# Sunrise Sunset Calculator

The sunrise sunset calculator will assist you in determining **the sunrise and sunset times** for a particular day for all populated latitudes. The Earth rotates at an angular velocity of **15°/hour**; therefore, there is a need for a formula to calculate sunrise and sunset based on the location. The sunrise and sunset times are a **function of location** and **day of the year**. Based on these timings, the calculator also estimates **how many hours of daylight a place would receive**.

Read on to understand what time is sunrise and sunset today? Or you want to know how to calculate sunrise and sunset time based on the formula.

## Sunrise and Sunset times

The term sunrise time refers to the time when the **sun first appears or when daylight has arrived**. Similarly, sunset time is defined as the time when the **sun disappears below the horizon**. For a given location having latitude `φ°`

and $n^{th}$ day of the year, the **sunrise time can be estimated** using the hour angle for sunrise/sunset, $\omega$.

Where **δ is the declination angle**. The sunrise angle is negative, whereas the sunset angle is positive. The declination angle is the **angle between the equator and the line joining centers of Earth and sun**. The angle of declination varies with each day, n such that:

where **n is the $n^{th}$ day of the year**. The declination angle has several formulae for estimation, the above approximation is based on the work of **P.I. Cooper from the year 1969**.

Once we have the hour **angle for sunrise, $\omega$, it is added (negative) from the solar noon** to determine the sunrise time.

The sunset hour angle $\omega$ is the **negative of the sunrise hour angle** or positive. The sunset time is then estimated by **adding it to the solar noon**:

The above equations are formulae to calculate sunrise and sunset times. Once we know the timings, we can determine the **hours of daylight** for a latitude using the equation:

Alternatively, the daylight hours equation can also be written as:

While the above methodology is correct, it does not take into account atmospheric refraction. This effect occurs due to the **sunlight refracting through the atmosphere and making the sun appear higher above the horizon than its actual position**. A variable `sin(a)`

is included in the sunrise and sunset formula to take this phenomenon into account. Therefore, the corrected sunset and sunrise equation is:

Where a is the **altitude angle** having the value of `-0.83°`

.

## How to calculate the times of sunrise and sunset for tomorrow?

To calculate sunrise and sunset times:

- Enter the
**date**for tomorrow. - Fill in the
**latitude**for your location (use positive for °N and negative for °S). - The calculator will return the
**declination angle**for the date and subsequently calculate the**sunrise and sunset times**for the particular day. - The tool will also return how many
**hours of daylight**you will receive.

By default, the calculator shows you results taking into account atmospheric refraction. To see the **uncorrected results**, active the `Advanced mode`

of the calculator.

## Example: Using the sunrise sunset calculator

When are sunrise and sunset today, given the date is **15th March**? Also, find out how many hours of daylight there is on that date? Take location as **45 °N**.

To know what time is sunrise and sunset today:

- Pick the
**date**for today as`15th March`

. - Enter the
**latitude**as`45°`

. - The
**declination angle**is returned as:

- Using the
**sunrise equation**:

and sunrise time is:

`12 - 87.6/15 = 6:09 am`

.

- Similarly, the
**sunset time**is:

`12 + 87.6/15 = 5:50 pm`

.

- Considering
**atmospheric refraction**, the sunrise and sunset hour angles become:

- The sunrise and sunset times are:
`6:04 am`

and`5:55 pm`

local time.

The **atmosphere refraction** has set the sunrise time **5 minutes early** based on the appearance of the first light and pushed the sunset time by **5 minutes**, increasing the **daylight hours by 10 minutes** for a day.

## References

Duffie, John A., and William A. Beckman. “Fundamentals.” Introduction. In Solar Engineering of Thermal Processes, 1–25. Hoboken, NJ: Wiley, 2013.

Kalogirou, Soteris. “Environmental Characteristics.” Essay. In Solar Energy Engineering: Processes and Systems, 49–71. Oxford, UK: Academic Press, 2014.

## FAQ

### What is atmospheric refraction?

The phenomenon that celestial objects appear higher above the horizon than they actually are is known as **atmospheric refraction**. This occurs because of the refraction of light reflected from the objects by the atmosphere.

### What is the angular velocity of earth?

The earth rotates with an angular velocity of **15° per hour**.

### How do I calculate sunrise hour angle?

To calculate sunrise hour angle:

- Find the
**latitude**and**day**of the year,`n`

. - Estimate the
**declination angle**using the equation:

`δ = 23.45 * sin((284 + n) * 360/365)`

. - Multiply the
**tangents of latitude**and**declination angle**. - Find the
**cosecant inverse**for the negative of the product. - Multiply the
**resultant with -1**to get the**hour angle for sunrise**.

### How do I calculate daylight hours?

To calculate daylight hours for today:

**Multiply**2 by the sunrise or sunset angle.**Divide**the product with 15 to get the daylight hours.

`Daylight hours = 2/15 * sunrise angle`