Solar Declination
Calculator
Results
- Solar declination (degrees)
- 23.449782
- Solar declination (radians)
- 0.409275
- Equation of time (minutes)
- -1.328236
Weather results
| Solar declination (degrees) | 23.449782 |
| Solar declination (radians) | 0.409275 |
| Equation of time (minutes) | -1.328236 |
formula-map diagram
- Solar declination (degrees)
- 23.449782
- Solar declination (radians)
- 0.409275
- Equation of time (minutes)
- -1.328236
Weather relationship
Formula
δ = 23.45° × sin(360° × (284 + n) ÷ 365) (Cooper 1969); EoT from the Spencer series= 23.449782846814
Note
This is a simplified model: it applies the published standard formula to the numbers you entered and ignores local terrain, radiation, precipitation type and instrument error. Wind chill is the 2001 NWS/Environment Canada regression, valid at or below 10 °C with wind at or above 4.8 km/h; the heat index is the Rothfusz regression, reliable above about 27 °C; dew point uses the Magnus approximation (a = 17.27, b = 237.7 °C) over liquid water; wet bulb uses Stull's approximation at standard sea-level pressure; pressure and density altitude assume the International Standard Atmosphere and dry air. Do not use these results for aviation, structural or safety decisions without an official forecast or a qualified professional.
More in Weather and climate
See all →Frequently asked questions
What is solar declination and why does it change through the year?+
Solar declination is the angle between the sun's rays and the Earth's equatorial plane at solar noon, and it changes because the Earth's axis is tilted about 23.4 degrees relative to its orbital plane, so different hemispheres tilt toward or away from the sun as the Earth orbits.
How is solar declination calculated for a given day of the year?+
Common approximations use a sinusoidal formula based on the day of the year and the axial tilt (roughly 23.44 degrees), since declination varies smoothly between about +23.44 degrees near the summer solstice and -23.44 degrees near the winter solstice for the Northern Hemisphere.
Why is declination zero at the equinoxes?+
At the spring and fall equinoxes, the Earth's tilt is oriented sideways relative to the sun rather than toward or away from it, so the sun's rays strike the equatorial plane directly, producing a declination of zero degrees and roughly equal day and night length worldwide on those dates.
What is solar declination used for practically?+
It's a key input for calculating sun position, day length, sunrise and sunset times, and the angle needed to properly orient solar panels for a given date and latitude, since the sun's path across the sky shifts substantially between winter and summer.
Does solar declination depend on the observer's location on Earth?+
No, declination is a property of the sun's position relative to Earth's equatorial plane at a given moment, so it's the same value everywhere on Earth at that instant; what does vary by location is how that declination combines with latitude to determine local sun angle, day length, and sunrise/sunset times.