Eclipse magnitude and obscuration
This app demonstrates the relationship between eclipse magnitude (a value between 0 and 1) and percentage obscuration for solar eclipses.
Astronomers describe how much of the Sun is covered by the Moon in a solar eclipse by a number called the magnitude.
The magnitude is how much of the solar diameter is covered by the moon; it has a value between 0 and 1 inclusive, where 1 is totally eclipsed.
This app shows the relationship between eclipse magnitude and obscuration (given as a percentage of the solar disk). For example, when the Sun and Moon have the same apparent diameter then a magnitude of 0.5 corresponds to about 39% obscuration.
The Earth has an elliptical orbit around the Sun and the moon has an elliptical orbit around the Earth. Those facts mean that the apparent sizes of the Sun and Moon look different from eclipse to eclipse. It also means that sometimes the Moon can look bigger than the Sun (so a total eclipse may be possible) or it can appear smaller (so it cannot completely hide the Sun and an annular eclipse may be possible. Realistic values for the Sun radius in this app are between 0.98 and 1.02. Typical values for lunar radius are 0.92 to 1.08.
I included a greater range of values for the Sun and Moon radii because they might be used to represent eclipses of other objects; moons around other planets, or exosolar planets passing in front of their parent stars.
The obscuration calculation uses simple area formulae for circular sectors and triangles. I'll post a link to my blog for this calculation in the near future.