How do I calculate the noon altitude of the sun?

Noon altitude = 90° − latitude + declination. Declination is 0° at the spring and autumn equinoxes, about +23.4° at the summer solstice, and about −23.4° at the winter solstice, so the equinoxes give 90° − latitude, the summer solstice 90° − latitude + 23.4°, and the winter solstice 90° − latitude − 23.4°. For Tokyo (35.7° N), that’s about 77.8° at the summer solstice, about 54.3° at the equinoxes, and about 30.9° at the winter solstice. This tool uses the declination for the selected day and shows the formula alongside the result.

How is shadow length calculated?

Shadow length = object height ÷ tan(sun altitude). At a sun altitude of 45° the shadow is as long as the height, at 30° about 1.73 times, and at 20° about 2.75 times. Around noon on the winter solstice in Tokyo, the sun’s altitude is about 31°, so a 170 cm person’s shadow is about 2.8 m and a 7 m two-story house’s shadow is about 11.7 m.

How far from the building in front do I need to be to get sunlight at the winter solstice?

A rough guide to the distance for sunlight to reach a window at noon on the winter solstice is (height of building in front − window height) ÷ tan(winter solstice noon altitude). In Tokyo, with a 7 m two-story house in front and a first-floor window at 1.5 m, you need at least 5.5 ÷ tan 30.9° ≈ 9.2 m. Enter the heights and distance in this tool to see a chart of the hours of sunlight on the window on the selected day and at the winter solstice.

How much does the sunrise direction change with the seasons?

At the spring and autumn equinoxes the sun rises almost due east, but around the summer solstice it rises about 30° north of due east, and around the winter solstice about 29° south of due east (for Tokyo). Sunsets shift the same way: north of due west in summer and south of due west in winter. The higher the latitude, the larger the shift.

What time is magic hour?

It’s the few dozen minutes around sunset. In the evening, golden hour begins when the sun’s altitude drops below about 6° (from 30–40 minutes before sunset to a little over ten minutes after), followed by blue hour, when the sky turns blue (roughly 15–30 minutes after sunset). The times change with the season and place, so choose a date and location in this tool to check.

Isn’t the sun highest at exactly 12:00?

Japan’s time is based on longitude 135° E (Akashi, Hyogo), so in Tokyo, further east, solar noon comes before 12:00 (around 11:40), and in Fukuoka, further west, it comes later (around 12:15). In addition, because of the equation of time, solar noon shifts by more than ten minutes earlier or later depending on the season, even at the same place.

When is the winter solstice?

The winter solstice is the day when the sun’s ecliptic longitude reaches 270°, which is December 21 or 22 each year. The summer solstice is around June 21, the spring equinox March 20 or 21, and the autumn equinox September 22 or 23. This tool calculates the spring equinox, summer solstice, autumn equinox, and winter solstice for the selected year, and you can switch to any of them with one button.

Sun Position & Shadow Length Calculator | Noon Altitude, Sunrise Direction, Magic Hour & Sunlight with a Building in Front

The Sun Position & Shadow Length Calculator takes a prefecture (or your current location or latitude/longitude) and a date and time, and calculates the sun’s altitude and azimuth at that moment, plus the length of an object’s shadow and the direction it falls. It also shows sunrise and sunset times and directions (how many degrees off due east or west), solar noon time and altitude, day length, and the golden hour and blue hour for photography, and draws the sun’s path seen from directly above, overlaid with the summer and winter solstices. Enter the height and distance of a house or apartment building in front, and it compares the hours of sunlight on your window or balcony on the selected day and at the winter solstice, and finds the distance needed for sunlight to reach at winter solstice noon. It also explains how to calculate the noon altitude (90° − latitude + declination) and includes a monthly quick reference table. All calculations run in your browser, and your location is never sent to a server.

Location and date/time

Location (prefectural capital)

Dates

Time 12:00

Tokyo (Shinjuku) (Tokyo)

The sun on 6/21/2026

Sunrise

4:26

ENE, 30° north of due east

Solar noon (highest point)

11:43

Noon altitude 77.8°

Sunset

19:00

WNW, 30° north of due west

Day length

14 h 35 min

Declination 23.44°

Selected dateSummer solsticeWinter solsticeCenter = straight overhead, edge = horizon, numbers = hours

Sun at 12:00

Altitude 77.2°Azimuth SSW (198° from north)

How to calculate the noon altitude

Noon altitude = 90° − latitude + declination = 90 − 35.7 + (23.4) ≈ 77.7°

Declination is 0° at the equinoxes, about +23.4° at the summer solstice, and about −23.4° at the winter solstice. The noon altitude shown includes atmospheric refraction, so it comes out slightly higher.

Summer solstice
77.8°
Spring/autumn equinox
54.3°
Winter solstice
30.9°

Shadow length and direction

Object height (m)

The shadow points NNE

Shadow at 12:00

39 cm

Times the height

0.23×

Shadow at winter solstice noon

2.84 m

Summer solstice: 37 cm

Time	Altitude	Sun azimuth	Shadow direction	Shadow of 1.7 m
5:00	5.5°	ENE	WSW	17.6 m
6:00	16.8°	ENE	WSW	5.64 m
7:00	28.6°	E	W	3.12 m
8:00	40.7°	E	W	1.98 m
9:00	52.8°	E	W	1.29 m
10:00	64.6°	ESE	WNW	81 cm
11:00	74.6°	SE	NW	47 cm
12:00	77.2°	SSW	NNE	39 cm
13:00	69.3°	WSW	ENE	64 cm
14:00	58.0°	WSW	ENE	1.06 m
15:00	45.9°	W	E	1.64 m
16:00	33.8°	W	E	2.54 m
17:00	21.8°	WNW	ESE	4.25 m
18:00	10.3°	WNW	ESE	9.38 m

Magic hour (golden hour & blue hour)

Golden hour is when the sun’s altitude is +6° to −4°, and blue hour is −4° to −6° (common guidelines in photography).

Morning

Civil dawn (sky begins to brighten): 3:56
Blue hour: 3:56 – 4:07
Golden hour: 4:07 – 5:04
Sunrise: 4:26

Evening

Sunset: 19:00
Golden hour: 18:22 – 19:19
Blue hour: 19:19 – 19:30
Civil dusk (gets dark): 19:30

Sunlight with a building in front (window/balcony)

Calculates the hours of sunlight on a window from the height and distance of a house, apartment building, or wall in front of it. Useful when house hunting or when a house will be built next door.

Height of building in front (m)

Distance to building (m)

Window height (m)

Window orientation

6/21 (selected date)

Hours of sunlight 6 h 45 min8:20–15:05

468101214161820

Winter solstice (12/22)

Hours of sunlight 3 h 20 min10:00–13:20

468101214161820

SunlitShadow of building in frontSun behind the windowNight

Angle from the window up to the roof

28.8°

Sunlight reaches the window when the sun is higher than this (when facing the window)

Noon altitude at winter solstice

30.9°

Sunlight reaches even at winter solstice noon

Distance needed for sun at winter solstice noon

9.2 m or more

(Building height − window height (5.5 m)) ÷ tan(winter solstice noon altitude)

The building in front is assumed to run parallel to the window and extend far enough to the left and right. Sunlight coming around the sides of the building, reflected light, and tree shadows are not included.

Monthly quick reference for Tokyo (Shinjuku) (Tokyo) (2026, 21st of each month)

Month	Sunrise	Solar noon	Noon altitude	Sunset	Day length	Noon shadow (× height)
1	6:48	11:53	34.4°	16:57	10 h 8 min	1.46×
2	6:22	11:55	43.7°	17:28	11 h 7 min	1.05×
3	5:44	11:49	54.5°	17:53	12 h 9 min	0.71×
4	5:02	11:40	66.1°	18:19	13 h 18 min	0.44×
5	4:32	11:38	74.5°	18:44	14 h 11 min	0.28×
6	4:26	11:43	77.8°	19:00	14 h 35 min	0.22×
7	4:41	11:48	74.8°	18:54	14 h 14 min	0.27×
8	5:04	11:44	66.5°	18:24	13 h 19 min	0.44×
9	5:28	11:34	55.1°	17:40	12 h 12 min	0.70×
10	5:53	11:26	43.7°	16:59	11 h 6 min	1.05×
11	6:22	11:27	34.4°	16:31	10 h 9 min	1.46×
12	6:47	11:39	30.9°	16:31	9 h 44 min	1.67×

Times are calculated with NOAA’s solar position formulas and may differ by about 1 minute from the National Astronomical Observatory of Japan’s almanac. Differences due to elevation, mountains, or buildings are not included.

ABOUT

About Sun Position & Shadow Length Calculator | Noon Altitude, Sunrise Direction, Magic Hour & Sunlight with a Building in Front

The Sun Position & Shadow Length Calculator calculates the sun’s altitude (angle above the horizon) and azimuth, and the length and direction of an object’s shadow, just by choosing a place, date, and time. It brings together sunrise and sunset times and directions, solar noon time and altitude, day length, and the golden hour and blue hour for photography on one screen, and shows the sun’s path in a diagram overlaid with the summer and winter solstices. Enter the height and distance of a house or apartment building in front, and you can compare the hours of sunlight on your window or balcony on the selected day and at the winter solstice, so it’s also useful for checking sunlight when house hunting or when a house will be built next door.

How to use Sun Position & Shadow Length Calculator | Noon Altitude, Sunrise Direction, Magic Hour & Sunlight with a Building in Front

1Choose a place from the prefecture list (you can also press “Use current location” or enter latitude and longitude directly)
2Choose a date. The “Summer solstice”, “Winter solstice”, “Spring equinox”, and “Autumn equinox” buttons jump straight to that date in the year
3Move the time slider to change the sun’s altitude and azimuth for that time and the sun’s position in the sun path diagram
4In “Shadow length and direction”, enter the height of an object (a person, pole, house, utility pole, etc.) to see the shadow’s length and direction and an hourly table of shadow lengths
5To check sunlight, enter the height of the building in front, the distance to it, the window height, and the window orientation, then compare the hours of sunlight on the selected day and at the winter solstice
6Press “Copy results” to copy the results, or “Copy URL with these settings” to send the settings to someone

Great for

Find out how far the shadow of a two-story house extends at noon on the winter solstice
Before viewing an apartment, check whether it gets sunlight in winter even with a building in front
Hearing that a house will be built next door, estimate how much sunlight the garden or first-floor windows will lose
Check how to calculate the noon altitude (90° − latitude ± 23.4°) for science homework
Find the sunrise direction and magic hour times to photograph sunrises and sunsets
Compare the sun’s height and direction by season to choose a spot for a vegetable garden or drying laundry
Check what time and in which direction the shadows of solar panels or a carport fall

Good to know

The sun’s position is calculated with the same formulas as NOAA’s (U.S. National Oceanic and Atmospheric Administration) Solar Calculator. Sunrise and sunset times may differ by about 1 minute from the National Astronomical Observatory of Japan’s almanac.
Sunrise and sunset are the times when the upper edge of the sun touches a flat horizon. Differences in visibility due to elevation, mountains, or buildings are not included.
Shadow length is the length on flat ground. Shadows on slopes, steps, or walls are not calculated. When the sun is low in the morning and evening, shadows become very long.
Sunlight with a building in front is calculated assuming the building runs parallel to the window and extends far enough to the left and right. Sunlight coming around the sides of the building, reflected light, and tree shadows are not included, so results lean toward less sunlight than in reality.
Golden hour is defined as the sun’s altitude between +6° and −4°, and blue hour between −4° and −6°. Perceived brightness varies with weather and air clarity.
Your current location is used only in your browser and is never sent to a server.

Questions this tool answers

Use Sun Position & Shadow Length Calculator | Noon Altitude, Sunrise Direction, Magic Hour & Sunlight with a Building in Front for searches like these:

Calculate shadow length hour by hour
Find the length of a building’s shadow at the winter solstice
Learn how to calculate the noon altitude and its values at the summer and winter solstices
Calculate the sun’s altitude and azimuth from a place and time
Find the direction of sunrise and sunset
Find the times of magic hour and blue hour
See how the distance to the neighboring house affects winter sunlight
Calculate the hours of sunlight on a balcony or window

FAQ

How do I calculate the noon altitude of the sun?: Noon altitude = 90° − latitude + declination. Declination is 0° at the spring and autumn equinoxes, about +23.4° at the summer solstice, and about −23.4° at the winter solstice, so the equinoxes give 90° − latitude, the summer solstice 90° − latitude + 23.4°, and the winter solstice 90° − latitude − 23.4°. For Tokyo (35.7° N), that’s about 77.8° at the summer solstice, about 54.3° at the equinoxes, and about 30.9° at the winter solstice. This tool uses the declination for the selected day and shows the formula alongside the result.
How is shadow length calculated?: Shadow length = object height ÷ tan(sun altitude). At a sun altitude of 45° the shadow is as long as the height, at 30° about 1.73 times, and at 20° about 2.75 times. Around noon on the winter solstice in Tokyo, the sun’s altitude is about 31°, so a 170 cm person’s shadow is about 2.8 m and a 7 m two-story house’s shadow is about 11.7 m.
How far from the building in front do I need to be to get sunlight at the winter solstice?: A rough guide to the distance for sunlight to reach a window at noon on the winter solstice is (height of building in front − window height) ÷ tan(winter solstice noon altitude). In Tokyo, with a 7 m two-story house in front and a first-floor window at 1.5 m, you need at least 5.5 ÷ tan 30.9° ≈ 9.2 m. Enter the heights and distance in this tool to see a chart of the hours of sunlight on the window on the selected day and at the winter solstice.
How much does the sunrise direction change with the seasons?: At the spring and autumn equinoxes the sun rises almost due east, but around the summer solstice it rises about 30° north of due east, and around the winter solstice about 29° south of due east (for Tokyo). Sunsets shift the same way: north of due west in summer and south of due west in winter. The higher the latitude, the larger the shift.
What time is magic hour?: It’s the few dozen minutes around sunset. In the evening, golden hour begins when the sun’s altitude drops below about 6° (from 30–40 minutes before sunset to a little over ten minutes after), followed by blue hour, when the sky turns blue (roughly 15–30 minutes after sunset). The times change with the season and place, so choose a date and location in this tool to check.
Isn’t the sun highest at exactly 12:00?: Japan’s time is based on longitude 135° E (Akashi, Hyogo), so in Tokyo, further east, solar noon comes before 12:00 (around 11:40), and in Fukuoka, further west, it comes later (around 12:15). In addition, because of the equation of time, solar noon shifts by more than ten minutes earlier or later depending on the season, even at the same place.
When is the winter solstice?: The winter solstice is the day when the sun’s ecliptic longitude reaches 270°, which is December 21 or 22 each year. The summer solstice is around June 21, the spring equinox March 20 or 21, and the autumn equinox September 22 or 23. This tool calculates the spring equinox, summer solstice, autumn equinox, and winter solstice for the selected year, and you can switch to any of them with one button.

Special Thanks

SOLO GUILD | サービス作るAIエンジニア

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