The highest decimal fractions were then determined, by sorting them in descending order, as shown below:
| CSU | 0.992468 |
| CDU | 0.963348 |
| Alliance 90/The Greens | 0.669392 |
| PDS | 0.556656 |
| F.D.P. | 0.550173 |
| SPD | 0.267963 |
Since the CSU, the CDU, Alliance 90/The Greens and the PDS had the four largest fractions, one seat was allocated to each of these parties. This operation completed the initial allocation of seats at the federal level in the following manner:
| SPD | 285 |
| CDU | 198 |
| CSU | 47 |
| Alliance 90/The Greens | 47 |
| F.D.P. | 43 |
| PDS | 36 |
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| Total | 656 |
The seats obtained by each party were then distributed in proportion to the votes received by its Land lists. For example, in Nordrhein-Westfalen the SPD received 5,097,425 of the 20,181,269 second votes cast for the party. Since the party was awarded 285 Bundestag mandates at the federal level, the proportionate share of party mandates in this Land was calculated as follows:
| 5,097,425 20,181,269 |
x | 285 | = | 71.985866 | |
for an initial total of 71 seats, which subsequently increased to 72 when all SPD mandates were allocated among its sixteen Land lists. The process was repeated with the CDU, Alliance 90/Greens, F.D.P. and PDS Land lists. In the case of the CSU, all its votes were cast in Bayern (Bavaria), the only state where the party is organized and contests elections, so no allocation among Land lists was necessary.
It should be noted that all Land lists of a party that qualifies for Bundestag representation participate in the Land-level allocation of party seats, even when they have received less than five percent of the vote in their respective Länder.
At this point, the direct mandates won by each party in a particular Land (if any) were deducted from its proportional seat allocation. For example, the 53 constituency seats won by the SPD in Nordrhein-Westfalen were subtracted from its proportional allocation of 72 seats, so the party was awarded nineteen list seats in that Land. In the case of Alliance 90/The Greens and the F.D.P. all their seats came from their respective party lists, as neither party won constituency seats.
However, in several Länder the number of constituency seats won by the SPD exceeded the Land list seat allocation. For example, in Brandenburg the SPD list was allocated nine seats, but the party secured twelve direct mandates, or three seats above the number to which it was entitled. As noted previously, the electoral law allows parties to keep these additional mandates. In this case, the SPD retained the surplus or overhang seats, and none of the individuals in the party Land list was elected. Nationwide, the SPD won thirteen overhang seats, thus securing 298 of the 669 seats in the expanded Bundestag.
Shortly thereafter, the SPD formed a coalition government with Alliance 90/The Greens. Although the overhang seats won by the SPD did not change the outcome of the election, the surplus mandates provided the ruling coalition with a comfortable Bundestag majority of twenty-one seats over the combined opposition parties, as opposed to a narrow eight-seat majority on a strictly proportional seat allocation.