Calculadora de Posição do Sol (Declinação)

Declinação solar δ = 23,45° × sen(360° × (284 + N) / 365).
Created by
Renato Passos, Eng. de Software
Reviewed by
Renato Passos, Eng. de Software

Last updated: Apr 18, 2026

Declinação solar
23,45 °
Meio-dia solar (UTC aprox.)
12 h

Formula

δ = 23,45°·sen(2π·(284+N)/365)

About this calculator

The Sun Position Calculator (Declination) determines the solar declination, an angle measuring the Sun's position relative to the celestial equator. Declination varies throughout the year, affecting day length, solar altitude, and solar radiation intensity. The calculator uses the formula δ = 23.45° × sin(2π × (284 + N) / 365), where N is the day of the year (1 to 365). The result is in degrees, ranging from -23.45° (winter solstice in the Northern Hemisphere) to +23.45° (summer solstice).

This tool is useful for solar energy professionals, architects, farmers, and astronomy enthusiasts. For instance, when sizing solar panels, declination helps calculate the optimal tilt angle to maximize energy capture. In agriculture, declination influences planting and harvest planning, especially at high latitudes. It is also used in daylighting design and climate studies.

When using the calculator, enter the day of the year (N) from 1 to 365. For leap years, consider day 366, but the formula is an approximation and may have slight variations. Note that the calculated declination is for true solar noon. For precise solar position (azimuth and altitude), other variables like latitude and longitude are needed. The calculator assumes a simplified circular orbit, ignoring Earth's eccentricity.

Frequently asked questions

What is solar declination?

It is the angle between the sun's rays and the celestial equator, varying throughout the year due to Earth's axial tilt.

What is the unit of the result?

The result is in degrees, ranging from -23.45° to +23.45°.

How to calculate for leap years?

Use day 366 for February 29, but the formula is an approximation; the difference is small.

Does this calculator work for any location on Earth?

Yes, solar declination depends only on the day of the year, not on geographic location.

Can I use the result for sizing solar panels?

Yes, declination is used to calculate the optimal tilt angle, but other factors like latitude and climate also matter.

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