Model sunrise geometry with configurable solar altitude options. See declination, hour angle, and status instantly. Use it for astronomy, ecology, travel, and energy studies.
The daylight duration is computed from the sunrise/sunset hour angle ω₀. For a chosen solar altitude threshold h₀, latitude φ, and solar declination δ:
If the computed cos(ω₀) falls outside [-1, 1], the location experiences polar day (24 hours) or polar night (0 hours) for that threshold.
| Latitude (°) | Date | Threshold (h₀) | Model | Day length (approx.) |
|---|---|---|---|---|
| 0.0000 | 2026-03-20 | −0.833° | Spencer | ~12.0 h |
| 40.7128 | 2026-06-21 | −0.833° | Spencer | ~15.1 h |
| 51.5074 | 2026-12-21 | −0.833° | Cooper | ~7.8 h |
| 69.6492 | 2026-06-21 | −0.833° | Cooper | 24.0 h (polar day) |
Day length is the time the Sun’s center stays above the local horizon. It changes through the year because Earth’s rotation axis is tilted. Near the equator, daylight stays close to 12 hours most days. At mid‑latitudes, seasonal swings become obvious, while near the poles the swing can reach 24 hours of continuous daylight or darkness.
Latitude controls the Sun’s apparent path across your sky. Higher latitudes make that path shallower in winter and steeper in summer. A practical rule: the same date produces longer daylight as you move from 20° to 40° to 60° latitude, but the winter penalty also grows quickly.
The date determines the solar declination, the Sun’s angular position north or south of Earth’s equatorial plane. Around June 21, declination is near +23.44°, producing long days in the Northern Hemisphere. Around December 21, declination is near −23.44°, producing shorter days there. Near the March and September equinoxes, declination is near 0°, and day length tends toward 12 hours worldwide.
This calculator lets you choose a “standard” sunrise/sunset altitude. A common engineering choice is −0.833°, which approximates refraction plus the Sun’s radius, making sunrise occur slightly earlier than pure geometry. If you set the altitude to 0°, you get a cleaner geometric estimate that is useful for comparisons.
Above roughly 66.56° (the Arctic and Antarctic Circles), the model can return 0 hours (polar night) or 24 hours (midnight Sun) for parts of the year. That is not a bug; it reflects that the chosen solar altitude threshold is never reached (or never crossed) during a full rotation.
You will see daylight duration, plus approximate sunrise and sunset times in local solar time (not a civil clock). Local solar noon is set at 12:00, so sunrise and sunset shift around that midpoint. For planning with time zones, treat these as a physics baseline and then apply your location’s longitude and time standard separately.
Day length is sensitive to refraction, terrain, and elevation. Mountains can delay sunrise and accelerate sunset, shortening real daylight. Refraction varies with pressure and temperature, so “standard” choices may be off by minutes on some days. The calculator prioritizes consistent, repeatable estimates for analysis and learning.
Use it for outdoor scheduling, solar energy feasibility checks, biological rhythm studies, agriculture planning, and classroom demonstrations. Comparing two latitudes on the same date quickly shows why winters feel darker in higher‑latitude cities. Export CSV or PDF to document seasonal studies and share results with teams or students.
Because the Sun’s daily path is close to symmetric around the horizon there. Declination changes shift the path slightly north or south, but the horizon crossing angles stay steep, keeping daylight close to 12 hours most of the year.
It approximates atmospheric refraction plus the Sun’s apparent radius. The Sun appears above the horizon a little earlier than pure geometry predicts, and it appears to set a little later, increasing estimated daylight by a few minutes.
At high latitudes in certain seasons, the Sun may not cross the selected altitude threshold during a full rotation. That produces continuous daylight (24 h) or continuous darkness (0 h) for that model setting.
No. They are in local solar time with solar noon fixed at 12:00. Civil time depends on longitude within your time zone, daylight saving rules, and local standards, which can shift reported times by many minutes or more.
Typically close for general use, but almanacs include detailed atmospheric models, elevation, and site‑specific corrections. Temperature, pressure, and terrain can shift observed sunrise/sunset by minutes, especially near the horizon.
Often, yes. Higher elevation can reduce horizon blockage and slightly change refraction conditions, letting you see the Sun sooner and longer. The effect is usually minutes, but it can be larger with significant terrain differences.
Use positive latitude for the Northern Hemisphere and negative for the Southern Hemisphere. For example, 40°N is +40, while 33°S is −33. The seasonal pattern flips between hemispheres automatically.
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.