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How many German aircraft did the RAF claim on 15 September 1940, and how many were there really?
Short answer
The RAF claimed to have shot down 185 German aircraft over the whole day (pending confirmation). The actual losses were far lower: 58 or around 61 aircraft, according to different sources (according to different sources).

The British claim
According to Allied Air Force Research, the RAF claimed to have shot down 185 German aircraft over the whole day (pending confirmation). In the afternoon combat alone it claimed 77 bombers and 29 fighters, a very large exaggeration of the German losses. There was another case of excess in one of that day's engagements, in which the British claimed 81 aircraft: Zehbe's Dornier was the subject of nine separate claims.
The actual losses
Allied Air Force Research notes that later reports lowered the figure to around 61 aircraft (according to different sources), and that it was still the Luftwaffe's biggest loss in more than a month. Other sources put the number of German aircraft destroyed over the whole day at 58 (according to different sources).
Why 15 September is remembered
Sunday 15 September was a clear and decisive defeat for the Luftwaffe, which is why it is known as Battle of Britain Day. That action was the climax of the battle. After the attack, Operation Sea Lion was postponed. Defeated in daylight, the Luftwaffe turned its attention to the night-time Blitz campaign, which lasted until May 1941.
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