Magnetic declination formula in surveying

magnetic declination formula in surveying
magnetic declination formula in surveying 


magnetic declination definition
magnetic declination definition

Magnetic declination at a place is the horizontal angle between the true meridian and the magnetic meridian shown by the needle at the time of observation. If the magnetic meridian is to the right side (or eastern side) of the true meridian, declination is said to be eastern or positive (a); if it to be the left side (or western side), the declination is said to be western or negative (b).

Mariners call declination by the name variation. The declination at any particular location can be obtained by establishing a true meridian from astronomical observations and then reading the compass while sighting along true meridian. Isogonic line is the line drawn through the points of same declination. The distribution of earth's magnetism is not regular and consequently, the isogonic lines do not form complete great circles, but radiating from the North and South magnetic regions they follow irregular paths. Agonic line is the line made up of points having a zero declination. 

Magnetic declination formula

Variations in Declination : 

The value of declination at a place never remains constant but changes from time to time. There are four types of variations in declination 

  • Diurnal variation 
  • Annual variation 
  • Secular variation 
  • Irregular variation. 

(a) Diurnal Variation 

The diurnal variation or daily variation is the systematic departure of the declination from its mean value during a period of 24 hours. It generally varies with the phase of the sunspot period. The difference in declination between morning and afternoon is often as much as 10' of arc. The extent of daily variations depend upon the following factors: 

  1. The Locality : More at magnetic poles and less at equator. 
  2. Season of the year : Considerably more in summer than in winter.
  3. Time: More in day and less in night. The rate of variation during 24 hours is variable.
  4. The amount of daily variation changes from year to year, 

(b) Annual Variation 

The variation which has a yearly period is known as annual variation. The declination has a yearly swing of about l' or 2' in amplitude. It varies from place to place.

(c) Secular Variation 

Due to its magnitude, secular variation is the most important in the work of surveyor. It appears to be of periodic character and follows a roller-coaster (sine-curve) pattern, It swings like a pendulum. For a given place, the compass needle after moving continuously for a period of years in one direction with respect to the true North, gradually comes to a stand still and then begins to move in opposite direction. Secular change from year to year is not uniform for any given locality and is different for different places. Its period is approximately 250 years. In Paris, the records show a range from 11" E in 1680 to 22° W in 1820. This magnitude of secular variation is very great,  is very important  in the work of the surveyor, and unless otherwise specified, it is the change commonly referred to.

(d) Irregular Variation 

The irregular variations are due to what are known as 'magnetic storms', earthquakes and other solar influences. They may occur at any time and cannot be predicted. Change of this kind amounting to more than a degree have been observed. 

Determination of True Bearing. 

All important surveys are plotted with reference to true meridian, since the direction of magnetic meridian at a place changes with time. If however, the magnetic declination at a place, at the time of observation is known, the true bearing can be calculated from the observed magnetic bearing by the following relation: 

magnetic declination formula in surveying

True bearing = magnetic bearing ± declination. 

Use plus sign if the declination is to the East and minus sign if it is to the West. The above rule is valid for whole circle bearings only. If however, a reduced bearing has been observed, it is always advisable to draw the diagram and calculate bearing.

Magnetic declination problems and solutions

1.The magnetic bearing of a line is 48° 24'. Calculate the true bearing if the magnetic declination is 5° 38' East. 


Declination = + 5° 38' 

True bearing = 48° 24' + 5° 38' = 54° 02'. 

2.The magnetic bearing of a line AB is S 28 ° 30' E. Calculate the true bearing if the declination is 7° 30' West. 


The positions of true meridian, magnetic meridian and the line have been shown below. Since the declination is to be West, the magnetic meridian will be to the West of true meridian. 

Magnetic declination problems and solutions
Magnetic declination problems and solutions

Hence, true bearing S 28° 30' E + 7 ° 30'. = S 36° 00' E.

3.In an old map, a line AB was drawn to a magnetic bearing of 5° 30' the magnetic declination at the time being 1° East. To what magnetic bearing should the line be set now if the present magnetic declination is 8° 30' East.


True bearing of the line = 5° 30' + 1° = 6° 30' 
Present declination = + 8° 30' (East) 
True bearing = Magnetic bearing +8° 30' 
Magnetic bearing = True bearing - 8° 30' 
= 6° 30' - 8° 30' 
= - 2° (i.e. 2° in the anti-clockwise direction) 
Magnetic bearing= 358°. 

4.Find the magnetic declination at a place if the magnetic bearing of the sun at noon is (a) 184 ° (b) 350° 20'. 


(a) At noon, the sun is exactly on the geographical meridian. Hence, the true bearing of the sun at noon is zero or 180° depending upon whether it is to the North of the place or to the South of the place. Since the magnetic bearing of the sun is 184°, the true bearing will be 180°. 

Now , True bearing Magnetic bearing + Declination 

180° = 184° + Declination or Declination = 4° = 4° W 

(b) Since the magnetic bearing of the sun is 350° 20', it is at the North of the place and hence the true bearing of the sun, which is on the meridian, will 360°

Now, True bearing Magnetic bearing +Declination 

360° = 350° 20' +Declination or Declination = 360° - 350° 20' = 9° 40' = 9° 40' E

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