Dedicated To The Tribal Aquaculture Program

March 2002-Volume 39

Topics Of Interest:

Calculating Area and Volume of Ponds and Tanks

Calculating Area 
Square or Rectangular Ponds 
Other Pond Shapes
Irregularly Shaped Ponds
Calculating Volume
Tanks
Ponds
Conversion Tables

Calculating Area and Volume of Ponds and Tanks

By:  Michael P. Masser and John W. Jensen, Alabama Cooperative Extension Service, August 1991

Good fish farm managers must know the area and volume of all ponds and tanks. Exact measurement of area and volume is essential in order to calculate stocking rates and chemical applications.  Stocking fish into a pond of uncertain area can result in poor production, more disease and possibly death. Chemical treatments can be ineffective if volume/area is underestimated and potentially lethal if it is overestimated.  Measurements and calculations described in this publication can be made in either English or metric units. All examples are given in English units. Conversion tables are also provided for those who wish to use metric units.  

Calculating Area 

Surface area calculation is an essential first step. Pond stocking rates, liming rates and other important management decisions are based on surface area.  An error in calculating surface area will inevitably lead to other problems.  Measure distances accurately, calculate area and double check all calculations.  You may not need to measure pond area yourself, the contractor who built the pond should have accurate records. The county field office of the U.S. Department of Agriculture Natural Resources Conservation Service (NRCS) assists with the construction of many ponds and has engineering records on ponds in each county.  Also, the county offices of the NRCS and the USDA Agricultural Stabilization and Conservation Service (ASCS) have aerial photos from which pond area can be estimated.

Surveying ponds using a transit is the most accurate way to determine area. Less accurate but acceptable methods of measuring pond area are chaining and pacing.  Inaccuracies in these methods come from mismeasurements and measurement over uneven/sloping terrain. Measurements made on flat or level areas are the most accurate.  

Chaining uses a measuring tape or other instrument of known length.  Stakes are placed at each end of the tape. The stakes are used to set or locate the starting point for each progressive measurement and to maintain an exact count on the number of times the tape was moved. Sight down the stakes to keep the measurement in a straight line. The number of times the tape was moved multiplied by the length of the tape equals total distance.

Pacing uses the average distance of a persons pace or stride. To determine your pace length, measure a 100-foot distance and pace it, counting the number of strides.  Pace in a comfortable and natural manner. Repeat the procedure several times and get an average distance for your stride.  

For example, if it took you 38, 39 and 40 paces to walk a measured 100-foot straight line then the average was 39 paces (38 + 39 + 40 3).  To get the length of your average pace divide 100 feet by 39 paces (100 ft 39 paces = 2.56 feet per pace). Now, whenever you pace a distance, simply multiply the number of paces by 2.56 to get the distance.  It is a good idea to always pace a distance more than once and average the number of paces.  The formula for calculating distances from pacing is: 

Distance (ft) = Total Number of Paces x Length of Average Pace

Square or Rectangular Ponds 

Ponds built in square or rectangular shapes are the most easily measured.  Square and rectangular areas are determined by multiplying length by width. Figure 1 illustrates some typical shapes and sizes of ponds.  

Figure 1.

Rectangular pond areas are estimated by the formula:

Area = length x width

Area of the rectangular pond in Figure 1 is:

Area = 500x 150= 75,000 square feet

To convert from square feet (ft²) to acres, divide by 43,560 (from Table 1).

Area = 75,000 43,560= 1.72 or 1.7 acres

In this example the area of the rectangular pond is 75,000 square feet or approximately 1.7 acres.  Areas of ponds which are almost square or rectangular can be estimated by calculating average length and width measurements.  If we designate the lengths as A and B, and the width as Y and Z then the formula for the area is:

For example, an almost rectangular pond that is 470 feet on one side and 525 feet on the other long side, and 140 feet on one end and 162 feet on the other end, has an area of 75,123 ((470 + 525 2) x (140 + 162 2)) square feet or 1.72 acres.

Other formulas are used to calculate ponds that are circular and triangular.  Even if your pond is not an exact shape, it maybe possible to get a reasonable estimate of its area by using one or a combination of these formulas.  Circular pond areas are estimated by the formula:

Area = 3.14 x radius²
(Radius is one-half the diameter)

For example, a circular pond with a radius of 75 feet has an area of 17,663 square feet (3.14 x 75 x 75) or 0.4 acres.  The radius can be measured directly or the diameter can be divided by 2. A measurement of the diameter in several directions will help to determine if the pond is truly circular.  Triangular pond areas are estimated by one of two formulas depending on whether the triangle has a square or 90 angle for one of its corners.  If a 90 angle is present the formula is:

Area = x length x width

For example, a triangular pond with a length of 250 feet and a width of 220 feet has an area of 27,500 square feet (250 x 220 2) or 0.63 acres. It is important to remember that the longest side (the hypotenuse) is not needed for the calculation, instead the two sides that touch the 90 angle are used.  If no 90 angle is present and the sides are unequal, the formula is: 

... and A, B and C are the lengths of the sides.  For example, a triangular pond with three sides of 80, 90 and 130 feet has an area of 3,549.6 square feet (where S = 150); and 

Many ponds in the Southeast are watershed ponds that have been built by damming valleys. These ponds are usually irregular in shape.  Check first with your county NRCS office for records on your pond, or for aerial photos in the NRCS or ASCS office. If no good records exist then a reasonable estimate can be made by chaining or pacing off the pond margins and using the following procedures to calculate area.  

1.  Draw the general shape of the pond on paper (graph paper works best).  

2.  Draw a rectangle on the pond shape that would approximate the area of the pond if some water was eliminated and placed onto an equal amount of land. This will give you a rectangle on which to base the calculation of area (See Figure 2 below).

3.  Mark the corners of the rectangle (from the drawing) on the ground around the pond and chain or pace its length and width. For example, a length of 350 paces and a width of 125 paces would be equal to 896 feet (350 paces x 2.56 feet/pace [pace length, from above]) by 320 feet.

4.  Multiply the length times width (see example above) to get the approximate pond area. For example, 896 feet x 320 feet =286,720 square feet or 6.58 acres (286,720 43,560).

Figure 2.

It is a good idea to repeat this procedure two or three times and compare your results. You may want to average these results if they differ.  If a single rectangle does not fit the pond drawing then try to fit some combination of rectangles, circles, and/or triangles. If some combination seems to fit, then calculate the areas of the different shapes, and add the corresponding areas together to get the total pond area.

Volume measurements are needed to calculate the proper concentration of most chemicals which are applied to water and to calculate holding or transport densities.

Most tanks used for holding and transporting fish are rectangular.  Rectangular volume is calculated by the formula:

Volume = length x width x depth

When measuring a tank, take inside measurements of length and width and the depth at the appropriate water level. If a standpipe or other type of overflow drain is present, then the height to the overflow should be the depth measurement.  If the bottom of the tank is sloped toward the drain an average depth measurement should be used. To get average depth of the tank, take three measurements: at the shallow end, in the middle, and at the overflow. Add these depths together and divide the total by 3.

For example, a rectangular tank, without a sloping bottom (see Figure 3), has a measured inside width of 36 inches, a length of 72 inches and a depth at the standpipe overflow of 24 inches. The calculated volume is 62,208 cubic inches (36 x 72 x 24).

Figure 3.

In many cases it will be necessary to convert cubic inches (in ³) to either cubic feet (ft³) or gallons.  Table 4 gives simple ways to make these conversions. Cubic inches are converted to cubic feet by multiplying by 0.000579 (or by dividing by 1728). Cubic inches are converted to gallons by multiplying by 0.00433 (or by dividing by 231).  A volume of 62,208 in³ is the same as 36 ft³ (62,208 x 0.000579 or 62,208 + 1728) and 269 gallons (62,208 x 0.00433 or 62,208 231).  

Circular tank volume (Figure 4) is determined by the formula: 

Volume = 3.14 x radius² x depth

Figure 4.

The radius is measured as the inside diameter of the tank. The radius is squared or multiplied by itself.  For example, a circular tank with an inside diameter of 72 inches and a standpipe depth of 24 inches has a volume of 97,667 cubic inches (3.14 x 36 x 36 x 24).  Using Table 4 the volume can be converted into cubic feet (97,666.56 1728 = 56.52) or gallons (97,666.56 231= 422.8).  

Ponds