I made an app on Geogebra which shows the link between solar eclipse magnitude (fraction of the solar diameter covered) and the obscuration (fraction of the solar disk area covered).
Play with the sliders. An eclipse magnitude of 0.5 (half the diameter covered) does not mean half the area is obscured.
The mathematics connecting the two quantities (sectors of circles and trigonometry) can be explored in more detail here. (I’m so happy the Internet Archive exists! Thought I’d lost this during switchover to WordPress).