Methods of Calculation of Areas in Surveying | Simpson’s Rule

Calculation of Areas in Surveying | Simpson’s Rule

In one of my previous articles, I discussed Midpoint Ordinate Rule and Average Ordinate Rule in detail with an example and listed out various important methods used for the calculation of areas in Surveying. In this article, we will deal with the next important method (rule) i.e. Simpson’s Rule along with a numerical example used for the calculation of areas in the field of Surveying.

Here are the five important rules (Methods) used for the calculation of areas in Surveying:

  1. Midpoint ordinate rule
  2. Average ordinate rule
  3. Simpson’s rule
  4. Trapezoidal rule
  5. Graphical rule

Simpson’s Rule


It states that, sum of first and last ordinates has to be done. Add twice the sum of remaining odd ordinates and four times the sum of remaining even ordinates. Multiply to this total sum by 1/3rd of the common distance between the ordinates which gives the required area.

Where O1, O2, O3, …. On are the lengths of the ordinates

d = common distance

n = number of divisions


This rule is applicable only if ordinates are odd, i.e. even number of divisions.

If the number of ordinates are even, the area of last division maybe calculated separated and added to the result obtained by applying Simpson’s rule to two remaining ordinates.

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Contour Analysis | Guide to Surveying and Levelling

Importance of Contouring in the field of Surveying

Contouring is an imaginary line on the ground obtained by joining points having same elevation.

Characteristics of Contours

Contour lines are closed, however they may be close on the map itself or outside the map depending upon the topography.

The spacing between contour lines depends upon the slope of the ground.

In steep slopes, the spacing is small, for gentle slopes the spacing is large.

If the contour lines are equally spaced, they indicate uniform slope.

Contour Analysis
Contour Analysis

If the contour lines are parallel, straight or equally placed, they represent plane surface.

In a series of contour lines on the plan or map indicates either a hill or depression.

In case of the hill, the values of the elevation go on increasing towards the centre whereas in case of depression, the values go on decreasing towards the centre.

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Plane Table Surveying | Methods of Plane Table

Guide to Plane Table Surveying

  • It is a graphical method of surveying in which field work and plotting are done simultaneously in the field.
  • It is very effective method of surveying for preparing small or medium size topographical plans.
  • It is not as accurate as the other survey methods and results.

Methods of Plane Table

  1. Radiation
  2. Intersection
  3. Traversing
  4. Resection


This method is useful in surveying small areas which can be commanded from one station.

From a station, the suitable is selected.

Rays are drawn to various objects.

The distance of the object from the station are measured and marked off on the ray.

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Duties of a Surveyor in the field of Surveying | Civil Engineering

Role of a Surveyor | Surveying and Levelling

Surveying is a subject that is studied by Civil Engineers as well as Architects. Some Civil Engineers take up Surveying as their profession but otherwise, there are surveyors who have the expertise in the field of surveying.

They have certain important duties as a Surveyor to be carried out. In this article, we will briefly discuss their division of work and their duties towards the field of Surveying.

The work of a surveyor can be divided into four parts:

  1. Field work
  2. Computing
  3. Mapping
  4. Setting

Field work

Making and recording measurements in the field.


Making the necessary calculations to determine areas, location, volume etc.

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Height of Instrument Method | Surveying and Levelling

Height of the Instrument Method

The following readings were observed with a levelling instrument, the instrument was shifted after 5th and 11th reading.

0.585, 1.010, 1.735, 3.295, 3.775(5th)

0.350, 1.300, 1.795, 2.575, 3.375

3.895 (11th), 1.735, 0.635, 1.605

Determine the RLs of various points if the reduced level (RL) of a point on which the first reading was taken is 136.440 gives the height of collimation method and applies the check.

Station BS IS FS HI RL Remarks

















RL of I point 






















1112 0.635 1.605 130.805


Sum of BS=2.670 Sum of FS =9.275

HL = RL + BS

= 136.440 + 0.585

= 137.025

RL = HL – IS


(Summation of BS)-(Summation of FS) = Last RL – First RL

2.670 – 9.275 = 129.835 – 136.440

-6.605 = -6.605

Conventional Signs or Symbols | Surveying and Levelling

Conventional Signs and Symbols used in Surveying

Here are a few important Conventional Signs and symbols useful in the field of Surveying:

  1. Marsh or Swarm
  2. House
  3. Embankment
  4. Cutting
  5. Single Line Railway
  6. Double Line Railway
  7. Lake or Pond
  8. Road
  9. Railway Bridge
  10. Road Bridge
  11. River
  12. Fence
Marsh or Swarm
Marsh or Swarm

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Temporary Adjustments of Prismatic Compass | Guide to Surveying

Temporary Adjustments of Prismatic Compass | Compass Surveying

In this article, we will be discussing step by step method for making Temporary adjustments in Prismatic Compass necessary for carrying out Compass Surveys.

  1. Fixing the compass to thr tripod
  2. Centering the compass
  3. Levelling the compass
  4. Sighting the object
  5. Observation of bearings

Fixing the compass to the tripod

The box of prismatic compass is fixed to a spindle of ball and socket joint. By the ball and socket arrangement, this can be quickly levelled and rotated in any direction.

Centering the compass

The prismatic compass is centered over a survey station correctly by means of a plumb bob or by dropping a pebble from the centre of the instrument.

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Designation of Bearings | Compass Surveying

Designation of Bearings | Guide to Compass Surveying

In my previous article, I discussed different types of Bearings in Compass Surveying. In this article, we will discuss in brief different designations given to the bearings depending on measurement of angles.

Designation of Bearings

  1. Whole circle bearing
  2. Reduced Bearing (RB) or quadrantal bearing (QB)
  3. Fore Bearing (FB) or forward bearing (FB)
  4. Back bearing or Backward bearing (BB)
  5. Calculated bearing

Whole Circle bearing

Bearings measured from north in a clockwise direction is termed as whole circle bearing.

The value varies from 0 degrees to 360 degrees.

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Classification of Bearings | Surveying

Types of Bearings | Guide to Surveying

It is an angle made by the survey line with reference to some fixed meridian.

Bearings are classified into three types:

  1. True bearing
  2. Magnetic bearing
  3. Arbitrary Bearing

True bearing

The angle made by a survey line with reference to the meridian is known as true bearing. It always remains constant.

Magnetic bearing

The angle made by a survey line with respect to magnetic meridian is known as magnetic bearing. It changes from place to place.

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Guide to Compass Surveying | Open and Closed Traverse

Compass Survey | Guide to Surveying and Levelling

Compass Survey is also known as Angular Surveying.

The branch of surveying in which the position of the object is located by angular measurements taken by the compass is known as “Compass Surveying”.

Purpose of Compass Surveying

When the area to be surveyed is relatively large, then the area cannot be divided into triangles.

For example:

Towns, colonies etc.

When the survey work is to be completed quickly

When the area is full of obstacles which prevent chaining.

Compass Surveying is unsuitable in areas having magnetic rock, iron core, power lines etc which attracts a magnet.


A traverse is formed by joining the points on the ground by means of series of connected straight line.

There are two types:

  1. Open traverse
  2. Closed traverse

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