Free Sunrise Sunset Calculator

Sunrise and Sunset Time Calculation

This Sunrise Sunset Calculator lets you determine the exact sunrise and sunset times for any populated latitude on a given day. By entering a location and a date, you can quickly obtain the local times for sunrise, sunset, and the total daylight duration. It serves as both a Sunrise Time Calculator and a Sunset Time Calculator, offering reliable Sunrise Sunset by Location functionality.

The Earth completes one rotation every 24 hours, which translates to an angular speed of $15^{\circ}$ per hour. This fundamental fact underlies the relationship between time and the Sun’s position in the sky. To compute precise sunrise and sunset moments, the calculator uses astronomical formulas that account for the observer’s latitude ($\phi$), the Sun’s declination angle ($\delta$), and the local hour angle ($\omega$).

Key Formula Components

The core equation for the hour angle at sunrise or sunset is:

$$\cos\omega = \frac{\sin z - \sin\phi \sin\delta}{\cos\phi \cos\delta}$$

where $z$ is the zenith distance of the Sun — equal to $90^{\circ}$ for the geometric sunrise/sunset — and the declination $\delta$ varies throughout the year. A common approximation for declination is:

$$\delta = 23.45^{\circ} \times \sin\left(\frac{360}{365}(n - 81)\right)$$

with $n$ being the day number (January 1 = 1). For higher precision, this tool calculates $\delta$ from the Sun’s true longitude and the obliquity of the ecliptic, reducing errors to fractions of a degree.

Once the hour angle is known, the raw local solar time for sunrise and sunset is obtained. These raw times must be adjusted for the observer’s longitude (converted to a time offset at $15^{\circ}$ per hour) and for the standard time zone offset. If daylight saving time (DST) is in effect for the chosen location, an additional hour is added during summer months.

Atmospheric Refraction Correction

In practice, the Sun appears above the horizon slightly earlier at sunrise and later at sunset than geometric calculations predict. This happens because atmospheric refraction bends sunlight, making the solar disc seem higher than its true position. To account for this, the calculator applies a correction of $0.83^{\circ}$ to the zenith distance:

$$z_{\text{corrected}} = 90^{\circ} + 0.83^{\circ}$$

The tool displays results with this correction by default. You can switch to “uncorrected” mode to see the pure geometric times.

How to Use the Calculator

1. Select the date of interest.
2. Enter the latitude (positive for north, negative for south) and the longitude (east/west).
3. Choose your time zone and indicate whether DST applies.
4. The calculator returns the predicted sunrise and sunset times (in local time) along with the total hours of daylight.

For example, on March 15 at $45^{\circ}\text{N}$, $15^{\circ}\text{W}$, after performing the full sequence of calculations (mean anomaly, true latitude, right ascension, and declination), the tool yields sunrise around 6:14 and sunset around 18:04, giving approximately 11.8 hours of daylight. The built‑in algorithm handles all these steps instantly.

Limitations

The formulas assume a spherical Earth and average atmospheric conditions, so small deviations (on the order of a minute) may occur. For latitudes above the Arctic or Antarctic circles, the simple model can fail on certain days when the Sun never rises or never sets — the calculator clearly flags such cases.

By integrating the keywords “Sunrise Today” and “Daylight Hours Calculator,” this tool provides fast, location‑specific estimates useful for photography, agriculture, solar energy planning, or simply knowing when to expect daylight.