Sunrise Sunset Calculator (2024)

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 use 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 if you want to know how to calculate the sunrise and sunset times based on the formula.

💡 The longer the day, the more energy you can collect with your solar panels. Check our solar panel calculator to estimate the exact values.

Sunrise and Sunset times

The term sunrise time refers to the time when the sun first appears or when daylight has arrived. Similarly, we define sunset time as the moment when the sun disappears below the horizon. For a given location having latitude ϕ\phiϕ and nth day of the year, we can estimate the sunrise time using the hour angle for sunrise/sunset, ω\omegaω.

ω=arccos(cos(z)sin(δ)sin(ϕ)cos(δ)cos(ϕ))\footnotesize\omega \!=\!\arccos\left(\frac{\cos(z)\!-\!\sin(\delta)\!\cdot\!\sin(\phi)}{\cos(\delta)\!\cdot\!\cos(\phi)}\right)ω=arccos(cos(δ)cos(ϕ)cos(z)sin(δ)sin(ϕ))

where:

  • δ\deltaδ — The declination angle;
  • ϕ\phiϕ — The latitude of the desired location; and
  • zzz — The angle of the Sun below the horizon, equal to 90°90\degree90° for the exact time of the desired phenomenon.

We take this angle as it is for the sunset while we subtract it from 360°360\degree360° to find the sunrise. The declination angle is the angle between the equator and the line joining centers of the Earth and the Sun. The angle of declination varies with each day, nnn such that:

δ=arcsin(0.39872sin(L))\footnotesize\delta = \arcsin(0.39872\!\cdot\!\sin(L))δ=arcsin(0.39872sin(L))

where LLL is the true latitude of the Sun (its projected position on the Earth). Note that there are multiple ways to calculate the Sun's declination.

Sunrise Sunset Calculator (1)

In our case, we calculated it from LLL, with LLL being given by:

L=M+1.916sin(M)+0.02sin(2M)+282.634\footnotesize\begin{split}L &= M+1.916\sin(M)\\&\quad+0.02\sin(2\!\cdot\!M)+282.634\end{split}L=M+1.916sin(M)+0.02sin(2M)+282.634

MMM is a measure of the Sun's mean anomaly, a quantity that expresses the discrepancy between the true elliptic orbit of Earth and the ideal circular orbit with an identical period for a given moment of the year:

M=0.9856t3.289\footnotesize M = 0.9856\cdot t - 3.289M=0.9856t3.289

The value of ttt depends on the day number (the number of days elapsed since the first of January) and the time of the day:

t={n+6λhour24(sunrise)n+18λhour24(sunset)\footnotesize t =\begin{cases} n + \frac{6-\lambda_{\mathrm{hour}}}{24}\ \mathrm{(sunrise)}\\[1em] n + \frac{18-\lambda_{\mathrm{hour}}}{24}\ \mathrm{(sunset)}\end{cases}t={n+246λhour(sunrise)n+2418λhour(sunset)

The second part of both equations is an approximation of the local sunrise and sunset times. In the formula, λhour\lambda_{\mathrm{hour}}λhour is nothing but an expression of the latitude in hours. To find it, divide the value of the latitude in degrees by 151515.

Once we have the hour (angle for sunrise), ω\omegaω, we can calculate the local time of the sunrise and sunset by applying the following formula:

T=ω15+RA(0.06571t)6.622,\footnotesize T = \frac{\omega}{15} + \mathrm{RA}- (0.06571 \cdot t) - 6.622,T=15ω+RA(0.06571t)6.622,

where RA\mathrm{RA}RA is the Sun's right ascension, that we found with:

RA=115(arctan(0.91764tan(L))+(Lmod90°)(arctan(0.91764tan(L))mod90°))\footnotesize\begin{split} &\mathrm{RA} = \frac{1}{15}\!\cdot\!\Big(\arctan(0.91764 \cdot \tan(L))\\&+( L\!\!\!\!\mod 90\degree)\\&-(\arctan(0.91764 \cdot \tan(L))\!\!\!\!\mod 90\degree)\Big)\end{split}RA=151(arctan(0.91764tan(L))+(Lmod90°)(arctan(0.91764tan(L))mod90°))

Back to business: we need to adjust the times we calculated, taking into account the local latitude and the time zone. To do so, we subtract the former and add the latter:

Tlocal=Tλh+tz\footnotesize T_\mathrm{local} = T-\lambda_\mathrm{h}+\mathrm{tz}Tlocal=Tλh+tz

Remember to consider daylight savings if the desired location observes such time. Simply add 111 hour to the calculated time in the summer if this is the case!

To calculate the daylight hours, we compute the difference between the time of the sunset and the time of the sunrise:

tdaylight=Tlocal,sunsetTlocal,sunrise\small t_\mathrm{daylight} = T_\mathrm{local,\ sunset} - T_\mathrm{local,\ sunrise}tdaylight=Tlocal,sunsetTlocal,sunrise

While the above methodology is correct, it does not consider 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 small angle is included in the sunrise and sunset formula to take this phenomenon into account. Therefore, the corrected sunset and sunrise equation is:

 ⁣ω=arccos(cos(90+a)sin(δ)sin(ϕ)cos(δ)cos(ϕ))\!\footnotesize\omega \!=\!\arccos\!\left(\!\frac{\cos(90+a)\!-\!\sin(\delta)\!\cdot\!\sin(\phi)}{\cos(\delta)\!\cdot\!\cos(\phi)}\!\right)ω=arccos(cos(δ)cos(ϕ)cos(90+a)sin(δ)sin(ϕ))

where aaa is the altitude angle having the value of 0.83°.

🙋 You can read more about refraction in our index of refraction calculator.

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

To calculate sunrise and sunset times:

  1. Enter the date for tomorrow.
  2. Fill in the latitude for your location (use positive for °N and negative for °S).
  3. The calculator will return the declination angle for the date and subsequently calculate the sunrise and sunset times for that particular day.
  4. 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, activate 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 we will have on this date. Take location as 45°N45\degree\ \mathrm{N}45°N, 15°W15\degree\ \mathrm{W}15°W.

To know what time is sunrise and sunset today:

  1. Pick the date for today as 15th March.
  2. Enter the latitude as 45°45\degree45° and select the northern hemisphere.
  3. Enter the longitude as 15°15\degree15° and select the western hemisphere.
  4. The approximate times of sunrise and sunset are:

t={75+6124=75.2917(sunrise)75+18124=75.7917(sunset)\footnotesize \enspace \enspace t =\begin{cases}75 + \frac{6-1}{24}=75.2917\ \mathrm{(sunrise)}\\[1em]75 + \frac{18-1}{24}=75.7917\ \mathrm{(sunset)}\end{cases}t={75+2461=75.2917(sunrise)75+24181=75.7917(sunset)

  1. Calculate the mean anomaly in both cases:

Mrise=(0.985675.2083)3.289=69.9329Mset=(0.9856t)3.289=70.4257\footnotesize \begin{split}\enspace \enspace M_{\mathrm{rise}}&= (0.9856 \cdot 75.2083) - 3.289\\&=69.9329\\M_{\mathrm{set}} &=(0.9856 \cdot t) - 3.289\\&=70.4257\end{split}MriseMset=(0.985675.2083)3.289=69.9329=(0.9856t)3.289=70.4257

  1. Find the Sun's true latitude. We spare you the calculations:

Lrise=354.3794°Lset=354.8776°\footnotesize \begin{split}\enspace \enspace L_{\mathrm{rise}}&= 354.3794\degree\\L_{\mathrm{set}} &=354.8776\degree\end{split}LriseLset=354.3794°=354.8776°

  1. Now, we compute the Sun's right ascension. Again, the mathematics is rather complex. Here is the result:

RArise=23.6560°RAset=23.6865°\footnotesize \begin{split}\enspace \enspace \mathrm{RA}_{\mathrm{rise}}&= 23.6560\degree\\\mathrm{RA}_{\mathrm{set}} &=23.6865\degree\end{split}RAriseRAset=23.6560°=23.6865°

  1. It's time to calculate the Sun's declination.

δrise=arcsin(0.39782sin(Lrise))=2.2335°δset=arcsin(0.39782sin(Lset))=2.0359°\footnotesize \begin{split}\enspace \enspace \delta_{\mathrm{rise}}&=\arcsin\left(0.39782\sin(L_\mathrm{rise})\right)\\&=-2.2335\degree\\\delta_{\mathrm{set}}&=\arcsin\left(0.39782\sin(L_\mathrm{set})\right)\\&=-2.0359\degree\end{split}δriseδset=arcsin(0.39782sin(Lrise))=2.2335°=arcsin(0.39782sin(Lset))=2.0359°

  1. Now, we can compute the hour angle. Use the formula corrected for refraction.

 ⁣ω=arccos(cos(90.833)sin(δ)sin(ϕ)cos(δ)cos(ϕ))\!\footnotesize \omega \!=\! \arccos\!\left(\!\frac{\cos(90.833)\!-\!\sin(\delta)\!\cdot\!\sin(\phi)}{\cos(\delta)\!\cdot\!\cos(\phi)}\!\right)ω=arccos(cos(δ)cos(ϕ)cos(90.833)sin(δ)sin(ϕ))

The result is:

ωrise=293.5714°ωset=89.1423°\begin{split}\omega_{\mathrm{rise}} &=293.5714 \degree\\\omega_{\mathrm{set}} &=89.1423 \degree\\\end{split}ωriseωset=293.5714°=89.1423°

Use the following formula to calculate the sunrise and sunset times:

T=ω15+RA(0.06571t)6.622λh\footnotesize\begin{split}T = &\frac{\omega}{15} + \mathrm{RA}- (0.06571 \cdot t)\\[.5em] &- 6.622 -\lambda_\mathrm{h}\end{split}T=15ω+RA(0.06571t)6.622λh

We can ignore both daylight savings and timezone: they both are equal to 0. The results are:

trise=7.223h=7h13mintset=19.093h=19h5min\begin{split}t_{\mathrm{rise}} &=7.223\ \mathrm{h} =7\ \mathrm{h}\ 13\ \mathrm{min} \\t_{\mathrm{set}} &=19.093\ \mathrm{h}=19\ \mathrm{h}\ 5\ \mathrm{min}\end{split}trisetset=7.223h=7h13min=19.093h=19h5min

Subtract these values to find the number of daylight hours:

tdaylight=tsettrise=19.0937.223=11.87h=11h52min\begin{split}t_\mathrm{daylight}& = t_{\mathrm{set}}-t_\mathrm{rise}\\&=19.093-7.223\\ &= 11.87\ \mathrm{h} \\&=11\ \mathrm{h}\ 52\ \mathrm{min}\end{split}tdaylight=tsettrise=19.0937.223=11.87h=11h52min

🔎 You can also quickly estimate the day duration with Omni's hours calculator.

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 angular velocity of Earth is 15° per hour. To calculate this result, consider these easy steps:

  1. A rotation of Earth is exactly one day long, approximately 24 h.

  2. A full rotation of Earth corresponds to 360°.

  3. Dividing the angle above by the time of a full rotation gives us the result:

    360°/24 h = 15° per h

This is also the apparent speed of the Sun and stars in the sky. Since the Sun has a diameter of half a degree, we can calculate the length of the sunrise:

0.5/15° per h = 0.033 h ~ 2 min

How do I calculate sunrise hour angle?

To calculate the sunrise hour angle:

  1. Find the latitude and day of the year, n.

  2. Estimate the declination angle of the Sun using the equation:

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

    Note that this equation can err up to 1.5°.

  3. Multiply the tangents of latitude and declination angle.

  4. Find the cosecant inverse for the negative of the product.

  5. Multiply the resultant with -1 to get the hour angle for sunrise.

How do I calculate daylight hours?

To calculate daylight hours for today:

  1. Calculate the time of sunset: you can do this knowing your latitude, longitude, and day of the year.
  2. Calculate the time of sunrise.
  3. Subtract the two quantities. The result is the number of daylight hours in a day.

For latitudes above the polar circles, the previous method fails for at least one day a year: there, you can experience 24 hours of sunlight or darkness at specific times of the year!

Sunrise Sunset Calculator (2024)

FAQs

What is the formula for calculating sunrise and sunset? ›

Sunrise/Sunset Calculations

Then the UTC time of sunrise (or sunset) in minutes is: sunrise = 720 – 4*(longitude + ha) – eqtime where longitude and hour angle are in degrees and the equation of time is in minutes.

How light is it 30 minutes before sunrise? ›

The light during this phase is a deep blue, and the horizon is still discernible. Civil Twilight: Begins approximately 30 to 40 minutes before sunrise. This is when the sky starts to lighten up, and the highest clouds catch the first pink, orange, and red hues.

What do you do 30 minutes after sunset to 30 minutes before sunrise? ›

Use your headlights: When it is too dark to see from 1,000 feet away. Beginning 30 minutes after sunset. Until 30 minutes before sunrise.

What time is sunset tonight near me? ›

Los Angeles, California, USA — Sunrise, Sunset, and Daylength, July 2024
Current Time:Jul 9, 2024 at 4:12:58 pm
Sun Distance:94.504 million mi
Next Equinox:Sep 22, 2024 5:43 am (Autumnal)
Sunrise Today:5:49 am↑ 62° Northeast
Sunset Today:8:06 pm↑ 298° Northwest
2 more rows

What is the theoretical sunrise and sunset? ›

Theoretical sunrise and sunset occurs when the True Sun's centre is on the observer's rational horizon. The true altitude of the Sun is then 0° and its true zenith distance 90°. The times of theoretical sunrise or sunset, can be obtained by solving the PZX triangle in which ZX is 90°.

What is 30 minutes before sunrise called? ›

During the blue "hour", red light passes through space while blue light is scattered in the atmosphere, and thus reaches Earth's surface. Blue hour usually lasts about 20–96 minutes right after sunset and right before sunrise. Time of year, location, and air quality all have an influence on the exact time of blue hour.

What is 90 minutes before sunrise? ›

About 90 minutes before the sunrise is a period called navaswan, which is the time just before the sky shifts from pitch black to that first hint of gray. This is considered the most peaceful time of the day and was when meditation was traditionally performed.

What is 48 minutes before sunrise? ›

Brahmamuhurta (Sanskrit: ब्रह्ममुहूर्त, lit. 'time of Brahma') is a 48-minute period (muhurta) that begins one hour and 36 minutes before sunrise, and ends 48 minutes before sunrise.

What is it called right before sunrise? ›

In its most general sense, twilight is the period of time before sunrise and after sunset, in which the atmosphere is partially illuminated by the sun, being neither totally dark or completely lit.

How early is dawn before sunrise? ›

The duration of the morning twilight (i.e. between astronomical dawn and sunrise) varies greatly depending on the observer's latitude: from a little over 70 minutes at the Equator, to many hours in the polar regions.

What does the sky look like 30 minutes before sunrise? ›

About 20 to 30 minutes before sunrise, if atmospheric conditions are right, the sky at the horizon to the east can develop a strong orange cast. On rare occasions, this light can be so strong it overpowers the blue light from the sky directly overhead, putting a diffuse warm glow over the landscape.

What is golden hour sunset? ›

The last hour before sunset and the first hour after sunrise are coveted by professional photographers. Referred to as “the golden hour” or “magic hour,” these times provide the perfect light to capture stunning photos. Learning to harness the power of the golden hour is a tool every photographer can use.

Why is it called nautical twilight? ›

Nautical Twilight:

Begins in the morning, or ends in the evening, when the geometric center of the sun is 12 degrees below the horizon. In general, the term nautical twilight refers to sailors being able to take reliable readings via well known stars because the horizon is still visible, even under moonless conditions.

How long after sunset does it get really dark? ›

Recap of How Long Darkness Takes After Sunset

So, there you have it, a complete answer. In summary, for the 48 contiguous states, it takes anywhere from 70 to 100 minutes for it to get dark after sunset. The further north you are, the longer it takes for true darkness to arrive after sundown.

Is there a formula for sunlight? ›

There isn't a formula for sunlight because what we experience as sunlight is a pure energy released from billions of fusion reactions taking place within the sun. Essentially elements are continuing to undergo high energy reactions which result in the result of light as waves of energy.

How does Google calculate sunrise and sunset? ›

Unlike the weather, sunrises and sunsets are quite predictable, and as a result, we don't use a data source. Instead, we calculate sunrise and sunset times based on latitude, longitude and the current time.

How to calculate the number of daylight hours? ›

To calculate the length of the daylight hours, you need to follow some simple steps:
  1. Find the time of the local sunrise t(rise) .
  2. Find the time of the local sunset t(set) .
  3. Subtract the two values. ...
  4. Convert back to the desired format if necessary.
Jan 18, 2024

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