Sunrise Sunset Interactive Calculator

Getting precise sunrise and sunset times at a location is a geometry problem—there's no guessing involved. The answers depend on your latitude, longitude, date, and where you are relative to Earth's orbit. The Sunrise Sunset Interactive Calculator runs through these details to give you sunrise, sunset, day length, solar noon, civil twilight, and solar elevation for any inputs you set. Anyone working with solar panels, outdoor photography, farming, or navigation soon finds accurate solar timing is necessary if you care about system yield, timing, or logistics. Below you'll find the actual formulas, a calculation walkthrough, engineering commentary, and an FAQ that gets into edge cases and corrections you might actually run into.

What is sunrise and sunset time?

Sunrise is when the Sun’s upper rim just appears above the horizon. Sunset is when it dips below again. These times shift every day depending on your exact location and the calendar.

Simple Explanation

Earth is a tilted, spinning sphere orbiting the Sun. Where you stand—relative to that tilt and the date—directly decides how much Sun you get. Near the equator, you’re looking at about 12 hours of sunlight year-round. Farther north or south, winters get darker and summers get endless. This calculator just runs the trig to figure out when the Sun hits your local horizon on any given day.

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How to Use This Calculator

1. Select your calculation mode from the dropdown — choose sunrise, sunset, day length, solar noon, civil twilight, or solar elevation angle.
2. Enter your latitude (positive for north, negative for south) and longitude (positive for east, negative for west), then select your date.
3. Enter your UTC offset — for example, Eastern Standard Time is -5, Pacific Daylight Time is -7. If you selected solar elevation mode, also enter the local time you want to evaluate.
4. Click Calculate to see your result.

Solar Position Diagram

Sunrise Sunset Calculator

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Solar Position Equations

Use the formula below to calculate the Julian Day Number, which anchors all subsequent solar position calculations to a continuous astronomical time reference.

Use the formula below to calculate Solar Mean Longitude.

Use the formula below to calculate Solar Mean Anomaly.

Use the formula below to calculate Ecliptic Longitude.

Use the formula below to calculate Solar Declination.

Use the formula below to calculate the Hour Angle at Sunrise/Sunset.

Use the formula below to calculate Solar Noon and Sunrise/Sunset Times.

Use the formula below to calculate Solar Elevation Angle.

Use the formula below to calculate Day Length.

Simple Example

Location: New York City (40.7128°N, -74.0060°W). Date: June 21, 2024. UTC offset: -5.

• Solar declination: approximately +23.4° (near summer solstice maximum)
• Hour angle at sunrise/sunset: approximately ±120°
• Sunrise: approximately 05:25 local time
• Sunset: approximately 20:31 local time
• Day length: approximately 15 hours 6 minutes

Theory & Practical Applications

Astronomical Foundation and Earth's Geometry

Finding sunrise and sunset times is an old geometry problem—the sort people did long before computers, for crops and calendars. Earth's sphere and its 23.439° axial tilt drive the timing. That tilt causes the seasonal swing in where the Sun is overhead, from +23.439° in June to -23.439° in December. When the Sun’s declination hits zero (the equinoxes), everyone on Earth gets roughly 12-hour days.

The reference for sunrise/sunset is the Sun’s upper limb (edge) crossing the horizon. Calculations add about 0.833° for atmospheric refraction—otherwise times will be off by two or three minutes at most populated latitudes. This refraction isn’t constant; if you get unusual pressure or temperatures, the real correction can wander by about a minute. If you need sub-minute accuracy for sunrise/sunset, you’ll have to feed in your local weather data and redo the trig. Most people can manage with the standard correction unless they need fine-tuning for optics, aviation, or research.

Coordinate System Transformations

The math switches between several coordinate systems. You start with the ecliptic plane (where planets orbit), shift to the equatorial system (using Earth’s axis), then finally to horizontal coordinates from the observer’s view (altitude and azimuth). The Sun’s ecliptic longitude λ shows where it sits in its yearly journey; declination δ tells you how high it will be at a given latitude. The tilt of Earth’s axis (the obliquity, ε) is what makes all these systems connect, but it decreases slightly every year—something you can generally ignore unless you’re working on time spans of centuries or more.

Hour angle, H, tells you how far the Sun is from local noon (westward by convention). For rise/set, you set solar elevation to -0.833°. If you try this at high latitudes near the solstice, you’ll notice the equations break when the cosine result runs outside [-1, 1]. This isn’t a bug; it just signals all-day sun or polar night. You start seeing this above 66.561° latitude when the declination is extreme enough.

Time Systems and Longitude Correction

It’s important to distinguish between sundial time (apparent solar time) and what clocks show (mean solar time). Because Earth’s orbit isn’t a circle and its axis is tilted, apparent solar noon can come up to ±16 minutes off what the clock says—this is the “equation of time.” The calculator includes 4(L - λ) to account for that annual swing. The four minutes per degree comes from Earth turning 360° in 24 hours, so 1° of longitude gives a 4-minute time change.

Your actual solar noon almost never matches your time zone mark (which sits exactly at 15° longitude intervals). For every degree of longitude you are east or west from your zone’s center, add or subtract 4 minutes. If you’re siting panels or designing schedules, you need to include this shift; otherwise, your optimization will be off by as much as local solar schedules drift from wall clocks.

Engineering Applications in Solar Energy Systems

When laying out solar arrays, you need to know exactly how the Sun moves overhead. For fixed mounts, “tilt equals latitude” is a common starting point, but in places far north or south, it won’t deliver top results all year. Adjusting the tilt to target either summer or winter productivity can yield more energy depending on load patterns. For instance, steeper tilts help in cold climates with winter heating needs, even though that reduces summer gains.

Dual-axis trackers boost yield by following the Sun precisely. These systems need to recalculate angles every several minutes, tracking to a degree or better. Above 60° latitude, things get tricky—near summer solstice the Sun barely sets and the azimuth can spin quickly, especially around midnight, while elevation changes hardly at all. Actuators and bearings need enough torque to handle wind and must minimize backlash or else tracking errors eat into the expected energy gains.

Worked Example: Solar Panel Siting Analysis

Example: A team is putting up a 50 kW rooftop array in Seattle (47.6062°N, 122.3321°W) with a 20° south-facing tilt, date is June 21. Required: sunrise/sunset (PDT, UTC-7), noon elevation, hours above 30° elevation, winter panel performance.

Solution Part (a): Sunrise and Sunset Times

First, days since J2000 for June 21, 2024:
Julian date = 2460483.5
n = 8938.5 days

Solar mean longitude:
L = (280.460 + 0.9856474 × 8938.5) mod 360°
L = 89.697°

Solar mean anomaly:
g = (357.528 + 0.9856003 × 8938.5) mod 360°
g = 5.985°

Ecliptic longitude:
λ = 89.697° + 1.915 × sin(5.985°) + 0.020 × sin(11.970°)
= 89.901°

Solar declination (summer solstice):
δ = arcsin(sin(23.439°) × sin(89.901°)) = 23.438°

Hour angle at rise/set:
cos(H₀) = (sin(-0.833°) - sin(47.6062°) × sin(23.438°)) / (cos(47.6062°) × cos(23.438°))
= -0.49916
H₀ = arccos(-0.49916) = 119.95°

Solar noon:
T_noon = 720 - 4(-122.3321) - 4(89.697 - 89.901) + (-7) × 60 = 790.14 minutes (13:10 PDT)

Sunrise: 790.14 - 4(119.95) = 310.34 min (5:10 AM PDT)
Sunset: 790.14 + 479.80 = 1269.94 min (9:10 PM PDT)

Day length: ≈ 16 hours

Solution Part (b): Solar Noon Elevation

Noon elevation: 90° - |47.6062° - 23.438°| = 65.8°
A 20° roof slope is much shallower than optimal for summer (Sun gets very high mid-day), so peak output won’t match theoretical during noon hours. It may do better in winter.

Solution Part (c): Time Window Above 30° Elevation

Set elevation to 30°, solve for hour angle:
cos(H) = (0.5 - 0.29396) / 0.61811 = 0.33333
H = ±70.53°
Time before/after noon = 70.53 / 15 = 4.70 h = 4:42
Start: 13:10 - 4:42 = 8:28 AM
End: 13:10 + 4:42 = 5:52 PM
Panels see >30° Sun for about 9.4 hours.

Solution Part (d): Winter Performance Assessment

Winter solstice: δ ≈ -23.439°
α_noon = 90° - |47.6062° - (-23.439°)| = 18.96°
Roof tilt: panel is at 70° to zenith; incident angle at noon: |70 - 71.05| ≈ 1°
So, in winter, this roof slope actually works out well for low Sun. However, days are short (about 8.5 hours), so annual yield depends much more on the long summer days.

Twilight Categories and Visual Perception

Civil twilight (Sun between -6° and 0° elevation) sets the limit for easy outdoor work without lamps. Nautical twilight (-12° to -6°) is for star/horizon navigation. Astronomical twilight (-18° to -12°) is when sky background starts to fade for telescopes. Past about 49° latitude during summer, nights are never fully dark—cities like St. Petersburg have long white “nights.”

For photography, the "golden hour" (first/last solar hour) and "blue hour" (civil twilight) give softer light and dramatic color shifts. Animal activity (especially for crepuscular species) also tracks civil/nautical twilight, so anyone planning fieldwork or lighting needs those timing windows more than strict sunrise/sunset to avoid or catch certain wildlife behaviors.

Polar Region Considerations

Above 66.561°, sunrise/sunset formulas start to give “no solution”—if |cos(H₀)| > 1 it simply means the Sun doesn’t cross the horizon that day. Summer brings weeks of perpetual daylight (midnight sun), winter brings darkness. Whether and for how long this happens depends on your latitude and the date. For φ = 70°N and δ = +23.439°, the sum exceeds 90°, so the Sun stays up all day at solstice.

For engineering: Solar arrays above the Arctic Circle must be sized along with battery or backup, as they get all their yield April-August and almost nothing for the rest of the year. This makes annual capacity estimates for these locations highly seasonal—more like batch collection systems than steady generators.

Software Validation and Accuracy Considerations

The equations used here will hit ±2 minute accuracy for dates within about ±50 years of 2000. If you need sub-minute accuracy on specialized projects or want to model historical events more than a century back or forward, you’ll need to add corrections for things like lunar pulls, planetary orbits, or changing atmospheric refraction. That’s where Jean Meeus’s algorithms and JPL data get used. For most engineering and energy work, this doesn’t matter.

Speed of computation matters for embedded applications—this workflow requires about 45 floating-point operations, making it suitable for fast updates on everything from microcontrollers to solar tracking systems. Only the arccos call for hour angle is performance-critical; if you need ultra-fast responses, precomputed tables by latitude and declination can shortcut this work to fast table lookups.

To go deeper into solar design or check related calculations—panel angle, sun tracks, system sizing—see the FIRGELLI Engineering Calculator Library.

Frequently Asked Questions