The document discusses various mathematical calculations related to vinyl records, including how record speed, circumference, weight, side length, song length, sales, and prices are determined. It also provides examples of how the value of rare records has increased significantly over time and analyzes data on the decreasing number of record stores in America in recent years.

1. The Mathematics of
Records
Ralph Bell
ED 325
November 7, 2011

2. Record Speeds
O A standard vinyl record has a speed of 33
revolutions per minute (rpm). If
you were listening to a song
that is 7 minutes and 4 seconds,
the record would spin 233.2
times during the song.
33 x 7 = 231
33/60 = .55 (record turns per second)
.55 x 4 = 2.2
231 + 2.2 = 233.2

3. Record Speeds
O A single is released on a smaller vinyl
record that turns at a speed of 45rpm.
If you were to listen to the same 7 min
4 sec song, the record would spin 318
times.
45 x 7 = 315
45/60 = .75
.75 x 4 = 3
315 + 3 = 318

4. Record Circumference
O A standard vinyl record has a diameter
of 12in. Therefore the circumference of
any standard record is 33.70 inches.
3.14 x 12 = 33.70
A single vinyl record has a diameter of
7in. Therefore the circumference of any
single is 22 inches
3.14 x 7 = 22
NCTM geometry: find
the distance between
points along
horizontal and vertical
lines

5. Record Weight
O Records are weighted in grams. Up until the
21st century, records were 125 grams.
Nowadays any new or re-released album
weights 180 grams. This means records are
55 grams heavier.
O 180 – 125 = 55
1 pound = 453.59237 grams
1 gram = 0.00220462262 pounds
180 grams = 0.396832 pounds
NCTM measurement = understand the need for measuring with
standard units and become familiar with standard units in the
customary and metric systems

6. Average Side Length
O Unlike a cd both sides of a record are played.
These are referred to as side a and side b. To
calculate the average side length of a Beatles
album one must add up multiple side lengths and
divide by the number of sides. Below are side a
lengths for the Beatles first 5 albums. To add
seconds divide the number of seconds by 60 and
add the decimal to the number of minutes
17:05+15:35+16:28+16:31+17:19
17.08+15.58+16.46+16.52+17.37= 82.96
82.96/5=16.592
.592 X 60 = 36
Average Side Length = 16 minutes 36 seconds
NCTM data analysis and probability: propose and justify
conclusions and predictions that are based on data and design
studies to further investigate the conclusions or predictions

7. Average Song Length
O To calculate the average song length on a
side add up the length of the songs and divide
by the number of songs. The Beatles album
Revolver has 7 songs on the first side.
2:39+2:08+3:02+3:01+2:26+2:40+2:37
2.65+2.13+3.03+3.02+2.43+2.66+2.62=18.55
18.55/7=2.65
.65 x 60 = 39
Average Song Length = 2 minutes 39 seconds
NCTM number and operations: work flexibly with fractions,
decimals, and percent's to solve problems

8. Record Sales
O In the year 2001 180,000 records were
bought. In the year 2010 223,000 records
were bought. This is an increase of
23.89% over 9 years.
223,000 – 180,000 = 43,000
43,000/180,000 = 0.2389
0.2389 x 100 = 23.89

9. Record Prices
O For various reasons records are more
expensive than cd’s. If you wanted to buy
the Grateful Dead album American
Beauty, it would cost $10.99 on cd and
$24.98 on vinyl. The vinyl record costs
$13.99 more.
24.98 – 10.99 = 13.99
The percent increase in price is 127%
13.99/10.99 = 1.27
1.27 x 100 = 127

10. Record Prices
O Double albums are even more expensive
compared to cd’s. The Bob Dylan album
Blonde on Blonde would also cost $10.99
on cd but the vinyl would cost $31.97. The
vinyl record costs $20.98 more.
31.97 – 10.99 = 20.98
The percent increase in price is 190%
20.98/10.99 = 1.90
1.90 x 100 = 190%

11. Valuable Records
O In 2009 a copy of the Beatles album
Yesterday and Today sold for $39,000 at
auction. The average price for an album in
1966 (year album came out) was $5.99.
This means the value of the record
increased by 650985.14%
39,000 – 5.99 = 38,994.01
38994.01/5.99 = 6509.8514
6509.8514 x 100 = 650985.14

12. Changing The Needle
O You should change the needle on your
record player after listening to 1,000 hours
of music. If the average record length is
50 minutes, you can listen to 1,200
records before you have to change the
needle.
1000 x 60 = 60,000
60,000/50 = 1,200

13. Record Stores
O In 2003 there were about 6,000 record
stores in America. Today there are about
1,884. In the past 8 years 4,116 record
stores have closed.
6,000 – 1,884 = 4,116
This is a decrease of 68.6%
4,116/6000 = 0.686
0.686 x 100 = 68.6