# Math and the Art of Grazing – Figuring Your Stocking Rate

Thanks to Krista Ehlert, Assistant Professor and South Dakota State University Extension Range Specialist, and Jameson Brennan for this article!

Like many of us Krista Ehlert has a love hate relationship with math. She says, “Growing up, I remember asking the question, “Why do we need to learn this?” The “this” being math, and I posed the question to my algebra, geometry, calculus and statistics teachers from grade school all the way through high school. All I ever received for an answer was, ‘You’ll use it someday.’” And sure enough, they were right! Math became very important for managing her bank account to save up for special trips, to provide for retirement or to add infrastructure to the ranch

“But you also have another bank account,” she says, “The  one full of grass out on your land, and it might be one of the most important accounts you have.” Here she lays out why, as graziers, we need math, and then she shows us how to use it to make the best use possible of our grass account.

I’m here to tell you that, while there are scientific principles that guide grazing management and ecological interactions, grazing itself is also an art — one that has a bit of math to it! One way to perfect that art is by understanding how much:

1) You want to leave in your ‘grass account’,

2) How much you can take from your account,

3) How long you can leave your account ‘open’ and when you need to ‘close it’ for the year and

4) How many animals you can support without irritating the (grass) bank.

## Math Example

Let’s walk through an example to put the math into perspective:

You know the following:

• Number of acres in the pasture
• Forage production (in pounds per acre)**
• Number of animals and their associated class (pairs, stockers, bulls)
• Average weight of the animals

You want to know:

• How many grazing days that pasture can support

## Step 1. Calculate ‘total forage production.’

• 400 acres × 2,000 pounds production per acre** = 800,000 pounds total forage

** The average forage production per acre can be obtained through several methods. The USDA NRCS Web Soil Survey website is a great start, or you can use a “clip and weigh” method, or a Grazing Stick. Your local NRCS service center or Extension Agent can get you started with any of these methods.

## Step 2. Calculate ‘forage allocated for consumption.’

This is where “take half, leave half” comes in. You want to leave half of that total forage behind. This is for several reasons. Leaving approximately 50% behind means that in a normal year, there’s enough leaf structure and root growth to allow for adequate regrowth of your bank account next year. Although we leave behind 50%, your cow will not consume the entire other 50%, instead it is utilized. This means that 25% of that will end up in the cow’s stomach and the other 25% is beneficially “used” through trampling, manure coverage or insects. Figure 1 demonstrates this concept.

Now because you are leaving half behind (50%) + about 25% is beneficially used = 75%, leaving us 25% to put into our cattle. This 25% is known as the grazing efficiency.

The math becomes:

800,000 × 0.25 (25% grazing efficiency) = 200,000 pounds allocated for consumption across that 400-acre pasture.

## Step 3. Calculate ‘forage demand.’

This is where you must know your pastures and the state of production your animals are at. A general rule of thumb is that a lactating cow with a calf at her side requires close to 3% of her body weight (2.7% to be specific) based on dry matter intake.

Forage quality, though, adjusts the amount a cow will consume. For example, high quality forage (> 59% TDN (Total Digestible Nutrients)) equates to high digestibility, meaning that the cow will intake about 2.7% of her body weight if she is lactating. In contrast, low quality forage (< 52% TDN) equates to low digestibility and that same lactating cow will consume about 2.2% of her body weight.

This table outlines the forage demand on a dry matter intake (DMI) basis and is presented as a percent of body weight (BW) (Hibbard and Thrift 1992, Lalman 2004).

#### Table 1

Forage Type and Maturity
Stage of Production
Forage DMI, % of BW

Low quality forage (< 52% TDN)

Examples: Dry winter forage, mature legume and grass hay, straw

Dry, Lactating
1.8, 2.2

Medium quality forage (52-59% TDN)

Examples: Dry summer/fall pasture, late-bloom legume hay, early-bloom grass hay

Dry, Lactating
2.2, 2.5

High quality forage (> 59% TDN)

Examples: Early-bloom and mid-bloom legume hay, pre-boot stage grass hay, lush pasture, silage

Dry, Lactating
2.5, 2.7

For this example, we are going to use the 2.7% and assume that we have high quality forage.

Our cows weigh approximately 1,300 lbs and we own 200 head. Each pair we have requires 35.1 pounds of forage per day.

1,300 lb × 0.027 (2.7% body weight consumed) = 35.1 pounds.

But wait! As you are reading this, it is a bit into the fall (August/September), so the calves are grazing some on their own and mom is still lactating. The majority of the calf’s nutrition comes from grass now. Thus, we should account for what the calf will be eating. If our calves are approximately 450 pounds, then our math looks like this:

450 pounds × 0.027 (2.7% body weight consumed) = 12.2 pounds forage required per calf per day.

This means that about 3 calves will eat as much as 1 cow per day at this time of year!

Now we can figure the intake per pair adjusted for this time of year:

35.1 pounds (cow) + 12.2 pounds (calf) = 47.3 pounds.

Now, we calculate the forage demand for the entire herd per day. We own 200 pairs so here’s the math:

200 × 47.3 pounds per day = 9,460 pounds of forage is needed to feed the entire herd for one day!

This is important! If we only accounted for the cows, and not the calves, the forage demand for the entire herd would equal 7,020 lbs for one day. This is a difference of about 2,400 pounds per day!

## Step 4. Calculate ‘grazing days’ in this pasture.

To calculate the grazing days we have in one pasture, we take the forage allocated divided by the forage demand per day to arrive at the number of grazing days. In our example we have 200,000 pounds of allocated forage and we know that we need 9,640 pounds of forage, so here’s our math:

200,000 pounds allocated divided by 9,460 pounds forage per day = 21 days of grazing can occur in this pasture.

Again, if we only accounted for the cows, then 200,000 pounds allocated divided by 7,020 pounds forage per day = 28 days of grazing. That’s an entire week of difference! If you only calculated for what the cows are eating and not the calves, you would have kept them in for 7 days longer, which might not sound like a lot, but it is something that can make a difference in a year that is droughty.

Simply put, 21 days of grazing can occur in that pasture, feeding your entire herd, and keeping the land managed in a way that soil and rangeland health are protected.

## Step 5. Record it and keep track!

Do you ever try to go to the grocery store without a list written down? How often do you get home and realize that you forgot the milk? I know this happens to me quite a bit! That’s why a written record is the best record! Be sure that you are writing down your calculations (so you remember how you did the math and can double check for mistakes) and so that you can see any patterns or changes in your stocking rate that have occurred over time.

## And We Have a Calculator for You!

Now that you’ve done some calculations by hand, we are pleased to present the SDSU Extension Grazing Calculator!

The grazing calculator eliminates the guesswork and mess associated with doing calculations by hand. It requires a few inputs on your end, and you’ll be able to save a downloadable Excel file for your record keeping. Click here to get started, or view the following information and instructional video to learn more about using the calculator.

## In Summary

It might seem a bit silly to check in on your stocking rate calculations, but it is something that is undoubtedly worth your time whether you’re a seasoned rancher or you’re still trying to get your feet under you. Calculating these as we approach fall and early winter are worthwhile, so that you have an idea of what you should be looking at for spring turnout and beyond. A new grazing season will be here before we know it!