Volume Calculation - Contour Method

Volume can be measured by a contour map, but the volume calculated by this method is approximate. It cannot be compared with the volume calculated by the cross-section method. As the full ground irregularities are not predicted by contours, and also as the contour intervals are not small, volume calculated from contours is likely to be an approximate one. To calculate volume by this method, general recommendations of contour interval is a maximum of 2 meters for a regular ground surface, and 0.5 meter for an irregular topography. This method is used mainly to find the capacity of a reservoir. To find out the capacity of a contour, two methods can be adopted.

  1. Average area method (Known as trapezoidal method)
  2. Prismoidal formula

By average end-area (trapezoidal) method

Volume = L x 1/2 (A1 + A2) cubic meter

contour

By Prismoidal formula

V= L (A + Square Root (A*B) + B) / 3

earthwork12.2

earthwork12.3

For the following Example,

 

Volume Calculation Using Average Method

Contour

Area

Previous Area

Average Area

Contour Interval

Area between Contours

Cumulative Volume (Cubic Meters)

2

0.52

0

2

2

0

0

4

3.068

0.52

1.794

2

3.588

3.588

6

7.74

3.068

5.404

2

10.808

14.396

8

14.534

7.74

11.137

2

22.274

36.67

10

23.824

14.534

19.179

2

38.358

75.028

12

37.008

23.824

30.416

2

60.832

135.86

14

55.65

37.008

46.329

2

92.658

228.518

16

78.886

55.65

67.268

2

134.536

363.054

18

114.916

78.886

96.901

2

193.802

556.856

20

262.949

114.916

188.9325

2

377.865

934.721

 

Volume Calculation Using Prismoidal Method

Contour

Area

Previous Area

Area

(A + Square Root (A*B) + B) / 3

Contour Interval

Area between Contours

Cumulative Volume (Cubic Meters)

2

0.52

0.00

0.00

2.00

0.00

0.00

4

3.07

0.52

1.62

2.00

3.23

3.23

6

7.74

3.07

5.23

2.00

10.45

13.69

8

14.53

7.74

10.96

2.00

21.92

35.61

10

23.82

14.53

18.99

2.00

37.98

73.59

12

37.01

23.82

30.18

2.00

60.35

133.94

14

55.65

37.01

46.01

2.00

92.03

225.96

16

78.89

55.65

66.93

2.00

133.86

359.82

18

114.92

78.89

96.34

2.00

192.68

552.50

20

262.95

114.92

183.90

2.00

367.80

920.30

 

Division of Square method Earthwork Area & Volume Calculation Summary

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