Category

# Calculations

An ellipse?  What the heck is an ellipse?  Simple.  Ellipses are circles.  Ok, did that confuse you?  Think of ellipses as special instance of a circle, meaning if you have an oval shape, it’s still considered a circle, but a special case of a circle.

If you have an oval shaped pond, you need to perform calculations for ellipses in order to figure out square footage and volume.  So, when we spoke about circles and some of your calculations were based off of the circle’s radius, it will be the same with an ellipse, but we’ll use the radius measurement just a little differently.

Major axis – The measurement that consists of the longest radius length from the center of the ellipse to the outer edge.

Minor axis –  The measurement that consists of the shortest radius length from the center of the ellipse to the outer edge.

Take a look at these pictures:

With an oval shaped ellipse, you will have two radius measurements.  One is longer and will be referred to as the major axis, while the other is shorter and will be referred to as the minor axis.  Remember when you calculated the area of a circle, you multiplied the radius by the radius and then by Pi?  This works the same.

For an ellipse, you multiply the major axis by the minor axis and then by Pi.  So if the pond was a 20 feet long and 10 feet wide oval shape, you would calculate,
20 (major axis) x 10 (minor axis) x 3.14 (Pi) = 628

Do not forget that you will have to measure the circumference (perimeter of the pond) in order to have the total square footage of the walls of the pond.  This is where it gets a little scary.  Because an oval is essentially a squashed circle, there are a lot of variables that would have to be taken into account in order to calculate the circumference.

First let me say that I will show you the varying calculations and you are free to follow along if math is your thing.  However, you may find that simply walking a tape measure around the perimeter of you pond is much easier.  Ok here we go for the mathematic enthusiast.

The first calculation you can do in order to find the circumference is an approximation only.  This means that you have to be sure that your major axis is no more than three times longer than the minor axis and your resulting calculation will be within 5% of being true.  That is the approximation part.  Your calculation could be as much as 5% incorrect.  But hey, let’s look at it anyways.

You are first going to multiply the major axis by itself and the minor axis by itself, and then add those two products together.  Then divide that answer by 2.  Take that total and divide it by the product of Pi multiplied by 2.
20 (major axis) x 2 = 400
10 (minor axis) x 2 = 200
So now you have 600 /2 = 300
Now, 3.14 (Pi) x2 = 6.28
The divide 300 by 6.28
30 / 6.28 = 47.77 feet

Now again, I stress that this formula is an approximation and can be off, up to 5%.  So let’s just assume you wanted a formula that calculated the circumference of the oval shape almost exactly.  Well all I am going to do is just show you the formula because it is nothing short of horrific!

Circumference = Pi(3.14) x (major axis + minor axis) / 4 x [ 3 x (1+L) + 1 / (1-L) ] And that’s assuming L = h/4 = (major axis – minor axis) x 2 / [2 x (major axis + minor axis)] x 2
As well as assuming h = (major axis – minor axis) x 2 / (major axis + minor axis) x 2

Now do you see why I say that it is probably just easier to walk a tape measure around your pond?  There is just no way I even care to calculate the circumference when it would take less time to physically measure it.  I certainly do not expect you to either.  So save yourself the time and headache and just tape measure the circumference.

Now that you have the circumference measurement, you need to multiply that by the height of the pond, like this (assuming the height or depth is 3 feet):
47.77 (circumference) x 3 (height) = 143.31 square feet

So the floor area square footage plus the wall square footage would be:
628 (floor area) + 143.31 (walls) = 771.31 total square feet

Again, to calculate how much Pond Shield epoxy you would need to coat this pond, you divide the total square footage by 60 square feet.  Remember 60 square feet is the amount of coverage a quart and a half kits gives you at a minimal thickness of 10 mils.
771.31 / 60 = 12.8 (rounded up to 13 total quart and a half kits)

To calculate volume of a oval (ellipse) shaped pond, you multiply Pi (3.14) by the major axis and multiply that by the minor axis and then multiply that by the height or depth and divide the total by 4.like this,
3.14 x 20 x 10 x 3 / 4 = 471 cubic feet

Then on to my obsession with water weight.  How much would that weigh?  3,956.4 pounds.  That is quite a bit of water for a small elliptical shaped pond.  Oh, I almost forgot.  Not that we have talked about elliptical shaped ponds, remember Part 2’s question at the end?  Have you figured it out yet?

I will see you when we discuss triangular shaped ponds in part 4.

OK, here are moving on to rectangles.  FYI – all of these particular calculations will work for those of you with square ponds too.  As I said in part 1 of this series, you’re going to eventually need to know the total square footage of your pond as well as the volume.

The square footage will assist you in calculating how much of any construction material you’ll need to actually build the pond and the volume will allow you to calculate the needs of water that your pond holds.

Squares are pretty simple to calculate too.  Unlike circles, there are only three measurements you’ll need to take in order to get the information you need out of your calculations.  There is length, width and height.

• Length – This measurement is the longest extent of the pond, measured from end to end.
• Width – The measurement is the longest extent from side to side on the pond.
• Height – The measurement that is the longest extent from top to bottom of the pond.  You’d also refer to it as depth of the pond.

When we calculated the square footage of the walls of a circular pond, there was only one wall.  So keep this in mind when calculating the square footage of a rectangular pond.  It has four walls and all need to be accounted for.  Let’s assume that the length of the pond is 24 feet, the width is 14 feet and the depth is 4.5 feet.

To calculate the total square footage of the floor you would multiply the length by the width like this,
24 (length) x 14 (width) = 336

So the floor has 336 square feet.

For the walls, you would multiply the length by the height for each wall and then add them all together.  So,
24 (length) x 4.5 (height) x 2 (walls) = 216
14 (width) x 4.5 (height) x 2 (walls) = 126

So for this rectangular pond, add the floor square footage to both wall square footage totals and you will end up with a total square footage for the entire pond.
336 (floor) + 216 (walls) + 126 (walls) = 678

Again, to calculate how much Pond Shield epoxy you would need to coat this pond, you divide the total square footage by 60 square feet.  Remember 60 square feet is the amount of coverage a quart and a half kits gives you at a minimal thickness of 10 mils.
678 / 60 = 11.3 (rounded up to 12 total quart and a half kits)

Now because we already know the length, width, and height, it will be very easy to calculate volume.  As a reminder, it is important to know the total volume of water your pond contains for purposes of water chemistry or how many fish you can safely house.  You know, that sort of thing.

To calculate volume of a rectangular shaped pond, you multiply the length by the width by the height of the pond like this,
24 (length) x 14 (width) x 4.5 (height) = 1512 cubic feet

Do you know how much all that water weighs?  12,700.8 pounds!  Yes, I make a big deal out of the total weight of the water.  I will tell you why.  If you are planning some sort of holding tank, something indoors, something on a pedestal of sort, weight becomes a serious issue and you need to know what that will be in the end.

Next time we will talk about ellipse shaped ponds and how to calculate square footage and volume for those.  I will give you a hint.  They are similar in nature to a circular pond, but do you know what the difference is?  I will let you know in part 3.

Now that you’ve gotten your pond built, it might be a wise idea to know both the total pond square footage and the pond volume.  Sure you can find an automatic calculator online somewhere, but it pays to have the calculations referenced and at least understand how they work.

Let’s talk about square footage first, since that’s probably going to be the first piece of information you might need to know.  It does not matter whether you are lining your pond with a rubber liner, Polyurea, or you plan a structured pond that can be waterproofed with Pond Shield epoxy.  In any of those scenarios, you will still need to calculate the total square feet of the pond.

There are some very basic shape categories that almost any pond shape will fall into.  Circles, ellipses, rectangles, polygons, general triangles and right triangles.  If you have trouble deciding, picture your pond as though you were floating above and looking down at it.

One point I would like to bring up before we move forward is the actual volume of a single cubic foot.  One single cubic foot will hold 7.48 gallons of water.  As a side note, one gallon of water weighs 8.4 pounds.  So, on cubic foot of water volume would weigh almost 63 pounds.  That does not sound like much now, but just wait until you see how many cubic feet of volume your pond ends up being!

So today, I would like to talk about calculating square footage and then we’ll move onto calculating volume for circular ponds.  These are pretty basic shapes and the formulas are pretty simple.  Typical terminology for circles would be radius, diameter and circumference and for volume you’ll use height.  Of course then there is also Pi.

• Radius – The radius of a circle is measured as exactly one half of the diameter.
• Diameter – The diameter of a circle is measured as the length from one side of a circle to the other side, using the center as an intersection point.
• Circumference – The circumference of a pond is the measurement of the outside shape or outline of the circle.
• Height – This is simple, it is the measurement of how high the walls of the circle are.
• Pi – This is my favorite.  It even has a symbol   It represents the ratio of any circle’s circumference in relation to its diameter.  Confused yet?  Not to worry.  For the most part, it will be represented as a number in our calculations.  That number being 3.14.

So with that said, let’s see what we can do with that information.  If you plan to calculate the total square footage of your circular pond, you have to know the radius, the circumference and the height.  So let’s say that your pond has a radius of 10 feet, meaning that from side to side it is 20 feet (diameter).  Knowing this will enable you to figure out the circumference.  Let’s say that:

Height = 3 feet

Radius x 2 = Diameter (20 feet) Just showing you this so that you see how radius and diameter relate to one another
10 x 2 = 20

Circumference (62.8) = Pi (= 3.14) x Diameter (20)  So you multiply the radius times two in order to find the diameter and then multiply the diameter times Pi and you will have the circumference.
62.8 = 3.14 x 20

So to calculate the square footage of the walls of the circle, you multiple the circumference by the height.
62.8 x 3 = 188.4

The floor of the pond would be calculated by multiplying the radius by the radius and then multiplying that total by Pi.
10 x 10 x 3.14 = 314

Finally the total square footage of the circular pond would be the total area of the floor added to the total square footage of the walls.
188.4 + 314 = 502.4 square feet

Now to figure out how many kits of Pond Shield epoxy you are going to need to coat the project, divide the total number of square feet a kit will yield by the total square feet of the pond.

A quart and a half kit yields 60 square feet of material at a thickness of 10 mils.  10 mils is the recommended minimal thickness that the epoxy should be applied.  So,
502.4 / 60 = 8.37 kits (round that up to 9 total quart and a half kits)

Fortunately, the volume of this type of shape is simple.  You already have all of the components to calculate square footage and some of those will allow us to calculate volume.  In doing so, we’ll multiply the radius by the radius, and then multiply that by Pi, and finally multiply that by the height.  So,
10 x10x 3.14 x 3 = 942 cubic feet

The over-all weight of the water is simple too,
942 cubic feet x 8.4 pound per gallon = 7,912.80 pounds.  I told you it would be a lot!

Check back tomorrow and we’ll look at another shape and its calculations.