Gardener Math

Now that we have broken ground on the Grow It Yourself test garden - and you have dug into yours? - there are a couple of things we have to do before we can start planting.

First, we need to improve the soil by adding organic matter, and then we will need to get some fertilizer.

The fun thing about gardening is that you get to do math.

The gardener of today is faced with any number of calculations throughout the season, such as how much compost to get and how much fertilizer to add. To save you from the classic conundrum of standing in the garden center parking lot figuring out how many 2 cubic foot bags of soil you need to cover a 43 square foot area, we offer you some handy formulas and common calculations.


So if, like us, you’ve ripped out a chunk of lawn (or you’ve uncovered a dusty old garden beneath the weeds), you are going to need to add organic matter like compost to the soil to make it productive enough to grow award-winning vegetables and support a healthy population of soil life. (Fun fact: There are over 4 billion micro-organisms in just 1 teaspoon of healthy soil!) Compost is usually the easiest thing for urbanites to get their hands on - either in bags or in bulk.

Now before we get to the math, if you remember nothing else in your gardening life, remember this:

Soil Is Everything.

You can scrimp on tools, seeds, and even plants, but to get lots of healthy vegetables and to make it all worthwhile, you need to go all out on building healthy soil, especially in a brand new garden. It can be a bit of an investment the first year (see money saving tips below), but I promise you it’ll be worth it, and you’ll only have to add a bit in subsequent years.

Compost Math

How much compost do I need to add?

New gardens: Adding 4-6 inches will give your garden a great start. (This will be forked into the top 10 to 12 inches of soil - we’ll show you how)

Established gardens or raised beds: Add 1 to 2 inches every year (either dumped on top or worked into the top 4 to 6 inches of soil)

To figure out how much compost you need to buy or charm your way into:

1. Measure your garden (in feet). The Grow It Yourself test garden is 13 feet long and about 6 feet wide and we want to add 4 inches of compost. (We will supplement this with homemade compost and try to get it to 6 inches deep.)

2. Calculate volume (cubic feet). We all remember how to do this, right?

For a square or rectangular garden area:

Volume: length x width x depth (in feet) = cubic feet

Remember to convert everything to the same units (feet). So if you want 4 inches like we do, convert inches to feet by dividing 4 by 12 (= 0.33).

So the calculation for our garden is:

13 feet x 6 feet x 0.33 feet = 19.5 cubic feet. We’ll call it 20.

But my garden is a circle!

For a round garden, raised bed, or container, you need to use a different formula:

Volume of a cylinder: 3.14 x radius squared x height

Say you have a round garden bed that is 6 feet across (diameter) and you want to add 6 inches of compost (height).

The calculation is:

a) 3.14 x 3 feet (the radius) squared x 0.5 feet

b) 3.14 x 9 x 0.5 = 14 cubic feet

Same goes for a container, though in this case you’d be filling it with potting soil, not compost.

For a container that is 12 inches (1 foot) across and 2 feet tall:

a) 3.14 x 0.5 squared x 2

b) 3.14 x 0.25 x 2 = 1.57 cubic feet

But my garden is a half circle!

It’s more common than you think. Here’s ours.

Measure it, pretend it is a circle and use the formula above, then divide in half.

3. Go get it

With our cubic foot number and favourite pocket notebook, off we went to the nursery.

Most bags of compost are 1 cubic feet, but check the bag to make sure, and then do the math to figure out how many you will need. Since we needed 20 cubic feet of compost, we needed 20 bags. But hm, they were 5 bucks a pop, so it was going to be over $100 with tax. (And also a little heavy for the trusty sedan - check to see if your nursery offers delivery.) This was more than I wanted to spend, so I considered my bulk options.

Remember from school:

1 cubic yard = 3 feet x 3 feet x 3 feet = 27 cubic feet

I figured 20 cubic feet is kinda close to 27 cubic feet and we have to top up the existing garden with compost too, so we decided to order 1 yard in bulk from our local soil and rock supply place. It cost around $40 plus delivery, and it comes right to your driveway.

Fertilizer Math

Before you plant your garden, you should add a balanced vegetable fertilizer to the soil. We recommend using organic fertilizer because we are organic gardeners and that’s that. Popular liquid fertilizers in brightly coloured packages that promise Miracles are basically crack for plants, and you will go broke supporting their dirty habit. A balanced organic fertilizer (like 4-6-4 or 10-12-8) will release slowly to plants over the season and contain only ingredients found in nature.

There are dry/granular fertilizers that come in boxes and bags, and liquid fertilizers in little jugs. Use the dry stuff for the garden and liquid for pots.

What are those 3 numbers on the box?

Those numbers represent Nitrogen, Phosphorous, and Potassium, or, if you recall from the Periodic Table: NPK.

Here’s what each one does:

Nitrogen (N): promotes green leafy growth. Important for veggies like lettuce.

Phosphorous (P): promotes fruiting. Important for tomatoes, peppers, squash, and other veggies that produce a fruit. If you are growing these, look for a fertilizer with a higher middle number (4-6-4).

Potassium (K): promotes strong roots and overall health

We’ll show you how and when to add fertilizer to the garden, but for now, the math:

1. Calculate the area, or square footage, of your garden

Area of a square or rectangle: length x width

Area of a circle: 3.14 x radius squared

Area of a large or irregularly shaped area: divide into squares, rectangles, triangles (try it, it’s fun!), or circles, then calculate the area of each and add together.

2. Look on the back of the fertilizer box and check the application rate

In this case, pay attention to the rates for vegetables and for new plantings.

The instructions on this box are nice and clear with application rates that make sense for small city gardens: it tells me what I need in volume: 1-1/3 cups for every 10 square feet. Easy enough. Just refer to your square footage and do the math. Sometimes application rates are given as cups per “row feet”. We ignore row feet because for no good reason it confuses us.

Sometimes, though, the application rates are given by weight rather than volume, like 5 pounds per 100 square feet. This is not as user-friendly and calls for a formula:

1. Calculate the area (square feet) of your garden

2. Check the back of the box for your application rate (i.e., number of pounds per 100 square feet)

3. Square feet of area x __ pounds of fertilizer ÷ __ square feet = pounds per square foot

Example? Let’s.

Test garden: 13 feet x 6 feet = 78 square feet

Application rate on the box: 5 pounds per 100 square feet

5 pounds fertilizer ÷ 100 square feet = 0.05 pounds per square foot

78 square feet x 0.05 pounds = 3.9 pounds of fertilizer

Let’s call it 4 pounds. Now check the weight on the front of your fertilizer box.

4 pounds! Perfect.

See? Math is fun.

Note: If it doesn’t come out even like this, there is no need to weigh anything. You can just convert weight (pounds) to volume (cups):

Dry/granular fertilizer: 1 pound = 16 ounces = 2 cups

Liquid fertilizer: 1 pound = about 1.5 cups


Money saving tips

In future posts we will show you how to build a compost pile and start a worm compost bin so you can make some of your own compost for free!

If your budget is small this year, hunt around for free or cheap compost or well-composted manure. Check out Craigslist, talk to your Parks Department, or try to track down some local farmers or ranchers - people with chickens, horses, or other animals will often part with manure if you pick it up. Just make sure it is well-aged/composted (at least 6 months to a year). Don’t add fresh manure to a vegetable garden.

Keep in mind that not all compost is created equal. Any time you are procuring compost (or topsoil or even woodchips) from a free or cheap source, make sure to ask what went into them. You don’t want to bring compost made out of weed seeds, cat litter, or diseased plants into your garden.

Another option is pooling your resources. If you have a gardening neighbor or nearby friend, you could go in on a yard of compost together and split it.

Next up: Choosing seed and plants


I agree that the gardener of today faced with any number of calculations. The life of a gardener is not that easy. First and foremost they really need to learn on how to calculate. Calculating square foot, cubic yard, volume and even on the fertilizer they really have to calculate. From the label of fertilizer to how much fertilizer they have to use. That’s why I am proud to all gardeners for providing us those nutritious foods from their garden!

I am so glad I found your website. It was a complete accident. This is my second year attempting a backyard 4×4 garden and I am trying to get it right. Thank you for the formulas! I was just about to head to the store and I would have just bought the compost and mixed it in without really thinking about the right ratios. [Can you tell I am a complete novice?] Thanks again!

Great, I’m glad it helped!

rachel cooley

rachel cooley’s avatar

ok, I’m not a math whiz far from it. but please tell me how you fiigure volume for your 13×6x.33=19.5 I get 25.74, maybe i need a new battery in my calculator?

Whoops, good question. I’ll check my battery.

I want to put in just a small garden nothing big. I staked out an area that is 4′ x 8′. I bought 2 bags of Garden Soil and they cover a 1.5 Cubic foot area. Being that I suck in Math( always have) I am asking you if you can tell me in “laymen” terms if this would be enough soil to cover my garden area? Now, I know I have to take out all the grassy area and rake up rocks and stuff. Can you help me!! :-(

Thank you so much,
Mary Reynolds