Solar Eclipse Coverage Calculator
Enter apparent angular diameters and center separation to estimate eclipse type, magnitude, and Sun coverage.
Note: This tool is educational and geometric. It does not include atmosphere, terrain, or exact orbital mechanics for a specific location/time.
What this eclipse calculator does
This eclipse calculator estimates how much of the Sun is covered by the Moon during a solar eclipse using three geometric inputs: the apparent diameter of the Sun, the apparent diameter of the Moon, and the angular distance between their centers. With these values, the calculator computes overlap area, eclipse obscuration percentage, and a practical eclipse classification (no eclipse, partial, annular, or total).
In short: it translates sky geometry into an easy-to-understand result you can compare across different eclipse scenarios.
Understanding the inputs
1) Sun apparent diameter
The Sun’s apparent size changes slightly during the year because Earth’s orbit is not perfectly circular. Typical values are roughly 31.5 to 32.5 arcminutes.
2) Moon apparent diameter
The Moon’s apparent size varies even more because its orbit is elliptical. Values around 29.5 to 33.5 arcminutes are common. This variation is the reason some central eclipses are total while others are annular.
3) Center separation
This is the angular distance between the center of the Sun and center of the Moon at a chosen instant. A smaller separation means better alignment and deeper eclipse coverage.
How the eclipse math works
The calculator treats the Sun and Moon as circles in the sky. It uses the standard overlap-of-two-circles formula:
- If circles do not touch, overlap is zero.
- If one circle is completely inside the other, overlap is the smaller circle’s area.
- Otherwise, overlap is found using arc-cosine terms and a triangle area term.
From overlap area, the tool computes:
- Obscuration (%): fraction of the Sun’s disc area covered by the Moon.
- Magnitude: fraction of the Sun’s diameter obscured along the line of centers.
- Eclipse type: geometric classification from alignment and size relationship.
Interpreting eclipse types
No eclipse
The Moon does not overlap the Sun’s disc (center separation is too large).
Partial eclipse
The Moon overlaps only part of the Sun’s disc. The overlap can be small or very deep, but the Sun is never fully covered.
Annular eclipse
The Moon is centered enough to pass across the Sun, but appears slightly smaller than the Sun. A bright ring (“annulus”) remains visible around the Moon.
Total eclipse
The Moon appears large enough and aligned enough to completely cover the Sun’s photosphere. This is when totality can occur.
Example use cases
- Compare how eclipse depth changes when Moon diameter increases by just 0.3 arcminutes.
- Estimate whether a central alignment is likely annular or total based on apparent diameters.
- Teach students the difference between eclipse magnitude and obscuration.
- Create quick “what-if” simulations before looking at detailed eclipse maps.
Important observing safety reminder
Never look directly at the Sun without certified solar viewing protection, except during the brief period of verified totality. Ordinary sunglasses are not safe for solar viewing. Use ISO 12312-2 eclipse glasses, approved solar filters, or indirect viewing methods.
Limitations of this tool
This calculator is intentionally simple and geometric. It does not include:
- Observer location (latitude/longitude),
- Exact ephemerides and time evolution,
- Atmospheric refraction and local weather,
- Baily’s beads, limb irregularities, or corona visibility modeling.
For planning real eclipse travel and exact contact times, combine this tool with professional eclipse predictions and local forecasts.