What Solar Azimuth represents
The atan2 expression preserves the correct quadrant. This page reports 0° north, 90° east, 180° south, and 270° west; hour angle is negative before local solar noon.
Solar Azimuth begins with latitude, solar declination, solar hour angle. Mark each value as observed, remotely sensed, modeled, assumed, or derived, and preserve its valid time and spatial support.
Where the model stops
Terrain, magnetic declination, refraction, coordinate convention, and time conversion are outside this geometry. State the clockwise-from-true-north convention downstream.
Solar Azimuth is transparent educational arithmetic, not a cloud observation, weather forecast, solar-resource assessment, flight rule, runway visual range report, instrument calibration, or operational safety authority.
Continue the Solar Azimuth workflow with the related Maximum-Overlap Total Cloud Cover Calculator, keeping the same observation support and conventions.
Uncertainty and sensitivity
Vary the least certain Solar Azimuth input over a credible range and retain the resulting spread in solar azimuth. Display precision cannot overcome observer classification, retrieval uncertainty, spatial variability, or an empirical coefficient.
A Solar Azimuth sensitivity range is not automatically a probability interval. It omits correlations, model-form error, sampling mismatch, sub-grid cloud structure, nonuniform visibility paths, and uncertainty outside the entered variables.
Cloud amount, overlap, and layers
Cloud fraction is an area or sky-dome proportion, while a ceiling is a height classification and optical depth is attenuation. Solar Azimuth should not substitute one quantity for another merely because each relates to cloud.
When layers enter Solar Azimuth, state whether overlap is random, maximum, observed, or ignored. Adding layer percentages directly can exceed 100% and double-count vertically aligned cloud.
Visibility and contrast conventions
Visibility from Solar Azimuth depends on the target contrast threshold and extinction units. Meteorological optical range fixes a two-percent contrast convention; a general contrast range or runway screening estimate may use another threshold.
Do not equate Solar Azimuth optical distance with prevailing visibility, slant range, night visual range, or official RVR without the required observation and processing conventions.
Solar geometry and radiation conventions
Solar elevation is measured above the geometric horizon, while azimuth here is clockwise from true north. Solar Azimuth must retain whether radiation is normal to the rays or incident on a horizontal surface.
Civil time is not solar hour angle. Longitude, time zone, equation of time, atmospheric refraction, shading horizon, and surface tilt belong in Solar Azimuth only when the displayed model explicitly includes them.
Keeping an auditable record
Save raw Solar Azimuth inputs, conversions, constants, coefficient sources, formula version, unrounded output, rounded result, and quality flags. A reviewer should reproduce the number without guessing a cover, angle, contrast, or height convention.
If a source value or assumption changes, create a dated Solar Azimuth revision. Preserve the earlier output and label whether the change is a correction, a new observation, or a separate scenario.
Formula and convention
The working relationship is A = mod[atan2(sinH, cosH sinφ − tanδ cosφ) + 180°, 360°]. Solar Azimuth uses only the displayed entries and does not retrieve imagery, station observations, ephemerides, forecasts, or runway systems.
Keep percentages as percentages at entry and convert them to fractions only where the formula shows it. For Solar Azimuth, retain angle direction, optical threshold, height reference, and distance unit with the answer.
Checked numerical example
At latitude 40°, declination 20°, and hour angle −30°, azimuth is approximately 119.06° from true north.
Reset restores this Solar Azimuth example. Repeat it independently with the stated constants and rounding before replacing demonstration values with observations or scenarios.
Collecting compatible inputs
Use true geographic latitude, declination, and solar hour angle. Do not enter a magnetic bearing or civil-clock angle without the necessary conversions.
Record site, coordinates, elevation, timestamp, time zone, path direction, wavelength or sensor band, target definition, cloud-layer method, solar-time convention, averaging period, and quality flags when relevant to Solar Azimuth.
Continue the Solar Azimuth workflow with the related Cloud-Adjusted Solar Radiation Calculator, keeping the same observation support and conventions.
Interpreting Solar azimuth
Morning values usually fall east of south and afternoon values west of south outside polar edge cases. Azimuth becomes physically indeterminate when the Sun is exactly at zenith.
Compare Solar Azimuth outputs only after aligning reference height, sky footprint, path, illumination, contrast convention, and temporal average. Similar numbers can describe different optical or geometric quantities.
Continue the Solar Azimuth workflow with the related Cloud Cover Percentage from Oktas Calculator, keeping the same observation support and conventions.
Boundary and monotonic checks
At local solar noon in this example geometry, azimuth is 180°. Near zenith, tiny input changes can swing azimuth sharply.
For Solar Azimuth, change one input at a time and predict whether the answer should rise, fall, or remain fixed. Unexpected behavior can expose percent-fraction, degree-radian, metre-kilometre, or layer-order mistakes.
Frequent clouds and visibility errors
Typical Solar Azimuth errors include mixing oktas and tenths, confusing AGL with MSL, adding overlapping layers, treating degrees as radians, using sea-level-reduced visibility, or applying a two-percent constant to a five-percent threshold.
Reject impossible Solar Azimuth combinations rather than forcing an answer. Keep a clear zero distinct from missing or obscured sky, preserve signs on hour angle, and verify every inverse distance and logarithm denominator before downstream use.
Checking this optical result
What does Solar Azimuth report?
Solar Azimuth reports solar azimuth from the displayed inputs and formula.
Can forecast or scenario inputs be used?
Yes. Label the Solar Azimuth output as a scenario; the page does not fetch or validate a forecast.
How can I verify Solar Azimuth?
Repeat A = mod[atan2(sinH, cosH sinφ − tanδ cosφ) + 180°, 360°] with the recorded conversions, then test the checked example and a physical boundary.
Why could another source disagree?
Another source may use different cloud overlap, optical threshold, solar convention, coefficient, sensor path, height reference, or rounding than Solar Azimuth uses.