Solar altitude/azimuth/sunrise/sunset/day length

Insert an example (preset)

Once you select the location, date, and time, the input will be filled in and you will receive the results immediately.

location date

time

Inputs

point

View on map

Latitude (°) Northern latitude is +, southern latitude is - (-90 to 90)

Longitude (°) East longitude is +, west longitude is - (-180 to 180)

Example: 35.6895, 139.6917 If you paste, it will be automatically split (no input will be sent).

date and time

date

time

time zone

Time zone (IANA / automatic) UTC offset (minutes/arbitrary) If entered, this will take precedence (e.g. JST=540, EDT=-240). This is useful when you want to fix DST.

Graph increments (minutes)

How to use (3 steps)

Enter latitude and longitude, date and time, and time zone.
Use "Calculate" to check the solar altitude, direction, sunrise/sunset, and day length.
Results can be shared with "Copy share_ESC_TOK_0__" (no input is sent).

Results

solar altitude

—

With refraction correction (approximation of standard state)

sun direction

—

North = 0°, East = 90° (clockwise)

sunrise/sunset

— / —

The center of the sun is 0.833° below the horizon (official definition)

photoperiod

—

h:mm

Taiyo Nanchu

—

South Central time of the day (approximate)

Nanchu altitude

—

maximum altitude

Supplementary information (declination, equation of time, hour angle, refraction)

Geometric altitude (without refraction): —
Refractive correction amount (approximate): —
Declination: —
Equation of time: —
Hour angle: —

Solar altitude (displayed) is "geometric altitude + refraction correction amount". *This column is a supplement for study purposes.

Astronomy tools

Find related tools for sunrise, twilight, moon phase, and observing planning.

Open astronomy hub

1 day solar altitude curve

Horizontal axis: time (local) / vertical axis: solar altitude (°). Input times are indicated by vertical lines and dots. When you trace the graph, the altitude and direction at that time will be displayed.

Shared URL contains input status (latitude, longitude, date and time, TZ, etc.).

Assumptions/Definitions/Disclaimers

Azimuth is displayed clockwise with "north = 0°, east = 90°".
Sunrise/sunset is defined as the moment when the center of the sun passes 0.833° below the horizon (including representative values of atmospheric difference and solar radius).
This tool is an approximation using the NOAA approximation formula. Depending on the conditions, there may be an error of several 0.5 degrees in solar altitude/azimuth, and an error of several minutes in sunrise/sunset.
Calculation results for educational and guideline purposes. Please do not use it for safety judgment, design, or legal purposes.

How to use this calculator effectively

This guide helps you use Solar altitude/azimuth/sunrise/sunset/day length calculator in a repeatable way: define a baseline, change one variable at a time, and interpret outputs with explicit assumptions before you share or act on results.

How it works

The page applies deterministic logic to your inputs and shows rounded output for readability. Treat it as a comparison workflow: run one baseline case, adjust a single parameter, and measure both absolute and percentage deltas. If a result seems off, verify units, time basis, and sign conventions before drawing conclusions. This approach keeps your analysis reproducible across teammates and sessions.

When to use

Use this page when you need a fast estimate, a classroom check, or a practical what-if comparison. It works best for planning and prioritization steps where you need direction and magnitude quickly before investing in deeper modeling, manual spreadsheets, or formal external review.

Common mistakes to avoid

Changing multiple parameters at once, which hides the true cause of output movement.
Mixing units (percent vs decimal, monthly vs yearly, gross vs net) across scenarios.
Comparing with another tool without aligning defaults, constants, and rounding rules.
Using rounded display values as exact downstream inputs without re-checking precision.

Interpretation and worked example

Run a baseline scenario and keep that result visible. Next, modify one assumption to reflect your realistic alternative and compare direction plus size of change. If the direction matches your domain expectation and the size is plausible, your setup is usually coherent. If not, check hidden defaults, boundary conditions, and interpretation notes before deciding which scenario to adopt.

FAQ

Which direction is "0°" in the solar direction?

North is 0° and increases clockwise. East is 90°, south is 180°, and west is 270°.

Why is sunrise/sunset sometimes displayed as "None"?

At high latitudes, depending on the season, there are days when the sun does not set (midnight sun) or does not rise (polar night), in which case sunrise/sunset cannot be defined.

How accurate are the calculation results?

This tool is an approximation based on approximate formulas (NOAA series) for general use. Depending on the conditions, there may be an error of several 0.5 degrees in solar altitude/azimuth, and an error of several minutes in sunrise/sunset.

Why does the result change when I change the time zone?

Sunrise/sunset etc. are displayed in local time. Even at the same moment, the displayed time will change if the displayed time zone is different.

What should I do first on this page?

Start with the minimum required inputs or the first action shown near the primary button. Keep optional settings at defaults for a baseline run, then change one setting at a time so you can explain what caused each output change.

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