TABLE 1. Slide Rule Scale Symbols and Meanings
Symbol
Mathematical
Relationship
Range
Description
Function
A
B
AI
x2
x2
1/x2
1 - 100
1 - 100
1 - 0.01
BI
1/x2
1 - 0.01
C
D
CF
CI
x
x
πx
1/x
1 - 10
1 - 10
3.1 - 31
1 - 0.1
2-cycle, Square of D, on stock
2-cycle, Square of C, on slide
2-cycle, Reciprocal of A or
2-cycle, Reciprocal Square of D
2-cycle, Reciprocal of B or
2-cycle, Reciprocal Square of C
1-cycle, Principal scale, on slide
1-cycle, Principal scale, on stock
1-cycle, Folded at π or √10
1-cycle, Reciprocal of C
CIF
DF
DI
1/πx
πx
1/x
0.33 – 0.03
3.1 - 31
1 - 0.1
1-cycle, Folded at π, Reciprocal of CF
1-cycle, Folded at π or √10
1-cycle, Reciprocal of D
DIF
K
L
LL, Ln
1/πx
x3
log10(x)
ln(x)
0.33 – 0.03
1 - 1000
0-1
0 – 2.7
1-cycle, Folded at π, Reciprocal of DF
3-cycle, Cube of D
Linear scale
Natural logarithm of x
LL0
LL1
LL2
LL3
LL00
LL01
LL02
LL03
R1
R2
P
S
T
T1
T2
ST
e0.001x
e0.01x
e0.1x
ex
-0.001x
e
e-0.01x
e-0.1x
e-x
√x
√10x
√(1-(0.1x)2)
sin-1(x)
-1
tan (x), cot-1(x)
tan-1(x), cot-1(x)
tan-1(x), cot-1(x)
sin-1(x), tan-1(x)
1.001 – 1.01
1.01 – 1.11
1.1 – 3.0
2.5 – 100,000
0.999 – 0.990
0.99 – 0.90
0.91 – 0.35
0.4 – 0.00001
1 – 3.2
3 - 10
0.996 - 0
5.8° - 90°
5.8° - 90°
5°-49°/41°-85°
41°-85°/5°-49°
0.58° – 5.8°
Exponent of x·103
Exponent of x·102
Exponent of x·101
Exponent of x
Exponent of -x·103
Exponent of -x·102
Exponent of -x·101
Exponent of -x
R1 is the square root of D
R2 is the square root of 10D
Cosine of sin-1(D)
D is the sine of angle S
D is the tangent/cotangent of angle T
D is the tangent/cotangent of angle T
D is the tangent/cotangent of angle T
D is the sin or tan of angle ST
Ch
Th
Sh1
Sh2
H1
H2
V
W
§
cosh-1(x)
tanh-1(x)
sinh-1(x)
sinh-1(x)
√(1+(0.1x)2)
√(1+x2)
Volts
%
0.1 - 3
0.1 - 3
0.1 – 0.9
0.85 – 3
1.005 - 1.5
1.4 - 10
0.5 – 10
20 - 100
D is the hyperbolic cosine of Ch
D is the hyperbolic tangent of Th
Hyperbolic sine of angle S
Hyperbolic sine of angle S
cosh of sinh-1 of 0.1D
cosh of sinh-1 of D
Voltage drop
Efficiency
Arbitrary symbol
Find Squares & Square Roots
Find Squares & Square Roots
Reciprocals,
Chain Multiplication & Division
Reciprocals,
Chain Multiplication & Division
Basic Multiplication & Division
Basic Multiplication & Division
Multiplies result by π
Reciprocals,
Chain Multiplication & Division
Divides result by π
Multiplies result by π
Reciprocals,
Chain Multiplication & Division
Divides result by π
Find Cubes & Cube Roots
Mantissa of base10 logarithm of D
Raise D to any power or
extract any root
Log Log scales
Log Log scales
Log Log scales
Log Log scales
Reciprocal Log Log scales
Reciprocal Log Log scales
Reciprocal Log Log scales
Reciprocal Log Log scales
Double Length Square Root Scale
Double Length Square Root Scale
Pythagorean scale
Trigonometric sine
Trigonometric tangent & cotangent
Trigonometric tangent & cotangent
Trigonometric tangent & cotangent
Trigonometric sine or tangent for
small angles
Hyperbolic Cosine
Hyperbolic Tangent
For small values
For larger values
Hypotenuse Scale
Hypotenuse Scale
For motors & generators
For motors & generators
For unlabeled scales with no
standard symbol
Convenience
Convenience
in
cm
Ruler in inches
Ruler in centimeters