# 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

By Prismoidal formula

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