Calculator
Example Data Table
These rows are illustrative sample cases for quick comparison.
| ZIP Code | City | Latitude | Longitude | Date | Noon Altitude | Annual Tilt Guide |
|---|---|---|---|---|---|---|
| 90210 | Beverly Hills, CA | 34.09° | -118.41° | 2026-06-21 | 79.36° | 34.09° |
| 10001 | New York, NY | 40.75° | -73.99° | 2026-03-20 | 49.22° | 40.75° |
| 60601 | Chicago, IL | 41.89° | -87.62° | 2026-09-22 | 48.07° | 41.89° |
| 85001 | Phoenix, AZ | 33.45° | -112.07° | 2026-12-21 | 33.10° | 33.45° |
Formula Used
Core solar geometry
Day number: n = day of the year.
Declination: δ = 23.45 × sin[360 × (284 + n) / 365]
Equation of time: EoT = 9.87 sin(2B) − 7.53 cos(B) − 1.5 sin(B)
Where: B = 360 × (n − 81) / 364
Time correction: TC = 4 × (longitude − 15 × UTC offset) + EoT
Solar time: Solar Time = Clock Time + TC / 60
Hour angle: H = 15 × (Solar Time − 12)
Angles and panel alignment
Solar elevation: α = asin[sinφ sinδ + cosφ cosδ cosH]
Solar zenith: θz = 90 − α
Solar azimuth: calculated from latitude, declination, and hour angle using atan2.
Surface incidence: θ = acos[sinα cosβ + cosα sinβ cos(As − Ap)]
Daylight hours: 2 × acos(−tanφ tanδ) / 15
Annual tilt guide: approximately equal to site latitude.
Summer tilt guide: latitude − 15°
Winter tilt guide: latitude + 15°
How to Use This Calculator
- Enter your ZIP or postal code.
- Confirm the country code. US is the default.
- Select the date you want to evaluate.
- Enter the local clock time for the solar check.
- Optionally enter a UTC offset for better clock alignment.
- Optionally enter panel tilt and panel azimuth.
- Click the calculate button.
- Review elevation, azimuth, incidence, daylight, and tilt guidance.
- Use the graph to compare daily angle behavior.
- Export the result as CSV or PDF when needed.
FAQs
1) What does ZIP-based solar angle mean?
The calculator converts a ZIP or postal code into latitude and longitude. It then uses date, time, and solar geometry formulas to estimate the sun’s position and panel-facing angle conditions.
2) Does the tool automatically know my timezone?
It estimates UTC offset from longitude when the field is blank. That works for many quick checks, but entering your known UTC offset gives more reliable clock-based results, especially during daylight saving periods.
3) Can I use this for countries outside the United States?
Yes, if the public ZIP lookup endpoint supports that country code. Enter the two-letter country code with the postal code. Results depend on whether the lookup service returns a valid location.
4) Which output matters most for panel orientation?
Panel incidence is usually the most practical angle. It shows how directly sunlight hits the panel surface. Lower incidence generally means stronger direct solar capture, assuming shading and weather are ignored.
5) Why are sunrise and sunset marked as approximate?
The model simplifies horizon effects. It does not include terrain blocking, atmospheric refraction details, building shadows, or daylight saving corrections unless you manually enter the UTC offset.
6) Is this enough for tracker design or engineering drawings?
It is strong for planning, estimation, and educational checks. Detailed engineering should also consider weather files, shading studies, structural rules, local codes, and professional design software.
7) Why can solar elevation become negative?
A negative elevation means the sun is below the horizon. That usually happens before sunrise or after sunset, so direct solar energy on the panel surface is effectively zero.
8) How should I choose the tilt value?
For a quick annual setting, use a tilt near local latitude. Lower tilts usually favor summer performance. Higher tilts often favor winter production and can help with water runoff.