Solar position results
Wednesday, July 22, 2026 · 06:37:41 PKT at 24.86070°, 67.00110°.
Calculator inputs
Choose a location, local date, time zone, atmospheric settings, panel angle, shadow object, and time-series range.
Sunrise, sunset, and twilight
Times use the selected local time zone. Event thresholds use the Sun’s center and standard astronomical definitions.
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
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.
| Location | Latitude | Longitude | Date | Time zone | Action |
|---|---|---|---|---|---|
| Boulder, USA | 40.0150° N | 105.2705° W | June 21 | America/Denver | |
| London, UK | 51.5074° N | 0.1278° W | March 20 | Europe/London | |
| Karachi, Pakistan | 24.8607° N | 67.0011° E | December 21 | Asia/Karachi | |
| Sydney, Australia | 33.8688° S | 151.2093° E | September 22 | Australia/Sydney | |
| Tromsø, Norway | 69.6492° N | 18.9553° E | June 21 | Europe/Oslo |
Formula used
The engine follows the familiar NOAA worksheet sequence derived from Meeus-style solar geometry.
Current intermediate values
| Julian day | 2,461,243.56783565 |
|---|---|
| Julian century | 0.2655323158 |
| Geometric mean longitude | 119.83426596° |
| Geometric mean anomaly | 9,916.44029031° |
| Earth orbit eccentricity | 0.0166974629 |
| Sun equation of center | -0.53088041° |
| True solar longitude | 119.30338555° |
| Apparent solar longitude | 119.29997898° |
| Earth–Sun distance | 1.01603763 AU |
| Mean obliquity | 23.43583808° |
| Corrected obliquity | 23.43808709° |
| Cosine of zenith | 0.1428882140 |
How to use this calculator
Follow these steps for a reliable, reproducible solar-position report.
- Enter decimal coordinates or switch to degrees, minutes, and seconds.
- Confirm the longitude sign convention shown beside the field.
- Select an IANA time zone for automatic daylight-saving handling.
- Enter the local date and clock time for the observation.
- Keep standard atmospheric settings, or enter local pressure and temperature.
- Enter an object height when shadow length is required.
- Enter panel tilt and azimuth for incidence-angle analysis.
- Choose a time-series range and interval for charts and exported data.
- Select Calculate. Review azimuth, elevation, twilight, and warning messages.
- Download CSV, JSON, or PDF for records and further analysis.
Accuracy and limitations
Solar geometry is predictable, but observed horizons and atmospheric conditions vary.
- The equations model an idealized solar center and astronomical horizon.
- Pressure, temperature, humidity, and weather can change apparent refraction.
- Buildings, mountains, trees, and terrain can delay visible sunrise or advance sunset.
- Observer elevation is reported, but detailed dip-of-horizon correction is not applied.
- Results may be less reliable near the poles and far outside modern calendar dates.
- Panel incidence does not estimate photovoltaic energy, clouds, shading, or equipment losses.
- Golden-hour and blue-hour limits are practical photographic conventions, not rigid standards.
- This educational calculator is not an official NOAA product or legal certification tool.
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.