Solar Angle Calculator
At latitude 23° N at solar noon on 21 June the sun stands 89.5502 ° above the horizon, almost overhead.
21 March ≈ 80, 21 June ≈ 172, 23 September ≈ 266, 21 December ≈ 355.
89.550217153186 °
Full answer, then cut to fewer decimals (not rounded):
- 89.550217153186 °
- 89.55021715318 °
- 89.5502171531 °
- 89.550217153 °
- 89.55021715 °
- 89.5502171 °
- 89.550217 °
- 89.55021 °
- 89.5502 °
- 89.550 °
- 89.55 °
- 89.5 °
- Declination δ
- 23.44978285 °
- Hour angle
- 0 °
- Azimuth (clockwise from north)
- 0.00006921887895 °
- Zenith angle
- 0.4497828468 °
- Day length
- 13.41468065 h
- Sunrise (solar time)
- 5.292659676 h
Step-by-step solution
- δ = 23.45 sin(360(284 + n)/365) = 23.44978285°
- sin α = sin φ sin δ + cos φ cos δ cos h = 0.9999691874
- α = 89.55021715°
Solar Angle Formula
sin α = sin φ sin δ + cos φ cos δ cos h
δ = 23.45 sin(360(284 + n)/365); h = 15° × (t − 12)
Worked Example
Latitude 23° N at solar noon on 21 June:
- δ = 23.45 sin(360(284 + n)/365) = 23.44978285°
- sin α = sin φ sin δ + cos φ cos δ cos h = 0.9999691874
- α = 89.55021715°
Hour angle: 0 ° · Azimuth (clockwise from north): 0.00006921887895 ° · Zenith angle: 0.4497828468 ° · Day length: 13.41468065 h · Sunrise (solar time): 5.292659676 h
GATE tip
Use solar (sun) time, not clock time: India’s IST differs from local solar time by up to about an hour.
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Frequently asked questions
What is the noon altitude formula?
α_noon = 90° − |φ − δ|: at the equinoxes it is 90° minus the latitude.
How are shading devices sized?
From the sun’s altitude and azimuth at the critical hours: horizontal overhangs suit south facades, vertical fins east and west.
Sources
- The International System of Units (SI), 9th edition (SI Brochure), Bureau International des Poids et Mesures .
Last reviewed: . Factors are stored exactly and computed with 50-digit decimal arithmetic. See how we verify conversion factors.
Cite this page
APA
Scientific Converters. (2026, October 15). Solar Angle Calculator. Retrieved October 29, 2026, from https://scientificconverters.com/calculators/solar-angle-calculator/
IEEE
Scientific Converters, "Solar Angle Calculator," scientificconverters.com. Accessed: Oct. 29, 2026. [Online]. Available: https://scientificconverters.com/calculators/solar-angle-calculator/