# bones calulating height

```TRAINING LAB – SKELETAL REMAINS: DETERMINING A VICTIM’S HEIGHT
NAME___________________________________________
Background: As a Forensic Anthropologist you have been trained to identify skeletal
remains – but what can the bones you identify tell you about the victim? One important
piece of information a bone can help you uncover is the victim’s approximate height.
Knowing the victim’s height can be an important first step in discovering the victim’s
identity.
1. You will be trained to analyze skeletal remains to determine a victim’s height.
Procedures:
1. Use a meter stick and accurately measure the length of your Femur to the nearest
0.5 centimeter. Record your measurement in Table 1.
2. Repeat Step #1 and measure the length of your Tibia, Humerus, and Ulna to the
nearest 0.5 centimeter. Record these measurements in Table 1.
3. Finally, measure your height to the nearest 0.5 centimeter. Record your height in
Table 1.
4. Anthropologists have measured the heights and bone lengths of many humans to see
if there is a relationship between bone length and height. After analyzing a large mass
of data they discovered a distinct relationship between bones and height. Formulas were
derived from this data that will allow a Forensic Anthropologist to measure the length of
a single bone from a person and calculate that person’s approximate height (the height is
usually accurate to 1 or 2 inches). These important formulas can be found in Table 2.
5. Use your Femur length measurement (from Table 1) and the correct Femur formula
(from Table 2) to calculate your approximate height in centimeters. Record your
Calculated Height in Table 1.
6. Repeat Step #5 to calculate your approximate height using your Tibia, Humerus, and
Ulna length measurements. Check carefully to make sure you are using the correct
formula for each calculation. Record each Calculated Height in Table 1.
7. Convert all your Table 1 Centimeter Heights (Actual and Calculated) into the more
familiar Feet and Inches. Follow these simple steps:
Step #1 – Use the following Formula to convert centimeters into inches. Round your
Height in Centimeters
Height in Inches =
2.54 Centimeters per Inch
Step #2 – Convert total Inches to Feet and Inches (48 inches = 4 feet,
60 inches = 5 feet, 72 inches = 6 feet).
EXAMPLE: 65 inches = 5 feet 5 inches
Record all Feet and Inch heights in Table 1.
357
Part 2 – Measuring Skeletal Remains To Determine A Victim’s Height
1. Your Supervisor has a collection of skeletal remains from various crime scenes that have
been sent to you for analysis. Studies of the skulls found with these bones helped
investigators determine each victim’s race and sex. They need your help to determine
each victim’s approximate height. Below is the information that is known about each
of the bones.
Bone Name
Race
Sex
Ulna
Caucasian
Male
Femur
African-American
Female
Fibula
Unknown
Unknown
Asian
Male
Tibia
African-American
Male
Humerus
Caucasian
Female
Measure the total lengths of each of the bones as accurately as possible. Determine the
Approximate Height (in Feet and Inches) of each of the victims. Record
Part 3 – Using Height Calculations To Analyze A Crime Scene
1. A shallow grave, filled with the skeletal remains of what is believed to be at least two
people, was recently discovered in a nearby county. Only a mix of arm and leg bones
were found in the grave, which has made it difficult for the sheriff’s department to
determine exactly how many victims were buried. The sheriff’s department carefully
measured each bone’s length (bone length is the only information they have been able
to gather from the skeletal remains). This bone length data just arrived in our lab today.
They would like for you to use height calculations to help determine the number of
victims in the grave.
2. The bone length data can be found in Table 4 – “Bone Evidence Summary Sheet”.
Complete the “Bone Evidence Summary Sheet” so we can send the results back to
the Sheriff’s Department.
358
DATA TABLES – SKELETAL REMAINS: DETERMINING A VICTIM’S HEIGHT
NAME___________________________________________
Table 1 – My bone lengths and calculated height
Bone Name
Bone Length
(cm)
Calculated
Height
(cm)
Calculated
Height
(inches)
Calculated
Height
(ft./inches)
Femur
Tibia
Humerus
Ulna
My Actual Height (cm)
My Actual Height (inches)
My Actual Height (ft/inches)
Table 3 – Estimated heights calculated from skeletal remains
Bone Name
Bone Length
(cm)
Calculated
Height
(cm)
Ulna
Femur
Fibula
Tibia
Humerus
359
Calculated
Height
(inches)
Calculated
Height
(ft./inches)
Table 4 – Bone Evidence Summary Sheet
Bone Name
Bone Length
(cm)
Ulna
24cm
Femur
45cm
Fibula
34cm
Humerus
32cm
Humerus
30cm
24.5cm
Femur
41cm
Tibia
36.5cm
Fibula
39cm
24.5cm
Tibia
33.5cm
26.5cm
Femur
48cm
Humerus
36cm
Calculated
Height
(cm)
Calculated
Height
(inches)
Calculated
Height
(ft./inches)
How many different victims do you believe were buried in the mass grave?
List the Estimated Height of each victim below. Next to each victim’s height write the
number of bones from the grave that you believe belong to that victim.
360
Table 2 – Formulas used to calculate Estimated Height (cm) from Bone Length
(all bone measurements MUST be made in Centimeters)
Bone Name
Humerus
Race
Male
Female
Caucasian
(2.89 x length) + 78.10cm
(3.36 x length) + 57.97cm
African-American
(2.88 x length) + 75.48cm
(3.08 x length) + 64.67cm
Asian
(2.68 x length) + 83.19cm
use unknown formula
(4.62 x length) + 19.00cm
Unknown
Caucasian
(3.79 x length) + 79.42cm
(4.74 x length) + 54.93cm
African-American
(3.32 x length) + 85.43cm
(3.67 x length) + 71.79cm
Asian
(3.54 x length) + 82.00cm
use unknown formula
(3.78 x length) + 74.7cm
Unknown
Ulna
Caucasian
(3.76 x length) + 75.55cm
(4.27 x length) + 57.76cm
African-American
(3.20 x length) + 82.77cm
(3.31 x length) + 75.38cm
Asian
(3.48 x length) + 77.45cm
use unknown formula
(4.61 x length) + 46.83cm
Unknown
Femur
Caucasian
(2.32 x length) + 65.53cm
(2.47 x length) + 54.13cm
African-American
(2.10 x length) + 72.22cm
(2.28 x length) + 59.76cm
Asian
(2.15 x length) + 72.57cm
use unknown formula
(2.71 x length) + 45.86cm
Unknown
Tibia
Caucasian
(2.42 x length) + 81.93cm
(2.90 x length) + 61.53cm
African-American
(2.19 x length) + 85.36cm
(2.45 x length) + 72.56cm
Asian
(2.39 x length) + 81.45cm
use unknown formula
(3.29 x length) + 47.34cm
Unknown
Fibula
Caucasian
(2.60 x length) + 75.50cm
(2.93 x length) + 59.61cm
African-American
(2.34 x length) + 80.07cm
(2.49 x length) + 70.90cm
Asian
(2.40 x length) + 80.56cm
use unknown formula
(3.59 x length) + 36.31cm
Unknown
361
QUESTIONS – SKELETAL REMAINS: DETERMINING A VICTIM’S HEIGHT
NAME________________________________
1. On the average, how far off (in inches) were your calculated heights from your actual
height?
2. Which of your bone(s) gave you the most accurate estimation of your actual height?
3. Which of your bone(s) gave you the least accurate estimation of your actual height?
4. The formulas that you used for calculating your estimated height are based on
results?
5. Why would knowing the sex of a bone allow you to make a more accurate estimation
of the victim’s height?
6. You measure a bone and calculate the height of the victim is 5 feet 11 inches. Why is
it correct to say that this is the victim’s Estimated Height?
362
TEACHER NOTES
Lab/Activity: Training Lab – Skeletal Remains: Determining A Victim’s
Height
Equipment To Prepare:
1 meter stick/group – to measure the lengths of bones
1 “Height Measuring” Station – students will need to measure their correct height (in cm)
during the Training Lab. This process can be sped up by taping two meter sticks to a
a wall (one from the floor up and the second continuing onward from the end of the
first). Students can stand in front of the two meter sticks and a third meter stick (or
similar) can be placed flat on the student’s head to help determine their correct
height.
1 calculator/group – to calculate heights
1 each of the following bones placed in a tray or a central location for student access (these
can be a random assortment of right or left bones from different disarticulated sets).
However, if you have female disarticulated bones you could place female bones for
the Femur and Humerus – although male bones will work fine for all.
The bones should not be labeled in any way.
1 Humerus (female)
1 Femur (female)
1 Tibia
1 Ulna
1 Fibula
These bones will be used for Part 2 of the Training Lab. All the students in the class
can use these same bones SIX bones (it doesn’t take long to measure the length of a
bone – so their isn’t much wait time).
You should also measure the lengths of the SIX bones you use, calculate approximate
heights (according to the instructions in Part 2 of the Training Lab), and record
these results in the supplied KEY (found after these Teacher Notes).
This Training Lab usually takes 1 day to complete if students measure and calculate very
quickly. Otherwise, it will spill over to a second day.
The formulas used in the Training Lab came from Bass, W.M. (1987), Human Osteology: A
Laboratory and Field Manual.
Students sometimes find great variability when calculating their own heights from bone
lengths. This is often due to inaccurate measurements (it is harder to measure the length of
a bone when it is inside your body), the fact that the bone formulas are based on adult
bones, and the fact that the calculations give an approximate height only.
Typical Results:
Keys to the Training Lab Tables and Questions follow these Teacher Notes.
363
DATA TABLES – SKELETAL REMAINS: DETERMINING A VICTIM’S HEIGHT
KEY
NAME___________________________________________
Table 1 – My bone lengths and calculated height
Bone Name
Bone Length
(cm)
Calculated
Height
(cm)
Calculated
Height
(inches)
Calculated
Height
(ft./inches)
Femur
Tibia
Humerus
Ulna
FOR EACH STUDENT
My Actual Height (cm)
My Actual Height (inches)
MEASURE THE BONES YOU
USE, CALCULATE HEIGHTS,
AND RECORD HERE.
Table 3 – Estimated heights calculated from skeletal remains
My Actual Height (ft/inches)
Bone Name
Bone Length
(cm)
Calculated
Height
(cm)
Ulna
Femur
Fibula
Tibia
Humerus
364
Calculated
Height
(inches)
Calculated
Height
(ft./inches)
Table 4 – Bone Evidence Summary Sheet
Bone Name
Bone Length
(cm)
Calculated
Height
(cm)
Calculated
Height
(inches)
Calculated
Height
(ft./inches)
Ulna
24cm
157.47
62
5' 2&quot;
Femur
45cm
167.81
66
5' 6&quot;
Fibula
34cm
158.37
62
5' 2&quot;
Humerus
32cm
166.84
66
5' 6&quot;
Humerus
30cm
157.6
62
5' 2&quot;
24.5cm
167.31
66
5' 6&quot;
Femur
41cm
156.97
62
5' 2&quot;
Tibia
36.5cm
167.43
66
5' 6&quot;
Fibula
39cm
176.32
69
5' 9&quot;
24.5cm
167.31
66
5' 6&quot;
Tibia
33.5cm
157.56
62
5' 2&quot;
26.5cm
174.87
69
5' 9&quot;
Femur
48cm
175.94
69
5' 9&quot;
Humerus
36cm
185.32
73
6' 1&quot;
How many different victims do you believe were buried in the mass grave?
4
List the Estimated Height of each victim below. Next to each victim’s height write the
number of bones from the grave that you believe belong to that victim.
Victim #1 Height = 5’ 2” 5 bones
Victim #2 Height = 5’ 6” 5 bones
Victim #3 Height = 5’ 9” 3 bones
Victim #4 Height = 6’ 1” 1 bone
365
QUESTIONS – SKELETAL REMAINS: DETERMINING A VICTIM’S HEIGHT
KEY
NAME________________________________
1. On the average, how far off (in inches) were your calculated heights from your actual
height?
ANSWERS WILL VARY – SOME WILL BE VERY CLOSE,
WHILE OTHERS WILL VARY GREATLY
2. Which of your bone(s) gave you the most accurate estimation of your actual height?
3. Which of your bone(s) gave you the least accurate estimation of your actual height?
4. The formulas that you used for calculating your estimated height are based on
results?
STUDENTS ARE STILL GROWING, THEREFORE, IT IS MORE LIKELY THAT
VARIATION.
5. Why would knowing the sex of a bone allow you to make a more accurate estimation
of the victim’s height?
FEMALE BONES ARE TYPICALLY SHORTER THAN MALE BONES. CALCULATIONS
WOULD BE MORE ACCURATE IF THE FORMULA IS BASED ON FEMALE BONES
ONLY – RATHER THAN USING A FORMULA THAT AVERAGES BOTH MALE AND
FEMALE BONE LENGTHS TOGETHER.
6. You measure a bone and calculate the height of the victim is 5 feet 11 inches. Why is
it correct to say that this is the victim’s Estimated Height?
THESE FORMULAS ARE BASED ON AVERAGE BONE LENGTHS. SOME
PEOPLE MAY BE SOMEWHAT TALLER THAN THE CALCULATED HEIGHT,
WHILE OTHERS MAY BE SOMEWHAT SHORTER THAN THE CALCULATED
HEIGHT. CALCULATED HEIGHTS SHOULD ALWAYS BE REPORTED AS
“ESTIMATED” HEIGHT.
366
TRAINING LAB – SKELETAL REMAINS: DETERMINING A VICTIM’S SEX
NAME___________________________________________
Background: Humans look different from each other on the outside – each of us with our
own external characteristics. We can easily recognize males and females, and one
individual from another, because we have had years of experience observing these external
differences. Forensic Anthropologists have also discovered male and female differences in a
part of the body we’re NOT used to observing – the male and female skeletal system. Not
only can a victim’s approximate height be determined by skeletal remains, but the sex of
the victim can also be determined with a fair degree of accuracy – especially after you have
1. You will be trained to analyze skeletal remains to determine if a victim is a male
or a female.
Procedures:
There are several different bones that can help determine if skeletal remains came from a
male or female victim. In this Training Lab you will work with the bones that are most
commonly used by Forensic Anthropologists for sex determination.
You do NOT have to begin with Part 1 for this Training Lab. If other groups are using the
Part 1 skulls you should move on to another section of the lab and come back to Part 1
later.
Part 1 – Using The Skull And Mandible For Sex Determination
1. Your Supervisor has set out skulls for you to observe. You may be asked to observe
one or two different numbered skulls (your Supervisor will tell you how many different
skulls you should observe).
2. Bring one of the skulls back to your lab station. Please DO NOT point to parts of the
skull with your pen or pencil and mark on the skull.
3. Write the number of the skull you are observing in Table 5 – “Sex Determination Of
Skeletal Remains - SKULL” (the number can be found on the top of the skull).
4. Carefully observe the characteristics of your skull using Table 1 – “Characteristics of Male
and Female Skulls” as your guide (Table 1 can be found on the next page). This Table
describes Male and Female characteristics that are generally visible on skulls. Labeled
diagrams of Male and Female skulls/mandibles have also been included to assist you.
5. Record each of your skull’s characteristics in Table 5. Record your observation in the
“Male” column if you observed a Male characteristic, in the “Female” column if you
observed a Female characteristic, and in the “Can’t Determine” column if the observed
characteristic seemed to be between Male and Female.
6. Look at all your observations and decide if you have a Male or Female skull (do you have
more characteristics recorded in the Male or Female column)? Record your final result
in Table 5.
7. Repeat Steps #3 - #6 for a second skull (if supplied by your Supervisor).
8. Check the KEY found in the front of the room to see if your conclusions are correct!
367
Table 1 - Characteristics of Male and Female Skulls
AREA OF
SKULL
MALE
FEMALE
From A Side View - Appears to be
sloping backward
From A Side View - Appears to be more
straight up and down
Usually more square-shaped
Usually more round-shaped
More of a rounded, less sharp edge
More of a sharp edge
Larger
Smaller
Larger
Small or missing
Orbit
Shape
Upper Edge
Of Orbit
Mastoid
Process
External Occipital
Protuberance
Mandible
Angle
Chin Shape
o
Angle much larger than 90
More of a square shape
More of a rounded, pointy shape
MALE SKULL/MANDIBLE
FEMALE SKULL/MANDIBLE
Upper orbit
has more of a
sharp edge
Upper orbit
has more of a
rounded edge
More square
orbit shape
Chin shape is
more square
More rounded
orbit shape
Chin shape is more
rounded/pointy
External
Occipital
Protuberance
larger
External
Occipital
Protuberance
small or
missing
Mastoid
process smaller
Mastoid
process larger
Mandible Angle closer to 900
o
Closer to a 90 Angle
Mandible Angle much larger
than 900
368
Part 2 – Using The Pelvis (Coxal Bones, Sacrum, Coccyx) For Sex
Determination
1. The next bone to observe is the Pelvis. You may be asked to observe more than one
numbered Pelvis (your Supervisor will tell you how many you should observe).
2. Bring a Pelvis back to your lab station. Please DO NOT point to parts of the Pelvis with
your pen or pencil and make marks on the bone.
3. Write the number of the Pelvis you are observing in Table 6 – “Sex Determination Of
Skeletal Remains - PELVIS”.
4. Carefully observe the characteristics of your Pelvis using Table 2 – “Characteristics of
The Male and Female Pelvis” as your guide (Table 2 can be found below). Labeled
diagrams of the Male and Female Pelvis have also been included to assist you.
5. Record each of your Pelvis’s characteristics in Table 6. Record your observation in the
“Male” column if you observed a Male characteristic, in the “Female” column if you
observed a Female characteristic, and in the “Can’t Determine” column if the observed
characteristic seemed to be between Male and Female.
6. Look at all your observations and decide if you have a Male or Female Pelvis (do you
have more characteristics recorded in the Male or Female column)? Record your final
result in Table 6.
7. Repeat Steps #3 - #6 for a second Pelvis (if supplied by your Supervisor).
8. Check the KEY found in the front of the room to see if your conclusions are correct!
Table 2 – Characteristics of the Male and Female Pelvis
AREA OF
PELVIS
Front View Of The
Subpubic Angle
Top View Of The
Pelvic Cavity Shape
MALE
FEMALE
o
Less than a 90 angle
Like a &quot;V&quot; shape
The space you see inside is more
&quot;heart&quot; shaped and small
o
90 angle or larger angle
Like an &quot;L&quot; shape
The space you see inside is more
oval/circular in shape and larger
Sacrum Shape
Sacrum is longer and thinner. Sacrum is shorter and wider. The
The Sacrum and coccyx are tilted
Sacrum and coccyx are tilted
toward the inside of the Pelvic
backward away from the Pelvic
Cavity and are easily visible from
Cavity and are not very visible
a top view.
from a top view.
Pubic Bone Width
(in mm) From The
Center Of The Pubis
Symphysis To The
Obterator Foramen
(the large hole)
Measure with a ruler (mm). The Measure with a ruler (mm). The
Pubic Bone Width at this location Pubic Bone Width at this location
is less than 30mm.
is greater than 35mm.
**PUBIS SYMPHYSIS**
where the two coxal bones
meet in the front (ventral)
369
MALE PELVIS
FEMALE PELVIS
Sacrum longer
and thinner
Sacrum shorter
and wider
Sacrum is tilted
inward with
coccyx pointing
into the space
Front view of
subpubic angle
is less than 900
“V-shaped”
Measure the width of
the pubic bone here
(in mm). If it is less
than 30mm = Male,
greater than
35mm = Female
Sacrum is tilted
backward with
coccyx barely
pointing into the
space
Front view of
subpubic angle is
greater than 900
“L-shaped”
Top view of pelvic
cavity – space is
large and oval or
circular shaped
Top view of pelvic
cavity – space is
small and “heart”
shaped
IF YOU ONLY HAVE ONE COXAL BONE
#2 – width
of the Pubic
Bone here
1. You can still accurately estimate what the
subpubic angle would be (less than or
greater than 900).
2. You can still measure the width of the Pubic
Bone from the center of the Pubis Symphysis
to the Obturator Foramen.
#1 – Subpubic Angle
370
Part 3 – Using The Humerus For Sex Determination
1. The next bone to observe is the Humerus. You may be asked to observe more than one
numbered Humerus (your Supervisor will tell you how many you should observe).
2. Bring a Humerus back to your lab station. Please DO NOT point to parts of the Humerus
with your pen or pencil and make marks on the bone.
3. Write the number of the Humerus you are observing in Table 7 – “Sex Determination Of
Skeletal Remains - HUMERUS”.
4. Carefully observe the characteristics of your Humerus using Table 3 – “Characteristics of
the Male and Female Humerus” as your guide (Table 3 can be found below). You will
be taking measurements of the Humerus (in millimeters) to determine sex. You can
either place a millimeter ruler behind the Humerus when taking measurements, or you
can use a caliper (for a more accurate measurement) if one is available.
5. Record each of your Humerus’s characteristics in Table 7. Record your observation in the
“Male” column if you observed a Male characteristic, in the “Female” column if you
observed a Female characteristic, and in the “Can’t Determine” column if the observed
characteristic seemed to be between Male and Female.
6. Look at all your observations and decide if you have a Male or Female Humerus (do you
have more characteristics recorded in the Male or Female column)? Record your final
result in Table 7.
7. Repeat Steps #3 - #6 for a second Humerus (if supplied by your Supervisor).
8. Check the KEY found in the front of the room to see if your conclusions are correct!
Table 3 – Characteristics of the Male and Female Humerus
MEASUREMENTS
OF THE HUMERUS
MALE
COULD BE MALE
OR FEMALE
FEMALE
Transverse Diameter
greater than
47 mm
43 to 47 mm
less than
43 mm
Vertical Diameter
closer to 48.8 mm
45.8 mm
closer to 42.7 mm
Width Between
Epicondyles
closer to 63.9 mm
60.4 mm
closer to 56.8 mm
Total Length Of The
Humerus
closer to 339.0 mm
322.5 mm
closer to 305.9 mm
Vertical
Diameter of