## Solar declination angle

It is angle between the equator and a line drawn from the center of the earth to the center of the sun. The plane of the equator and a line drawn from the center of the sun to the sun of the earth is called as declination angle, δ. The declination angle varies seasonally due to tilt of earth on its axis of rotation and rotation of earth around the sun. If the earth axis is not tilted, the declination angle is zero.

The declination is zero at the equinox (21st/22nd March and 21st/22nd September). It is positive during summer in the northern hemisphere and negative during winter in the southern hemisphere. The declination angle reaches 23.45 degree on June 21/22 and minimum on December 21/22 in the northern hemisphere.

### Formula for solar declination angle

The declination angle is given by formula

δ = 23.45 Sin (360 (n – 81) / 365)

Where n = Number of days, starting from 1st January

 Date Day Number (n) Date Day Number (n) 1st January 1 31st July 212 31st January 31 31st August 243 28th February 59 30th September 273 31st March 90 31st October 304 30th April 120 30th November 334 31st May 151 1st December 335 30th June 181 31st December 365

Calculation of Declination angle for New Delhi, India as on 1.9.2023

 Day No. of day Declination Formula Declination Angle 31st January 1 δ = 23.45 Sin (360 (1 – 81) / 365) – 23.01 31st January 31 δ = 23.45 Sin (360 (31 – 81) / 365) – 17.8 28th February 59 δ = 23.45 Sin (360 (59 – 81) / 365) – 8.67 31st March 90 δ = 23.45 Sin (360 (90 – 81) / 365) + 3.61 30th April 120 δ = 23.45 Sin (360 (120 – 81) / 365) + 15.20 31st May 151 δ = 23.45 Sin (360 (151 – 81) / 365) + 21.9 30th June 181 δ = 23.45 Sin (360 (181 – 81) / 365) + 23.18 31st July 212 δ = 23.45 Sin (360 (212 – 81) / 365) + 18.17 31st August 243 δ = 23.45 Sin (360 (243 – 81) / 365) + 8.10 30th September 273 δ = 23.45 Sin (360 (273 – 81) / 365) – 3.81 31st October 304 δ = 23.45 Sin (360 (304 – 81) / 365) – 15.05 30th November 334 δ = 23.45 Sin (360 (334 – 81) / 365) – 21.96 31st December 365 δ = 23.45 Sin (360 (365 – 81) / 365) – 23.08

The declination angle changes between + 23.45 degree to 0 degree and again 0 degree to – 23.45 degree in a year.

Declination angle of Sun New Delhi 1.9.2023 (Data source: PVsyst)

Example

Calculate declination angle as on 31st January, 2023 for Mumbai.

Solution

The declination angle is calculated by formula

δ = 23.45 Sin (360 (n – 81) / 365)

Where n = Number of days, starting from 1st January

n = 31

declination angle δ = 23.45 Sin (360 (31 – 81) / 365)

= – 17.8o

### FAQs on solar declination angle

#### What is solar declination angle?

It is angle between the equator and a line drawn from the center of the earth to the center of the sun.

- 23.45

+ 23.45

#### What is yearly change in solar declination angle?

- 23.45 to +23.45

#### What is formula to find out solar declination angle?

δ = 23.45 Sin (360 (n – 81) / 365)

Where n = Day number, starting from January 1st

#### On which date, solar declination angle becomes zero?

The declination is zero at the equinox (21st/22nd March and 21st/22nd September).

#### Why solar declination angle varies through year?

Because earth axis is tilted at 23.45 degree on its own vertical axis

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