Free Sunset Calculator

Sunset Time Calculation: From Theory to Accurate Results

A sunset is more than a daily spectacle; it’s a precisely predictable astronomical event. This sunset calculator helps you determine the exact moment when the Sun disappears below the horizon—along with the corresponding dusk time, evening twilight phases, and even the solar noon for any location on Earth. By understanding the geometry behind the Earth‑Sun system, you can compute these times yourself or trust the tool to handle the heavy math.

What Is Sunset and How Does It Differ From Twilight?

Astronomically, sunset (or sundown) occurs when the upper edge of the Sun’s disk crosses the horizon, ending its visibility from a given point. However, complete darkness doesn’t begin immediately. The period after sunset is divided into three distinct twilight stages, each defined by the Sun’s angular position below the horizon:

• Civil twilight – Sun between $0^\circ$ and $6^\circ$ below the horizon. Artificial lighting is not yet required, and the brightest stars become visible.
• Nautical twilight – Sun between $6^\circ$ and $12^\circ$ below. The horizon remains discernible, but navigation by stars becomes practical.
• Astronomical twilight – Sun between $12^\circ$ and $18^\circ$ below. When the Sun passes $18^\circ$, true night begins, and faint nebulae or galaxies can be observed.

A sunrise sunset calculator typically reports these twilight boundaries alongside the main event. The evening twilight calculator inside this tool lets you explore each phase individually.

The Astronomical Foundation: Why Sunset Times Change

The Earth rotates around the Sun on a tilted axis ($\approx 23.45^\circ$ relative to its orbital plane). This tilt causes the solar declination—the angle between the Sun’s rays and the equatorial plane—to oscillate between $+23.45^\circ$ (June solstice) and $-23.45^\circ$ (December solstice). During equinoxes the declination is $0^\circ$. Together with the observer’s latitude $\phi$ and longitude $\lambda$, this declination determines when the Sun reaches the horizon.

Step‑by‑Step: The Core Sunset Time Formula

Calculating the sunset time involves several intermediate quantities. Here’s an overview of the process:

1. Day number $n$ – the day of the year (1 for January 1st).
2. Sun’s mean anomaly – $M = 0.9856^\circ \times n - 3.289^\circ$ (approximate).
3. True longitude $L$ – corrected for orbital eccentricity.
4. Right ascension $\text{RA}$ – the celestial “longitude” of the Sun.
5. Solar declination $\delta$ – computed from $L$.
6. Hour angle $h$ – the angular distance from the local meridian. For sunset (center of Sun on horizon) we use $z = 90^\circ$, giving:

$$\cos h = -\frac{\sin \phi \sin \delta}{\cos \phi \cos \delta}$$

This yields the hour angle in degrees. Convert it to hours (divide by 15) to obtain the UTC sunset time:

$$T_{\text{UTC}} = 12 + \frac{h_{\text{hours}}}{15} - \frac{\lambda_{\text{hours}}}{15}$$

Finally, adjust for the local time zone and daylight saving (DST) to get the local sunset time.

Accounting for Atmospheric Refraction

The formulas above (using $z = 90^\circ$) ignore the bending of sunlight by the atmosphere. In reality, refraction makes the Sun appear higher than it is, so the visible sunset occurs later than the geometric sunset. The average refraction at the horizon is $0.58^\circ$. To compensate, the effective zenith angle is set to $90.833^\circ$ (including both refraction and the Sun’s semi‑diameter). The corrected hour angle becomes:

$$\cos h_{\text{corr}} = \frac{\sin(-0.833^\circ) - \sin \phi \sin \delta}{\cos \phi \cos \delta}$$

This adjustment typically adds about 6 minutes to the sunset time. For twilight phases, the refraction effect is negligible because the Sun is already well below the horizon.

What You Can Do With This Tool

Whether you need the exact sunset time for photography planning, want to know when civil dusk begins, or require the solar noon for aligning solar panels, the sunset time calculator provides high‑accuracy results for any date and location. It handles both geometric and refraction‑corrected values, so you can see the difference the atmosphere makes. Additionally, the same underlying model can be used to compute sunrise times and total daylight duration—making it a versatile sunrise sunset calculator for enthusiasts and professionals alike.