It depends on many factors, like your computer speed and memory, programming language edition of ChartDirector, and whether you are writing a desktop or web application.
In general, the total number of points can be over 100 million. However, you can only display around 1 million points on the screen updating at real time. To see the other data points, you can use the scroll bar to scroll the chart back and forth.
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Real-time chart: number of points