Concept of Solar declination angle

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 31^st 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)

                               = – 17.8^o

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.

What is minimum value of solar declination angle?

 - 23.45

What is maximum value of solar declination angle?

+ 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 1^st

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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