How much dirt do you need?

Posted on March 19, 2011

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For this year’s garden I need about 8 cubic feet of potting soil and another two cubic feet of peat moss or compost.  How did I come to this conclusion?  Math.

What? Math in gardening?  Yup.  It turns out there really is a use for that stuff.

Every year I need to freshen up the soil in my self watering containers.  Tired soil means unhappy plants.  Last year I bought 1 bag, 2 cubic feet, of Happy Frog Organic potting soil, mixed it with last year’s soil (after removing old roots and such) and a bag of composted mint and I was good to go.  This year I’m adding three large containers and one small one, so I need an extra bag of soil to make up the difference.  That brings me up to 4 cubic feet of soil and 1 cubic foot of compost.  So far we’re just talking addition, because I know how much soil it takes to fill my existing containers.

But what if you have a new container to fill?  How can you save yourself repeated trips to the garden center for one more bag of soil?  You can determine the volume of your container or bed using math.  The equation itself is pretty simple, though you’ll probably want a calculator, the important part is matching up your units of measurement.  But I’m getting ahead of myself…

First, the equation you’ll use depends on whether your container is round or square.  Let’s assume it’s round.  Mostly because mine is round. (Don’t worry, I’ll go over square beds later.)  What you’ll need to know is the height and diameter of your container or bed.  The diameter is the distance across the top of the cylinder.  You’ll also need pi.  3.14, not the baked kind.  Though perhaps you can grow something that can later be put into a pie after you figure out how much dirt you need.  (Some will argue that you should use tau instead of pi, but I’m not going to get into that here.)

Volume= πr²h

Volume equals pi times the squared radius times the height of your container.  First let’s make sure we have our units right.  My bed is going to be 42 inches across and 6 inches high.  If I use those numbers I will get my answer in cubic inches, so first I have to convert my measurements to feet.  6 inches is obviously half a foot, so h=.5 .  Now I just have to divide 42 by 12 to get my diameter in feet.  D=3.5 .  Of course, I don’t need the diameter, I need the radius, so I’ve got to cut that number in half.  r=1.75 .

Now we’ve got our numbers. Volume= 3.14 x (1.75)² x .5

Plug it all into a calculator and voilá!  Volume= 4.808125

So, I need almost 5 cubic feet of material to fill my round bed.  The soil I purchase comes in bags of 2 cubic feet each, so I can just buy 2 bags of soil, and add 1 cubic foot of compost to fill things out.

Added to the soil I need for my containers that makes for a total of 8 cubic feet of soil and 2 cubic feet of compost.  Yeah, I’m a geek, but I only want to make one trip to the garden center this year.  I like to be prepared.

If your bed is square just convert your numbers to feet (or meters) and use this equation: Volume= l x w x h  when l is your length, w is your width, and h is your height.

There you have it.  I hope you’ve enjoyed this geeky excursion into the world of gardening math.

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Posted in: Gardening