NOAA Solar Position Calculator

Calculate solar azimuth, elevation, twilight, sunrise, sunset, shadows, panel incidence, and detailed astronomical values for any global location, date, and time accurately.

☀ NOAA/Meeus-style equations 🧭 True-north azimuth 📊 Time-series charts ⬇ CSV, JSON, and PDF

Solar position results

Wednesday, July 22, 2026 · 06:37:41 PKT at 24.86070°, 67.00110°.

Daylight
Solar azimuth 71.3752° Clockwise from true north · ENE
Apparent elevation 8.3207° Includes enabled refraction correction
Geometric elevation 8.2150° Uncorrected center of the Sun
Solar zenith angle 81.7850° Angular distance from overhead
Solar declination 20.2961° North of the celestial equator
Equation of time -6.4800 min Apparent versus mean solar time
Solar hour angle -90.1981° Before local solar noon
True solar time 05:59:12 359.21 minutes after solar midnight
Relative air mass 6.6161 Kasten–Young approximation
Refraction correction 0.1057° 1,010.0 hPa · 10.0°C
Panel incidence 91.8726° Panel front is not illuminated
Shadow length 13.6749 m Toward 251.38° · WSW

Calculator inputs

Choose a location, local date, time zone, atmospheric settings, panel angle, shadow object, and time-series range.

1. Location

Presets fill latitude, longitude, and time zone.
The result engine converts everything internally.
North is positive. South is negative.
East is positive. West is negative.
Metres. Stored for reporting and horizon context.
Click the map to choose coordinates.Lat 24.8607°, Lon 67.0011°

2. Date, clock, and time zone

Handles daylight-saving transitions for the selected date.
Example: +05:00 or −04:00. Historical DST is not applied.

3. Atmosphere and refraction

hPa. Standard near sea level is about 1010 hPa.
Degrees Celsius.

4. Shadow and solar-panel tools

Degrees east-positive. This does not change true solar azimuth.
0° is horizontal. 90° is vertical.
Clockwise from true north.

5. Time-series settings

48 calculated rows

Sunrise, sunset, and twilight

Times use the selected local time zone. Event thresholds use the Sun’s center and standard astronomical definitions.

Normal
Astronomical dawn04:29 PKTSolar elevation −18°
Nautical dawn05:00 PKTSolar elevation −12°
Civil dawn05:30 PKTSolar elevation −6°
Sunrise05:55 PKT67.11° true
Solar noon12:38 PKTSun crosses the local meridian
Sunset19:21 PKT292.79° true
Civil dusk19:46 PKTSolar elevation −6°
Nautical dusk20:16 PKTSolar elevation −12°
Astronomical dusk20:47 PKTSolar elevation −18°
Day length13:26:42Sunrise through sunset
Morning blue hour05:30 PKT–05:39 PKTApproximately −6° through −4°
Morning golden hour05:39 PKT–06:27 PKTApproximately −4° through +6°
Evening golden hour18:49 PKT–19:37 PKTApproximately +6° through −4°
Evening blue hour19:37 PKT–19:46 PKTApproximately −4° through −6°
Current statusDaylightBased on apparent solar elevation

Solar visualisations

The compass uses true north. The daily charts use the generated time-series values shown below.

Compass and current Sun

Shadow geometry

Sun path: azimuth versus elevation

Sun pathCurrent SunHorizon

Solar elevation through time

Time-series results

48 rows from 2026-07-22 00:00 PKT through 2026-07-22 23:30 PKT.

Local time UTC time Azimuth Elevation Geometric Zenith Air mass Declination Eq. time Hour angle Panel incidence Status
2026-07-22 00:00:00 PKT 2026-07-21 19:00:00 UTC 347.4607° -43.8256° -43.8316° 133.8316° −1 20.3506° -6.4685 min 170.3840° 162.1410° Night
2026-07-22 00:30:00 PKT 2026-07-21 19:30:00 UTC 357.2058° -44.7401° -44.7459° 134.7459° −1 20.3465° -6.4694 min 177.8838° 164.6485° Night
2026-07-22 01:00:00 PKT 2026-07-21 20:00:00 UTC 7.0841° -44.4888° -44.4946° 134.4946° −1 20.3424° -6.4703 min -174.6165° 163.9157° Night
2026-07-22 01:30:00 PKT 2026-07-21 20:30:00 UTC 16.6373° -43.0903° -43.0965° 133.0965° −1 20.3383° -6.4711 min -167.1167° 160.3014° Night
2026-07-22 02:00:00 PKT 2026-07-21 21:00:00 UTC 25.4963° -40.6424° -40.6491° 130.6491° −1 20.3342° -6.4720 min -159.6169° 155.0288° Night
2026-07-22 02:30:00 PKT 2026-07-21 21:30:00 UTC 33.4547° -37.2913° -37.2989° 127.2989° −1 20.3301° -6.4729 min -152.1171° 148.9343° Night
2026-07-22 03:00:00 PKT 2026-07-21 22:00:00 UTC 40.4623° -33.1973° -33.2061° 123.2061° −1 20.3260° -6.4738 min -144.6173° 142.4196° Night
2026-07-22 03:30:00 PKT 2026-07-21 22:30:00 UTC 46.5746° -28.5090° -28.5196° 118.5196° −1 20.3219° -6.4746 min -137.1176° 135.6743° Night
2026-07-22 04:00:00 PKT 2026-07-21 23:00:00 UTC 51.8986° -23.3521° -23.3655° 113.3655° −1 20.3178° -6.4755 min -129.6178° 128.7947° Night
2026-07-22 04:30:00 PKT 2026-07-21 23:30:00 UTC 56.5560° -17.8271° -17.8450° 107.8450° −1 20.3137° -6.4764 min -122.1180° 121.8340° Astronomical twilight
2026-07-22 05:00:00 PKT 2026-07-22 00:00:00 UTC 60.6631° -12.0102° -12.0372° 102.0372° −1 20.3096° -6.4772 min -114.6182° 114.8230° Astronomical twilight
2026-07-22 05:30:00 PKT 2026-07-22 00:30:00 UTC 64.3228° -5.9481° -6.0030° 96.0030° −1 20.3054° -6.4781 min -107.1184° 107.7719° Civil twilight
2026-07-22 06:00:00 PKT 2026-07-22 01:00:00 UTC 67.6235° 0.6636° 0.2107° 89.7893° 29.5500 20.3013° -6.4789 min -99.6186° 100.3874° Daylight
2026-07-22 06:30:00 PKT 2026-07-22 01:30:00 UTC 70.6403° 6.6961° 6.5675° 83.4325° 8.0368 20.2972° -6.4797 min -92.1188° 93.6486° Daylight
2026-07-22 07:00:00 PKT 2026-07-22 02:00:00 UTC 73.4379° 13.1072° 13.0390° 76.9610° 4.3328 20.2931° -6.4806 min -84.6190° 86.6992° Daylight
2026-07-22 07:30:00 PKT 2026-07-22 02:30:00 UTC 76.0742° 19.6476° 19.6027° 70.3973° 2.9523 20.2889° -6.4814 min -77.1193° 79.7548° Daylight
2026-07-22 08:00:00 PKT 2026-07-22 03:00:00 UTC 78.6038° 26.2729° 26.2403° 63.7597° 2.2504 20.2848° -6.4822 min -69.6195° 72.8573° Daylight
2026-07-22 08:30:00 PKT 2026-07-22 03:30:00 UTC 81.0830° 32.9616° 32.9367° 57.0633° 1.8337 20.2807° -6.4831 min -62.1197° 66.0363° Daylight
2026-07-22 09:00:00 PKT 2026-07-22 04:00:00 UTC 83.5766° 39.6983° 39.6789° 50.3211° 1.5632 20.2765° -6.4839 min -54.6199° 59.3275° Daylight
2026-07-22 09:30:00 PKT 2026-07-22 04:30:00 UTC 86.1698° 46.4700° 46.4546° 43.5454° 1.3778 20.2724° -6.4847 min -47.1201° 52.7801° Daylight
2026-07-22 10:00:00 PKT 2026-07-22 05:00:00 UTC 88.9919° 53.2635° 53.2515° 36.7485° 1.2468 20.2682° -6.4855 min -39.6203° 46.4675° Daylight
2026-07-22 10:30:00 PKT 2026-07-22 05:30:00 UTC 92.2699° 60.0633° 60.0540° 29.9460° 1.1533 20.2641° -6.4863 min -32.1205° 40.5040° Daylight
2026-07-22 11:00:00 PKT 2026-07-22 06:00:00 UTC 96.4747° 66.8442° 66.8373° 23.1627° 1.0871 20.2600° -6.4871 min -24.6207° 35.0722° Daylight
2026-07-22 11:30:00 PKT 2026-07-22 06:30:00 UTC 102.8116° 73.5515° 73.5467° 16.4533° 1.0422 20.2558° -6.4879 min -17.1209° 30.4607° Daylight
2026-07-22 12:00:00 PKT 2026-07-22 07:00:00 UTC 115.5056° 79.9980° 79.9952° 10.0048° 1.0151 20.2517° -6.4887 min -9.6211° 27.0944° Daylight
2026-07-22 12:30:00 PKT 2026-07-22 07:30:00 UTC 156.5759° 84.9898° 84.9884° 5.0116° 1.0035 20.2475° -6.4895 min -2.1213° 25.4735° Daylight
2026-07-22 13:00:00 PKT 2026-07-22 08:00:00 UTC 228.1522° 83.2218° 83.2198° 6.7802° 1.0067 20.2433° -6.4903 min 5.3785° 25.9281° Daylight
2026-07-22 13:30:00 PKT 2026-07-22 08:30:00 UTC 251.3325° 77.2516° 77.2480° 12.7520° 1.0249 20.2392° -6.4911 min 12.8783° 28.3586° Daylight
2026-07-22 14:00:00 PKT 2026-07-22 09:00:00 UTC 260.2812° 70.6470° 70.6413° 19.3587° 1.0594 20.2350° -6.4919 min 20.3781° 32.3215° Daylight
2026-07-22 14:30:00 PKT 2026-07-22 09:30:00 UTC 265.4471° 63.8957° 63.8877° 26.1123° 1.1130 20.2309° -6.4927 min 27.8779° 37.3306° Daylight
2026-07-22 15:00:00 PKT 2026-07-22 10:00:00 UTC 269.1616° 57.1006° 57.0901° 32.9099° 1.1902 20.2267° -6.4934 min 35.3777° 43.0204° Daylight
2026-07-22 15:30:00 PKT 2026-07-22 10:30:00 UTC 272.2013° 50.2990° 50.2856° 39.7144° 1.2986 20.2225° -6.4942 min 42.8776° 49.1530° Daylight
2026-07-22 16:00:00 PKT 2026-07-22 11:00:00 UTC 274.9014° 43.5105° 43.4935° 46.5065° 1.4507 20.2183° -6.4950 min 50.3774° 55.5793° Daylight
2026-07-22 16:30:00 PKT 2026-07-22 11:30:00 UTC 277.4362° 36.7492° 36.7276° 53.2724° 1.6684 20.2142° -6.4957 min 57.8772° 62.2054° Daylight
2026-07-22 17:00:00 PKT 2026-07-22 12:00:00 UTC 279.9117° 30.0278° 29.9999° 60.0001° 1.9926 20.2100° -6.4965 min 65.3770° 68.9697° Daylight
2026-07-22 17:30:00 PKT 2026-07-22 12:30:00 UTC 282.4022° 23.3600° 23.3228° 66.6772° 2.5094 20.2058° -6.4972 min 72.8768° 75.8299° Daylight
2026-07-22 18:00:00 PKT 2026-07-22 13:00:00 UTC 284.9676° 16.7631° 16.7100° 73.2900° 3.4313 20.2016° -6.4980 min 80.3766° 82.7542° Daylight
2026-07-22 18:30:00 PKT 2026-07-22 13:30:00 UTC 287.6629° 10.2645° 10.1778° 79.8222° 5.4519 20.1974° -6.4987 min 87.8764° 89.7113° Daylight
2026-07-22 19:00:00 PKT 2026-07-22 14:00:00 UTC 290.5436° 3.9439° 3.7460° 86.2540° 12.4352 20.1933° -6.4994 min 95.3762° 96.6312° Daylight
2026-07-22 19:30:00 PKT 2026-07-22 14:30:00 UTC 293.6700° -2.4316° -2.5606° 92.5606° −1 20.1891° -6.5002 min 102.8761° 103.7270° Civil twilight
2026-07-22 20:00:00 PKT 2026-07-22 15:00:00 UTC 297.1113° -8.6731° -8.7108° 98.7108° −1 20.1849° -6.5009 min 110.3759° 110.8455° Nautical twilight
2026-07-22 20:30:00 PKT 2026-07-22 15:30:00 UTC 300.9482° -14.6419° -14.6639° 104.6639° −1 20.1807° -6.5016 min 117.8757° 117.8846° Astronomical twilight
2026-07-22 21:00:00 PKT 2026-07-22 16:00:00 UTC 305.2758° -20.3522° -20.3677° 110.3677° −1 20.1765° -6.5024 min 125.3755° 124.8846° Night
2026-07-22 21:30:00 PKT 2026-07-22 16:30:00 UTC 310.2042° -25.7421° -25.7540° 115.7540° −1 20.1723° -6.5031 min 132.8753° 131.8251° Night
2026-07-22 22:00:00 PKT 2026-07-22 17:00:00 UTC 315.8548° -30.7249° -30.7346° 120.7346° −1 20.1681° -6.5038 min 140.3752° 138.6677° Night
2026-07-22 22:30:00 PKT 2026-07-22 17:30:00 UTC 322.3483° -35.1893° -35.1974° 125.1974° −1 20.1639° -6.5045 min 147.8750° 145.3457° Night
2026-07-22 23:00:00 PKT 2026-07-22 18:00:00 UTC 329.7776° -38.9981° -39.0052° 129.0052° −1 20.1597° -6.5052 min 155.3748° 151.7332° Night
2026-07-22 23:30:00 PKT 2026-07-22 18:30:00 UTC 338.1622° -41.9945° -42.0009° 132.0009° −1 20.1555° -6.5059 min 162.8746° 157.5722° Night

Example data

Load a seasonal location example, then calculate its solar position.

LocationLatitudeLongitudeDateTime zoneAction
Boulder, USA40.0150° N105.2705° WJune 21America/Denver
London, UK51.5074° N0.1278° WMarch 20Europe/London
Karachi, Pakistan24.8607° N67.0011° EDecember 21Asia/Karachi
Sydney, Australia33.8688° S151.2093° ESeptember 22Australia/Sydney
Tromsø, Norway69.6492° N18.9553° EJune 21Europe/Oslo

Formula used

The engine follows the familiar NOAA worksheet sequence derived from Meeus-style solar geometry.

Convert local time to UTC.
UTC = local date and time − applicable time-zone offset
Calculate Julian day and century.
T = (JD − 2451545.0) / 36525
Find solar orbital terms.
L₀, M, e, equation of center, true longitude, and apparent longitude
Calculate solar declination.
δ = asin(sin ε · sin λ)
Calculate equation of time.
E = 4 · degrees(y sin 2L₀ − 2e sin M + 4ey sin M cos 2L₀ − ½y² sin 4L₀ − 1.25e² sin 2M)
Calculate true solar time.
TST = local minutes + E + 4 · longitude − 60 · UTC offset
Calculate solar hour angle.
H = TST / 4 − 180°
Calculate zenith and elevation.
cos Z = sin φ sin δ + cos φ cos δ cos H; elevation = 90° − Z
Calculate true-north azimuth.
Az = atan2(sin H, cos H sin φ − tan δ cos φ) + 180°
Apply atmospheric refraction.
apparent elevation = geometric elevation + pressure-and-temperature-adjusted correction
Calculate shadows and panel incidence.
shadow = height / tan elevation; cos θ = cos Z cos β + sin Z sin β cos(Az − γ)
Current intermediate values
Julian day2,461,243.56783565
Julian century0.2655323158
Geometric mean longitude119.83426596°
Geometric mean anomaly9,916.44029031°
Earth orbit eccentricity0.0166974629
Sun equation of center-0.53088041°
True solar longitude119.30338555°
Apparent solar longitude119.29997898°
Earth–Sun distance1.01603763 AU
Mean obliquity23.43583808°
Corrected obliquity23.43808709°
Cosine of zenith0.1428882140

How to use this calculator

Follow these steps for a reliable, reproducible solar-position report.

  1. Enter decimal coordinates or switch to degrees, minutes, and seconds.
  2. Confirm the longitude sign convention shown beside the field.
  3. Select an IANA time zone for automatic daylight-saving handling.
  4. Enter the local date and clock time for the observation.
  5. Keep standard atmospheric settings, or enter local pressure and temperature.
  6. Enter an object height when shadow length is required.
  7. Enter panel tilt and azimuth for incidence-angle analysis.
  8. Choose a time-series range and interval for charts and exported data.
  9. Select Calculate. Review azimuth, elevation, twilight, and warning messages.
  10. Download CSV, JSON, or PDF for records and further analysis.
Direction convention: Solar azimuth is measured clockwise from true north. Magnetic compass readings may require a local declination adjustment.

Accuracy and limitations

Solar geometry is predictable, but observed horizons and atmospheric conditions vary.

Understanding solar position calculations

Solar position connects astronomical time, geography, atmospheric optics, and practical design decisions.

What solar azimuth means

Solar azimuth describes the Sun’s horizontal direction. Zero degrees points toward true north. Ninety degrees points east. One hundred eighty degrees points south. Two hundred seventy degrees points west. The value turns clockwise around the observer. A magnetic compass may show another direction. Local magnetic declination causes that difference.

What solar elevation means

Solar elevation measures height above the horizon. Positive values place the Sun above the astronomical horizon. Negative values place its center below that horizon. Ninety degrees means the Sun is directly overhead. Elevation changes throughout each day. It also changes across seasons and latitudes.

Geometric and apparent elevation

Geometric elevation ignores atmospheric bending. Apparent elevation includes a refraction estimate. Refraction matters most near sunrise and sunset. Dense air bends light toward the observer. The Sun can therefore appear visible while its geometric center remains below the horizon. Pressure and temperature influence the correction.

Why time zones matter

Solar equations need a precise UTC instant. Local clock time alone is insufficient. The selected time zone supplies the applicable UTC offset. IANA time zones also represent daylight-saving changes. Manual offsets remain useful for unusual cases. They should be checked carefully for historical dates.

Solar noon and clock noon

Solar noon occurs when the Sun crosses the local meridian. It rarely matches twelve o’clock exactly. Longitude within the time zone shifts solar noon. The equation of time adds a seasonal shift. Civil clock rules create another difference. Solar noon usually gives the day’s highest elevation.

Twilight stages

Civil twilight extends to six degrees below the horizon. Nautical twilight extends to twelve degrees. Astronomical twilight extends to eighteen degrees. Sky brightness depends on weather and light pollution. These thresholds still provide useful planning references. They help photographers, observers, sailors, and outdoor workers.

Shadow calculations

A vertical object casts a longer shadow when elevation is low. Shadow length equals object height divided by the tangent of elevation. The shadow points opposite the Sun’s azimuth. Below-horizon results have no direct sunlight shadow. Terrain slope can change the measured ground length.

Solar panel incidence

Panel incidence is the angle between sunlight and the panel normal. Zero degrees represents perpendicular sunlight. Larger angles reduce direct-beam exposure. A back-facing panel has a negative incidence cosine. Real energy also depends on irradiance, clouds, temperature, shading, wiring, and equipment efficiency.

Time-series analysis

A single instant answers one positioning question. A time series reveals the daily path. It supports facade studies, photography schedules, shading checks, and tracking simulations. Smaller intervals improve chart detail. Larger intervals keep long reports manageable. Exported rows support further analysis in other software.

Frequently asked questions

These answers explain common inputs, conventions, and result differences.

Is this an official NOAA calculator?

No. It is an independent educational implementation of publicly documented NOAA/Meeus-style equations. It does not provide NOAA certification.

Why does my compass disagree with azimuth?

The calculator reports true-north azimuth. A compass points toward magnetic north. Local magnetic declination can create several degrees of difference.

Why is sunrise different from an observed sunrise?

Terrain, buildings, clouds, pressure, temperature, and horizon height affect visibility. Astronomical calculations usually assume a level horizon and standard refraction.

What does a negative elevation mean?

The Sun’s center is below the astronomical horizon. Values between zero and minus eighteen degrees may represent twilight.

Should I use apparent or geometric elevation?

Use apparent elevation for near-horizon visual planning. Use geometric elevation for pure astronomical geometry and some engineering workflows.

Can this estimate solar-panel electricity?

No. It calculates orientation geometry. Energy production also needs irradiance, weather, shading, module efficiency, temperature, inverter, and system-loss data.

What air-mass value appears below the horizon?

The table exports minus one when air mass is unavailable. The result card shows a dash for clearer presentation.

Why can polar sunrise or sunset be missing?

High latitudes can experience continuous daylight or darkness. The selected altitude threshold may never be crossed on that date.

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Important Note: All the Calculators listed in this site are for educational purpose only and we do not guarentee the accuracy of results. Please do consult with other sources as well.