Standards, 1400 Independence Avenue, SW. 

Analysis and Room 2607-S, STOP 0254 

Technology Branch Washington, DC 20250-0254 

Method for Grid Assessment of Beef Carcass Ribeye Area 

May 2011 

BACKGROUND

The Department of Agriculture (USDA), Agricultural Marketing Service (AMS), Livestock, and Seed 

(LS) Program will utilize carcass factors and measurements made by approved measurement tools. The 

LS Program approves the use of tools that increase the accuracy, precision, and repeatability in the 

prediction of quality and yield factors and grades. This document describes the methodology to be used 

for measuring the area of the ribeye muscle when an approved plastic grid is used. 

USDA Meat Grading and Certification (MGC) Branch graders evaluate ribeye size visually or through the 

use of tools such as grids or grading instruments. The following procedures are to be utilized for official 

determinations of ribeye size at MGC Branch correlations, for use in providing data for research studies 

or when requested to provide an accurate determination of ribeye size when approved instrument aided 

measurement are not used. 

The guidance for this document was based on a mathematical theorem for determining the area of a 

polygonal object located on a grid of equally spaced points, Pick’s Theorem (Pick, 1899; see also 

Steinhaus, 1999). As a mathematical theorem, it is a statement or formula that can be demonstrated to be 

true by accepted mathematical operations and arguments. 

PURPOSE AND SCOPE 

This document describes the procedures and requirements for the use of LS Program approved grids for 

use in measuring the area of a ribeye. The scope of this document encompasses the evaluation of yield 

factors and grades of livestock carcasses and carcass products. 

REFERENCE DOCUMENTS 

1. Georg Pick, 1899. “Geometrisches zur Zahlenlehre,” Sitzungber. Lotos, Naturwissen Zeitschrift, 

Prague, 19:311-319. 

2. Steinhaus, H., 1999. Mathematical Snapshots, Dover Publications, New York, New York. 

FORMULA DERIVED THROUGH PICK’S THEOREM 

The formula for area given by Pick’s Theorem is: 

൬ ൅ ݏݐ݋݀	ݎ݋݅ݎ݁ݐ݅݊ ൌ ݁ܽݎܣ

ݏݐ݋݀	ݕݎ݊݀ܽݑ݋ܾ

2 ൰	െ 1

For the case of measuring the area of a beef ribeye, the interior dots are those dots within the perimeter of 

the ribeye (those completely surrounded by lean) and the boundary dots are those on the perimeter of the 

ribeye (those touching lean). The scale of the USDA’s beef ribeye grid is a grid of equally spaced points 

representing a scale of 0.1 square inches. 

METHADOLOGY FOR GRID PLACEMENT 

USDA ribeye grids should be placed randomly on the surface of the ribeye. Aligning a grid to the long 

axis of the ribeye introduces a sampling bias and thus reduces the precision of measurement since not all 

dots have an equal probability of being located on an area of the ribeye. 
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OFFICIAL METHOD FOR MEASURING BEEF CARCASS RIBEYE AREA 

The area of the ribeye muscle shall be measured using the following method. 

1. Randomly place the ribeye grid on the cut surface of the ribeye so that the grid covers the entire 

ribeye muscle; 

2. Count the interior dots which are completely within the perimeter of the ribeye muscle; 

3. Count the boundary dots which are on the perimeter of the ribeye muscle and divide this number by 

two (2); 

4. Calculate the ribeye area by adding the result of steps 2 and 3, then subtract one (1); and, 

5. Multiply the result of step 4 by 0.1 square inches to obtain the area. 

RAPID METHOD FOR ESTIMATING BEEF CARCASS RIBEYE AREA 

An estimate of ribeye area may be made using the following method. 

1. Align the grid along the long axis of the ribeye with the edge of the squares aligned along the leanfat/rib/intercostal boundary so that the grid covers the entire ribeye muscle; 

2. Count the interior dots which are completely within the perimeter of the ribeye muscle; 

3. Count the boundary dots which are on the perimeter of the ribeye muscle and divide this number by 

two (2); 

4. Calculate the ribeye area by adding the result of steps 2 and 3; and, 

5. Multiply the result of step 4 by 0.1 square inches to obtain the area. 

The rapid method is only an approximation and on the average, slightly overestimates ribeye area. 

Because the grid is aligned with the long axis of the ribeye, the rapid method is also subject to a sampling 

bias. Caution should be considered for any measurement that is within 1.0 square inch (0.32 equivalent 

yield grade) of critical ribeye area requirement or that results in a change of yield grade. 

These processes are to be monitored on a continual basis by LS Program personnel. 

Questions or comments shall be submitted to: 

Chief, Standards, Analysis, and Technology Branch 

USDA, AMS, LS 

1400 Independence Avenue, S.W. 

Room 2607 South Building 

Washington, DC 20250-0254 

Phone: (202) 720-4486 

FAX: (202) 720-1112 

Email: Martin.OConnor@ams.usda.gov 

Approved: /S/ Martin E. O’Connor May 4, 2011 . 

Martin E. O’Connor, Chief 

Standards, Analysis, and Technology Branch 

The U.S. Department of Agriculture (USDA) prohibits discrimination in all its programs and activities on the basis of race, color, national origin, age, disability, and 

where applicable, sex, marital status, familial status, parental status, religion, sexual orientation, genetic information, political beliefs, reprisal, or because all or a part 

of an individual's income is derived from any public assistance program. (Not all prohibited bases apply to all programs.) Persons with disabilities who require 

alternative means for communication of program information (Braille, large print, audiotape, etc.) should contact USDA's TARGET Center at (202) 720-2600 (voice 

and TDD). To file a complaint of discrimination write to USDA, Director, Office of Civil Rights, 1400 Independence Avenue, S.W., Washington, D.C. 20250-9410 

or call (800) 795-3272 (voice) or (202) 720-6382 (TDD). USDA is an equal opportunity provider and employer. 
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Figure 1. Example of using the “OFFICIAL METHOD FOR MEASURING BEEF CARCASS RIBEYE 

AREA.” The grid is randomly placed on the surface of the ribeye. There are 98 “interior” dots (dots 

completely surrounded by lean). There are 9 “boundary” dots (the perimeter dots surrounded by the gold 

circle) and 9 divided by 2 is 4.5. The area is thus 0.1 x (98 + 4.5 – 1) or 0.1 x (101.5) or 10.15 square 

inches. 
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Figure 2. Example of using the “RAPID METHOD FOR ESTIMATING BEEF CARCASS RIBEYE 

AREA.” The grid is aligned along the long axis of the ribeye with the edge of the squares aligned along 

the lean-fat/rib/intercostal boundary. There are 100 “interior” dots (dots completely surrounded by lean). 

There are 9 “boundary” dots (the perimeter dots surrounded by the gold circle) and 9 divided by 2 is 4.5. 

The area is thus 0.1 x (100 + 4.5) or 0.1 x (104.5) or 10.45 square inches.