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Area Calculation - Simpsons One Third Rule

Simpson’s 1/3rd rule is one of the most popular methods of finding the area for a given set of points by the method of numerical integration. The basic idea is to divide the X-axis into equally spaced divisions as shown and to complete the top of these strips of area in such a way that we can calculate the area by adding up these strips
Earthwork Volume Simpsons One Third Rule
Simpson's rule is based on a parabolic model of the function to be integrated (that is instead of connecting 2 adjacent points merely by a straight line, a parabola is chosen such that the curve formed by joining these points is extremely smooth and thus helps in calculating the area).
Where sum of odd and even terms do not include the first and the last terms
Important points to be considered while applying Simpson’s Rule are:
  1. Number of intervals must be an even number.
  2. Minimum of 3 points are required
  3. Intervals are expected to be equal
Example 3:
Earthwork Volume Simpsons One Third Rule
Cutting Area

Sl. No. Easting Initial Level Final Level Cutting Depth Calculation - Area (Sq. meters)
1

345

20.70

20

0.70

Simpsons 1/3rd Rule= h/3(First Value + last value + 4 * (Sum of odd values) + 2 * (Sum of even values) H = 21 / 3 = 3 = 3/3 (0.70 + 0 + 4 * 0.5 + 2 * 0.1)
2

348

20.50

20

0.50

3

351

20.10

20

0.1

4

354

19.80

20

0

5

357

19.40

20

0

6

360

19.10

20

0

7

363

19.00

20

0

Total = 2.9

Filling Area

Sl. No. Easting Initial Level Final Level Cutting Depth Calculation - Area (Sq. meters)
1

345

20.70

20

0

Simpsons 1/3rd Rule= h/3(First Value + last value + 4 * (Sum of odd values) + 2 * (Sum of even values)
H = 21 / 3 = 3
= 3/3 (0 + 1.00 + 4 * 1.1 + 2 * 0.4)
2

348

20.50

20

0

3

351

20.10

20

0

4

354

19.80

20

0.20

5

357

19.40

20

0.60

6

360

19.10

20

0.90

7

363

19.00

20

1.00

Total = 6.6


Summary table

Sl.No

Section at

Trapezoidal Method

Net Area

Simpsons Rule

Cutting

Filling

Cutting

Filling

Cutting

Filling

1

729

2.75

6.50

2.75

6.50

2.9

6.6

2

732

15.75

15.75

15.9

3

735

78.90

78.90

79

4

738

126.90

126.90

125.8

5

741

72.00

72.00

72.4

6

744

29.55

29.55

30.1


Section - Nett Area Method    Section - Summary