# SSA - Biofilter Specific Surface Area Calculations

## How to Calculate SSA of Bare Liner,

Rock and Gravel used in Ponds,

Waterfalls, Streams, and Bogs

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Bare Liner SSA Calculations

Rock and Gravel SSA Calculations

Rock and Gravel "Rule of Thumb"

## Bare Liner SSA Calculations

The Specific Surface Area (SSA) of bare liner is easy to calculate. Simply calculate the square footage of each of the surfaces in a pond. Here is an example of a rectangular shaped, bare liner Koi pond that is 20 feet long by 10 feet wide by 5 feet deep.

First calculate the square footage of the bottom of the pond. 20' x 10' = 200 square feet. So the bottom of the pond has an SSA of 200.

Then calculate the square footage of one of the long sides of the pond. 20' long by 5' deep (20' x 5' = 100'). So one long side of the pond has an SSA of 100. Since their are two identical sides to this pond, multiply 100 x 2 = 200. So when adding both of the long sides together, the Total SSA of the long sides is 200.

Now calculate the square footage of one of the ends of the pond. 10' wide by 5' deep (10' x 5' = 50). So one end of this pond has an SSA of 50. When adding both ends of this pond together, the ends have a Total SSA of 100.

Now add the pond bottom SSA (200), the pond sides SSA (200), and the pond ends SSA (100) for a Total SSA of 500. (200+200+100=500).

This 20' x 10' x 5' bare liner Koi pond has a Total SSA of 500. You would then add this **SSA** to the **SSA of the filtration system** to accurately calculate **How Many Fish You Could Have in the Pond**.

If the pond is "oval" shaped, or "kidney bean" shaped, or some other shape, simply measure the the lengths of the sides and do the math as above. For example: An oval shaped Koi pond that has a maximum length of 20 feet and a maximum width of 10 feet and a depth of 5 feet.

Take a long measuring tape and lay it out on the pond's edge from the middle of one end of the pond to the other. Say the measurement read as 24 feet. Simply multiply the 24' length by the 5' depth (24' x 5' = 120 square feet. Since there are two sides to this oval pond, multiply 120 x 2 = 240.

To find the square footage of the oval shaped bottom of the pond, we use the **Surface Area of an Oval Formula of 0.8 x Length x Width**. So calculation of the square footage of the bottom of this oval pond is: 0.8 x 20 x 10 = 160

Add the bottom SSA of 160 to the sides SSA of 240 to calculate the Total SSA of 400. So an oval shape pond that is 20' long by 10' wide by 5' deep has a Total SSA of 400.

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## Rock and Gravelck and Gravel SSA Calculations

Figure the SSA based on spherical - or round rock. Actual SSA of each rock will vary based on the overall shape, and smoothness of the rock. The below figures are based on smooth round rocks. Some rocks will have higher SSA's, while others will have lower SSA's. These figures should be used as "averages".

The formula for surface area of a sphere is: 4 x Pi x radius squared. (Pi is 3.14 -remember that from Junior High algebra?) (Radius is 1/2 the diameter)

1/2" rock has a .25" radius.

4 x 3.14 x (.25 x .25) = .75 square inches of surface area on 1 piece of 1/2" gravel.

1 foot equals 12 inches. 12" divided by 1/2" rocks = 24 individual 1/2" rocks. 24 x 24 rocks = 576 1/2" rocks in one square foot. We need 2" of depth for SSA comparison. So 2" divided by 1/2" rocks = 4 rocks high. Now multiply the 576 rocks per square foot by 4 rocks high to get how many rocks are in 1 square foot at 2" thick. 576 x 4 = 2,304 individual 1/2" rocks in one square foot at 2" thick. Now multiply those 2,304 rocks by the surface area of .75" each to get how many square inches of surface area. 2,304 x .75 = 1,728 square inches of surface area. There are 144 square inches in 1 square foot, so divide the 1,728 square inches by 144 to convert square inches to square feet.

1,728 / 144 = 12.

**So 1/2" gravel has an average of SSA of 12.** You can add or subtract up to about 40% depending on how rough or smooth the gravel is.

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1" rock has a .5 radius.

4x3.14x(.5x.5) = 3.14" square inch surface area

12" / 1" rock = 12 rocks per linear foot.

12 rocks x 12 rocks = 144 rocks per square foot

2" / 1" = 2 rocks high

144x2=288 rocks per square foot at 2" thick

288 rocks x 3.14 square inches of surface area each = 904.32 total square inches

904.32 square inches / 144 = 6.28 square feet of surface area

**So 1" smooth rock has 6.28 SSA**

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2" rock has a 1" radius.

4x3.14x(1x1)= 12.56 square inches surface area

12" / 2" = 6 rocks per linear foot

6 rocks x 6 rocks = 36 rocks per square foot

2" / 2" = 1 rock high

36 x 1 = 36 rocks per square foot at 2" thick

36 rocks x 12.56 square inches of surface area each = 452.16 total square inches

452.16 / 144 = 3.14 square feet of surface area

**2" smooth rock has 3.14 SSA**

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4" rock has a 2" radius

4x3.14x(2x2)= 50.24 square inches of surface area

12" / 4" rock = 3 rocks per linear foot

3 rocks x 3 rocks = 9 rocks per square foot

9 rocks x 50.24 square inches each = 452.16 total square inches

452.16 / 144 = 3.14 square feet of surface area

**4" smooth rock has 3.14 SSA **

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8" rock has a 4" radius

4x3.14x(4x4) = 200.96 square inches of surface area

12" / 8"rock = 1.5 rocks per linear foot

1.5 rocks x 1.5 rocks = 2.25 rocks per square foot

2.25 rocks x 200.96 square inches each = 452.16 total square inches

452.16 / 144 = 3.14 square feet of surface area

**1 square foot of 8" smooth rock has a 3.14 SSA or 1.4 SSA each**

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16" rock has an 8" radius

4x3.14x(8x8) = 803.84 square inches of surface area

803.84 square inches / 144 = 5.58 square feet

**SO a 16" smooth rock has a 5.58 SSA**

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24" rock has a 12" radius

4x3.14x(12x12) = 1,808.64 square inches of surface area

1,808.64 square inches / 144 = 12.56 square feet

**SO a 24" smooth rock has a 12.56 SSA**

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## Rules of Thumb:

3/8" - 1/2" gravel has an average SSA of 12

4"-24" rock has an average SSA of 4

Calculate vertical sides at 4 SSA per square foot

Calculate horizontal surfaces at 12 SSA per square foot

Streams contain both - so calculate streams at 8 SSA per square foot.