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

Tuesday, September 1, 2026 · 13:39:07 PKT at 24.86070°, 67.00110°.

Daylight
Solar azimuth 226.7297° Clockwise from true north · SW
Apparent elevation 66.9238° Includes enabled refraction correction
Geometric elevation 66.9169° Uncorrected center of the Sun
Solar zenith angle 23.0831° Angular distance from overhead
Solar declination 8.2168° North of the celestial equator
Equation of time -0.0639 min Apparent versus mean solar time
Solar hour angle 16.7643° After local solar noon
True solar time 13:07:03 787.06 minutes after solar midnight
Relative air mass 1.0864 Kasten–Young approximation
Refraction correction 0.0069° 1,010.0 hPa · 10.0°C
Panel incidence 21.3992° Sun reaches the panel front
Shadow length 0.8521 m Toward 46.73° · NE

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 dawn04:54 PKTSolar elevation −18°
Nautical dawn05:22 PKTSolar elevation −12°
Civil dawn05:49 PKTSolar elevation −6°
Sunrise06:12 PKT80.43° true
Solar noon12:32 PKTSun crosses the local meridian
Sunset18:51 PKT279.40° true
Civil dusk19:14 PKTSolar elevation −6°
Nautical dusk19:41 PKTSolar elevation −12°
Astronomical dusk20:09 PKTSolar elevation −18°
Day length12:38:14Sunrise through sunset
Morning blue hour05:49 PKT–05:58 PKTApproximately −6° through −4°
Morning golden hour05:58 PKT–06:43 PKTApproximately −4° through +6°
Evening golden hour18:20 PKT–19:05 PKTApproximately +6° through −4°
Evening blue hour19:05 PKT–19:14 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 2026-09-01 00:00 PKT through 2026-09-01 23:30 PKT.

Local time UTC time Azimuth Elevation Geometric Zenith Air mass Declination Eq. time Hour angle Panel incidence Status
2026-09-01 00:00:00 PKT 2026-08-31 19:00:00 UTC 345.7141° -55.7980° -55.8019° 145.8019° −1 8.4228° -0.2433 min 171.9403° 171.3482° Night
2026-09-01 00:30:00 PKT 2026-08-31 19:30:00 UTC 358.9939° -56.7158° -56.7195° 146.7195° −1 8.4153° -0.2367 min 179.4419° 176.6737° Night
2026-09-01 01:00:00 PKT 2026-08-31 20:00:00 UTC 12.3653° -56.0462° -56.0501° 146.0501° −1 8.4078° -0.2302 min -173.0564° 172.3681° Night
2026-09-01 01:30:00 PKT 2026-08-31 20:30:00 UTC 24.7499° -53.8779° -53.8821° 143.8821° −1 8.4002° -0.2236 min -165.5548° 165.2896° Night
2026-09-01 02:00:00 PKT 2026-08-31 21:00:00 UTC 35.5083° -50.4574° -50.4622° 140.4622° −1 8.3927° -0.2171 min -158.0532° 157.9664° Night
2026-09-01 02:30:00 PKT 2026-08-31 21:30:00 UTC 44.5263° -46.0778° -46.0834° 136.0834° −1 8.3852° -0.2105 min -150.5515° 150.5815° Night
2026-09-01 03:00:00 PKT 2026-08-31 22:00:00 UTC 52.0028° -40.9975° -41.0041° 131.0041° −1 8.3776° -0.2040 min -143.0499° 143.1733° Night
2026-09-01 03:30:00 PKT 2026-08-31 22:30:00 UTC 58.2356° -35.4139° -35.4220° 125.4220° −1 8.3701° -0.1974 min -135.5483° 135.7547° Night
2026-09-01 04:00:00 PKT 2026-08-31 23:00:00 UTC 63.5092° -29.4687° -29.4789° 119.4789° −1 8.3625° -0.1909 min -128.0466° 128.3316° Night
2026-09-01 04:30:00 PKT 2026-08-31 23:30:00 UTC 68.0597° -23.2611° -23.2745° 113.2745° −1 8.3550° -0.1843 min -120.5450° 120.9070° Night
2026-09-01 05:00:00 PKT 2026-09-01 00:00:00 UTC 72.0732° -16.8604° -16.8794° 106.8794° −1 8.3475° -0.1778 min -113.0433° 113.4824° Astronomical twilight
2026-09-01 05:30:00 PKT 2026-09-01 00:30:00 UTC 75.6955° -10.3125° -10.3442° 100.3442° −1 8.3399° -0.1712 min -105.5417° 106.0559° Nautical twilight
2026-09-01 06:00:00 PKT 2026-09-01 01:00:00 UTC 79.0435° -3.6171° -3.7062° 93.7062° −1 8.3324° -0.1646 min -98.0401° 98.5968° Civil twilight
2026-09-01 06:30:00 PKT 2026-09-01 01:30:00 UTC 82.2146° 3.2340° 3.0056° 86.9944° 14.3809 8.3248° -0.1581 min -90.5384° 91.0754° Daylight
2026-09-01 07:00:00 PKT 2026-09-01 02:00:00 UTC 85.2961° 9.8579° 9.7678° 80.2322° 5.6608 8.3173° -0.1515 min -83.0368° 83.8075° Daylight
2026-09-01 07:30:00 PKT 2026-09-01 02:30:00 UTC 88.3727° 16.6136° 16.5600° 73.4400° 3.4606 8.3097° -0.1449 min -75.5351° 76.4671° Daylight
2026-09-01 08:00:00 PKT 2026-09-01 03:00:00 UTC 91.5356° 23.3998° 23.3626° 66.6374° 2.5054 8.3022° -0.1384 min -68.0335° 69.1309° Daylight
2026-09-01 08:30:00 PKT 2026-09-01 03:30:00 UTC 94.8935° 30.1822° 30.1545° 59.8455° 1.9835 8.2946° -0.1318 min -60.5318° 61.8186° Daylight
2026-09-01 09:00:00 PKT 2026-09-01 04:00:00 UTC 98.5893° 36.9316° 36.9102° 53.0898° 1.6613 8.2871° -0.1252 min -53.0302° 54.5457° Daylight
2026-09-01 09:30:00 PKT 2026-09-01 04:30:00 UTC 102.8276° 43.6115° 43.5946° 46.4054° 1.4480 8.2795° -0.1186 min -45.5286° 47.3336° Daylight
2026-09-01 10:00:00 PKT 2026-09-01 05:00:00 UTC 107.9239° 50.1680° 50.1545° 39.8455° 1.3010 8.2720° -0.1120 min -38.0269° 40.2168° Daylight
2026-09-01 10:30:00 PKT 2026-09-01 05:30:00 UTC 114.3957° 56.5117° 56.5010° 33.4990° 1.1982 8.2644° -0.1055 min -30.5253° 33.2576° Daylight
2026-09-01 11:00:00 PKT 2026-09-01 06:00:00 UTC 123.1303° 62.4795° 62.4711° 27.5289° 1.1270 8.2569° -0.0989 min -23.0236° 26.5812° Daylight
2026-09-01 11:30:00 PKT 2026-09-01 06:30:00 UTC 135.6275° 67.7529° 67.7463° 22.2537° 1.0799 8.2493° -0.0923 min -15.5220° 20.4673° Daylight
2026-09-01 12:00:00 PKT 2026-09-01 07:00:00 UTC 153.9058° 71.7089° 71.7035° 18.2965° 1.0528 8.2418° -0.0857 min -8.0203° 15.5927° Daylight
2026-09-01 12:30:00 PKT 2026-09-01 07:30:00 UTC 178.2065° 73.3710° 73.3661° 16.6339° 1.0432 8.2342° -0.0791 min -0.5187° 13.3883° Daylight
2026-09-01 13:00:00 PKT 2026-09-01 08:00:00 UTC 203.0213° 72.0861° 72.0808° 17.9192° 1.0505 8.2266° -0.0725 min 6.9830° 15.0750° Daylight
2026-09-01 13:30:00 PKT 2026-09-01 08:30:00 UTC 222.1846° 68.3745° 68.3681° 21.6319° 1.0752 8.2191° -0.0659 min 14.4846° 19.6765° Daylight
2026-09-01 14:00:00 PKT 2026-09-01 09:00:00 UTC 235.3344° 63.2311° 63.2230° 26.7770° 1.1194 8.2115° -0.0593 min 21.9863° 25.6702° Daylight
2026-09-01 14:30:00 PKT 2026-09-01 09:30:00 UTC 244.4665° 57.3310° 57.3207° 32.6793° 1.1871 8.2040° -0.0527 min 29.4879° 32.2898° Daylight
2026-09-01 15:00:00 PKT 2026-09-01 10:00:00 UTC 251.1755° 51.0236° 51.0105° 38.9895° 1.2852 8.1964° -0.0461 min 36.9896° 39.2192° Daylight
2026-09-01 15:30:00 PKT 2026-09-01 10:30:00 UTC 256.4158° 44.4864° 44.4700° 45.5300° 1.4254 8.1888° -0.0395 min 44.4912° 46.3192° Daylight
2026-09-01 16:00:00 PKT 2026-09-01 11:00:00 UTC 260.7426° 37.8159° 37.7951° 52.2049° 1.6282 8.1813° -0.0329 min 51.9929° 53.5212° Daylight
2026-09-01 16:30:00 PKT 2026-09-01 11:30:00 UTC 264.4917° 31.0693° 31.0425° 58.9575° 1.9326 8.1737° -0.0263 min 59.4945° 60.7880° Daylight
2026-09-01 17:00:00 PKT 2026-09-01 12:00:00 UTC 267.8788° 24.2845° 24.2489° 65.7511° 2.4203 8.1661° -0.0197 min 66.9962° 68.0970° Daylight
2026-09-01 17:30:00 PKT 2026-09-01 12:30:00 UTC 271.0531° 17.4912° 17.4405° 72.5595° 3.2956 8.1586° -0.0131 min 74.4978° 75.4320° Daylight
2026-09-01 18:00:00 PKT 2026-09-01 13:00:00 UTC 274.1265° 10.7218° 10.6387° 79.3613° 5.2346 8.1510° -0.0065 min 81.9995° 82.7750° Daylight
2026-09-01 18:30:00 PKT 2026-09-01 13:30:00 UTC 277.1915° 4.0568° 3.8631° 86.1369° 12.1699 8.1434° 0.0002 min 89.5011° 90.0670° Daylight
2026-09-01 19:00:00 PKT 2026-09-01 14:00:00 UTC 280.3331° -2.7513° -2.8665° 92.8665° −1 8.1359° 0.0068 min 97.0028° 97.5362° Civil twilight
2026-09-01 19:30:00 PKT 2026-09-01 14:30:00 UTC 283.6374° -9.4931° -9.5275° 99.5275° −1 8.1283° 0.0134 min 104.5045° 105.0171° Nautical twilight
2026-09-01 20:00:00 PKT 2026-09-01 15:00:00 UTC 287.2000° -16.0723° -16.0923° 106.0923° −1 8.1207° 0.0200 min 112.0061° 112.4474° Astronomical twilight
2026-09-01 20:30:00 PKT 2026-09-01 15:30:00 UTC 291.1344° -22.5115° -22.5254° 112.5254° −1 8.1132° 0.0266 min 119.5078° 119.8754° Night
2026-09-01 21:00:00 PKT 2026-09-01 16:00:00 UTC 295.5822° -28.7685° -28.7790° 118.7790° −1 8.1056° 0.0333 min 127.0094° 127.3042° Night
2026-09-01 21:30:00 PKT 2026-09-01 16:30:00 UTC 300.7246° -34.7780° -34.7863° 124.7863° −1 8.0980° 0.0399 min 134.5111° 134.7329° Night
2026-09-01 22:00:00 PKT 2026-09-01 17:00:00 UTC 306.7930° -40.4465° -40.4532° 130.4532° −1 8.0904° 0.0465 min 142.0127° 142.1592° Night
2026-09-01 22:30:00 PKT 2026-09-01 17:30:00 UTC 314.0721° -45.6392° -45.6448° 135.6448° −1 8.0829° 0.0532 min 149.5144° 149.5787° Night
2026-09-01 23:00:00 PKT 2026-09-01 18:00:00 UTC 322.8719° -50.1666° -50.1714° 140.1714° −1 8.0753° 0.0598 min 157.0161° 156.9823° Night
2026-09-01 23:30:00 PKT 2026-09-01 18:30:00 UTC 333.4301° -53.7756° -53.7798° 143.7798° −1 8.0677° 0.0664 min 164.5177° 164.3441° 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 day2,461,284.86049769
Julian century0.2666628473
Geometric mean longitude160.53426947°
Geometric mean anomaly9,957.13834955°
Earth orbit eccentricity0.0166974153
Sun equation of center-1.58899644°
True solar longitude158.94527303°
Apparent solar longitude158.94202502°
Earth–Sun distance1.00925530 AU
Mean obliquity23.43582338°
Corrected obliquity23.43802410°
Cosine of zenith0.9199370898

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.