Sunrise and sunset can be estimated from latitude and longitude by calculating the Sun’s apparent hour angle at a 90.833° solar zenith, applying it to solar noon when a horizon crossing exists, and converting the result to local civil time. The date and UTC offset matter just as much: solar geometry changes through the year, while civil time depends on political time zones and daylight saving rules. The Sunrise Sunset Calculator applies a NOAA-style approximation locally and reports apparent sunrise, sunset, solar noon, or a polar state in local clock time. It does not request location permission or send coordinates to a remote geocoding service. For a standalone PDF, run the calculation, copy the inputs and output into a separate document, and use that program’s Save as PDF command; the workflow described here does not assume a calculator download control. This article gives the browser steps, explains the underlying solar method, and shows how to preserve polar day and night labels in a reusable record.
The inputs that make the result reproducible
A sunrise or sunset calculation is reproducible only when the date, coordinates, and civil time offset are all explicit. Longitude helps determine solar noon, but it does not identify a time zone. The UTC offset performs that separate function and must reflect any daylight saving rule active on the selected date.
| Input | Accepted information | Purpose |
|---|---|---|
| Date | Gregorian date from 1901 through 2099 | Determines the date-dependent solar terms |
| Latitude | -89.8 through 89.8 degrees; north positive and south negative | Determines how the Sun’s path relates to the horizon |
| Longitude | -180 through 180 degrees; east positive and west negative | Determines the longitude component of solar noon |
| Civil UTC offset | The offset applying to that place on that date, including daylight saving time when necessary | Converts the astronomical result into local civil time |
Sign errors are a common source of misplaced results. New York uses a negative longitude, while Sydney uses a positive longitude. Likewise, a northern latitude is positive and a southern latitude is negative. Obtain coordinates from a reliable map or geographic record. A city-center coordinate is adequate for broad planning, but it may not represent the exact horizon at a location several miles away.
Calculate the times in the browser
- Open the Sunrise Sunset Calculator and choose the required Gregorian date. The supported calendar range runs from 1901 through 2099; a date outside that range is outside the tool’s intended accuracy scope.
- Enter the latitude and longitude. Use the required sign convention: north and east are positive, while south and west are negative. Latitude must be from -89.8 through 89.8 degrees, and longitude must be from -180 through 180 degrees.
- Enter the civil UTC offset that applies at the selected location on the selected date. Include daylight saving time when it is in force. Do not substitute the longitude for this field or assume the calculator will infer a historical time-zone rule.
- Read the displayed apparent sunrise, solar noon, and apparent sunset times. If the Sun does not cross the modeled horizon, read the polar day or polar night state instead. Clock values are rounded to the nearest minute, and any result shifted across midnight by the selected offset carries a previous-day or next-day marker.
Create a PDF research note
- Complete the calculation in the browser and keep the result page open. Decide whether the PDF should preserve one calculation record or several locations and dates.
- Open a word processor or another document program and create a page with a specific title, such as “Sunrise and Sunset Estimate for [Location] and [Date].”
- Paste the inputs into a labeled block: date, latitude, longitude, UTC offset, daylight-saving status when relevant, and the source of the coordinates.
- Copy the displayed times into a second block labeled “Apparent-horizon estimates.” Preserve any parenthetical previous-day or next-day marker. If the calculator reports polar day or polar night, copy that state rather than substituting made-up rise or set times.
- Add a note stating that the clock values are rounded to the nearest minute and use a modeled 90.833-degree solar zenith. Identify NOAA’s solar-calculation documentation and the U.S. Naval Observatory data service as reference sources.
- Use the document program’s Print or Save as PDF command, open the finished file, and check that the date, signs, UTC offset, units, polar labels, and day markers remain legible and correct.
To preserve the complete guide rather than one calculation record, use the browser’s Print command, select Save as PDF as the destination, and confirm the printed pages. This creates a portable document without treating the calculator’s minute estimates as official published schedules.
What the calculator computes
The method follows the compact solar-position equations documented by NOAA Global Monitoring Laboratory’s solar calculation details and derived from Jean Meeus’s astronomical algorithms. At the selected date’s Julian noon, the calculation derives terms including geometric solar longitude, solar anomaly, orbital eccentricity, apparent solar longitude, corrected obliquity, solar declination, and the equation of time. Solar noon then follows from longitude and the equation of time.
The central hour-angle relationship is cos H₀ = [cos(90.833°) − sin φ × sin δ] / [cos φ × cos δ], where φ is latitude, δ is solar declination, and H₀ is the sunrise hour angle. If the cosine lies within the interval from -1 to 1, an hour angle exists. After converting that angle from degrees into time units, the calculation subtracts it from solar noon for sunrise and adds it for sunset. The UTC-to-civil offset is then applied, the result is rounded to the nearest minute, and any calendar-day change is preserved.
When the hour-angle cosine is above 1, the calculation classifies the result as polar night. When it is below -1, it reports polar day. The 90.833-degree convention accounts approximately for atmospheric refraction near the horizon and the Sun’s visible radius. It does not mean the geometric center of the Sun is exactly on an unobstructed zero-degree horizon at the displayed minute. Solar declination and the equation of time are also displayed as diagnostic values, making the result easier to compare with another implementation.
Read each type of result
The calculator distinguishes clock events from cases in which no rise or set time exists. Read the output according to its stated meaning rather than trying to force every location into a daily sunrise-and-sunset pattern.
| Displayed result | Meaning | How to record it |
|---|---|---|
| Apparent sunrise | Modeled sunrise at the apparent horizon | Use as a nearest-minute local-clock estimate |
| Solar noon | The model’s estimate of the Sun’s local meridian transit | Keep separate from the rise and set estimates |
| Apparent sunset | Modeled sunset at the apparent horizon | Use as a nearest-minute local-clock estimate |
| Polar day | The Sun remains above the modeled apparent horizon for the local date | Record the state; no rise or set clock time exists |
| Polar night | The Sun remains below the modeled apparent horizon for the local date | Record the state; no rise or set clock time exists |
| Previous-day or next-day marker | The selected combination shifts an event across local midnight | Retain the marker in copied and PDF text |
Tromsø at the June and December solstices illustrates why the polar states matter: an independent reference can report the Sun continuously above or below the horizon rather than provide rise and set clock times. The calculator preserves that distinction instead of presenting a fabricated event.
Keep the estimate within its limits
Actual visibility can differ from the modeled time. NOAA explains that atmospheric refraction is modeled rather than measured. Weather, air density, elevation, nearby terrain, buildings, trees, coordinate precision, and the observer’s physical horizon can all move the point at which the Sun’s disk first appears or finally disappears. A city-center calculation cannot account for every obstruction across a large region.
NOAA states that its solar calculator is theoretically accurate to about one minute within plus or minus 72 degrees of latitude, with possible errors of up to ten minutes beyond that range. The browser tool’s golden tests compare six ordinary location-and-season cases with U.S. Naval Observatory rise and set output, allowing a three-minute difference for model and rounding choices. They also cover the June and December solstices at Tromsø to verify polar day and polar night handling. These comparisons support the approximation but do not turn its output into an official ephemeris.
Treat the results as estimates for planning, education, and comparison. They are not intended as official ephemerides, legal determinations, religious rulings, navigation data, or safety-critical instructions. For high-latitude schedules, field navigation, telescope work, or an exact observation, consult a full ephemeris that accounts for elevation, atmospheric pressure, temperature, and the required event definition. A well-made PDF should carry the same caution as the calculator itself and label every clock value as an apparent-horizon estimate.