• Second moment of area moment of inertiaCalculate the second moment of area and radius of gyration of common shapes about weak and strong axes
  • Cubic orientation of primary and shear stresses and principal stress cosine rotationCombine primary and shear stresses into equivalent and principal stresses & their cosines
  • Nucleus and electron shells of atomic elementFind, sort and reorganise the properties of nature's atomic elements with active periodic table
  • Formulas included in Engineering PrinciplesCalculate unknowns in principle engineering formulas: stress, moments, power, energy, capstans, fluids, etc.
  • Properties of a triangle with inscribed and circumscribed circlesCalculate the properties of triangles and triangular configurations including inscribed and circumscribed circles
Area Moment calculation1 Combined Stress calculation2 Elements calculation3 Engineering Principles calculation4 Trigonometry calculation5

Symbols

Wherever possible, CalQlata use standard symbols (as we understand them). However, as there is no such thing as universal consistency, CalQlata applies the following symbols to its calculations:

If you cannot find the symbol you are looking for, e.g. MA or yx in the list below, you should search for the first character, e.g. M (moment) & y (distance) and then look for the second character in the list of suffixes, e.g. A (end 'A') and x (horizontal direction).

Notes

  1. Beams includes Plates and Stress includes Fatigue
  2. In the Table below, we indicate the field of application (e.g. maths, engineering, etc.) before supplying the definition of the symbol.
  3. Capital Letters: angles (except as specified above)
  4. Lowercase Letters: dimensional lengths (except as specified above)
  5. () Text alternatives are displayed in normal brackets
  6. [] Units are displayed in square brackets
  7. {} Suggestions are displayed in curly brackets
Symbol Meaning

a

Maths: length

a

Hydrodynamics & Engineering: acceleration

see also Derivative Symbolism at the bottom of this page

a

Physics: Bohr radius

ap

Electrical: apparent power

A

Maths: angle

A

Engineering: area

A

Engineering: amplitude or deflection (dynamic)

Engineering: amplification factor

Atm

Engineering: atmospheres

b

Maths: length

b

Engineering: breadth (width)

B

Maths: angle

B

Engineering: buoyancy

c

Maths: length

c

Dynamics: viscous damping coefficient

c

Hydrodynamics: celerity

cp

Thermodynamics: specific heat capacity at constant pressure

cv

Thermodynamics: specific heat capacity at constant volume

Cp

Thermodynamics: heat capacity at constant pressure

Cv

Thermodynamics: heat capacity at constant volume

C

Temperature: Celcius or centigrade

C

Maths: angle & circumference

C

Electrical: capacitance

C

Engineering: coefficient

C

Fluids: Cauchy number

Ca or Cm

Hydrodynamics: added mass coefficient

Cd

Hydrodynamics: drag coefficient

Cᴸ

class

Engineering: centreline

clearance

d

Engineering: depth

d

distance

d

Time: day

e

Stress: strain

e

Maths: eccentricity

e

Physics: elementary charge

E

Stress: Young's modulus

E

Fluids: Euler number

E

Thermodynamics: total energy

ECF

Engineering: end cap force

Ef

Stress: flexural modulus

EI

Engineering: bending stiffness

ƒ

Fluid Dynamics: Colebrook's fanning friction factor
Note: see also dynamic viscosity (μ) below

ƒ

Engineering: frequency
Note: see also dynamic viscosity (μ) below

ƒⁿ

Engineering: natural frequency

F

Engineering: force

F

Temperature: Fahrenheit

F

Fluids: Froude number

g

gravitational acceleration

G

Engineering: shear modulus (modulus of rigidity)

h

Time: hour

h

Engineering: height

h

Thermodynamics: specific enthalpy

h

Stress: Weibull parameter

h

wind chill factor (kcal/m2/h)

h

Physics: Planck's constant

ħ

Physics: Dirac's constant

H

Engineering: composite second moment of area (product of Ixx & Iyy)

H

Thermodynamics: enthalpy

I

Engineering: second moment of area (moment of inertia)

Engineering: rotational (moment of) inertia

I

Electrical: current

J

Engineering: polar moment of inertia

J

Thermodynamics: mechanical equivalent of heat

Thermodynamics: mechanical equivalent of heat

k

Engineering: spring constant

k

Hydrodynamics: wave number

K

Temperature: Kelvin

K

Engineering: bulk modulus

Kc

Engineering: Keulegan-Carpenter number

Engineering: part length

L

Electrical: inductance

L

Engineering: total length

Lon & Lat

Survey: longitude and latitude

m

Engineering: mass

mₑ

Physics: mass energy

mᵣ

Physics: rest-mass

ḿ

Engineering: slope

Whilst 'm' means slope in maths (e.g. y=mx+C), engineering has no standard symbol for 'slope'
CalQlata has adopted this symbol for a slope in engineering but differentiated it from the symbol for mass (m) by giving it an accent (a slope!)
(ḿ = height ÷ distance)

mn

Time: minute

M

Fluids: Mach number (fluid flow)

M

Engineering: moment

MBR

Engineering: minimum bend radius

MMC+

Engineering: maximum metal condition

MMC-

Engineering: minimum metal condition

n

number

p

Engineering: pressure

p

Hydrodynamics: period

p

Electrical: power

p

Work & Energy: Power

pdl

Engineering: poundal

pf

Electrical: power factor

pₒ

Work & Energy: Power (if used alongside pressure)

P

Engineering: pitch

PC

Fluids: pressure coefficient

Q

Fluids: quantity flow rate e.g.:
Q = volumetric flow rate (e.g. m³/s)
Q̊ = mass flow rate (e.g. kg/s)
= molecular flow rate (moles/s)

Q

Electrical: charge

Q

Thermodynamics: heat energy

r

radius / inside radius

ɍ

radius of gyration

R

Temperature: Rankine

R

outside radius

R

Electrical: resistance

R

Thermodynamics: gas constant (ideal gas)

Rₐ

Thermodynamics: specific gas constant (ideal gas)

Rᵢ

Thermodynamics: universal gas constant (ideal gas)

Rᴺᵒ

Fluids: Reynold's number

RPS

revolutions per second

RPM

revolutions per minute

Rv

Fluids: velocity ratio

s

Thermodynamics: specific entropy

s

Stress: primary stress

s

Time: second

S

Thermodynamics: entropy

S

Stress: principal stress

Stress: maximum principal stress

Stress: minimum principal stress

Stress: most damaging principal stress

S

Fluids: Strouhal number

SG

specific gravity (relative density)

t

time

t

Engineering: thickness
Note: when 't' is used for time in the same calculation, 'th' shall be used for thickness

T

Engineering: torque

temperature

u

initial velocity

U

Engineering: energy

U

Stress: utilisation

U

Thermodynamics: internal energy

Uᴷ

Thermodynamics: kinetic energy

Uᴾ

Thermodynamics: potential energy

v

Hydrodynamics & Engineering: velocity

see also Derivative Symbolism at the bottom of this page

v

Thermodynamics: specific volume

V

volume

V

vector

V

Electrical: voltage

w

Engineering: distributed load (per unit length)

W

General: width

W

Engineering: weight

W

Fluids: Weber number

W

Thermodynamics: work

x

distance (horizontal)

X

Electrical: reactance

y

Maths & Engineering: distance (vertical)

y

Engineering: distance from neutral axis

y

Engineering: deformation or deflection (static)

z

Hydrodynamics: distance (vertical)

Z

Fluids: head

Z

Electrical: impedance

Z

Engineering: section modulus

Ø

Diameter

α

Engineering: linear expansivity

α'

Engineering: square (area) expansivity

α"

Engineering: cubic (volumetric) expansivity

αᴿ

Electrical: temperature coefficient of electrical resistivity

α

angle (degrees)

β

angle (degrees)

γ

specific weight

γ

Thermodynamics: ratio of specific heats

ε

Engineering: efficiency

ε

Maths: error

ζ

Engineering: stability parameter

ζ

Dynamics: viscous damping factor (damping ratio)

η

Hydrodynamics: profile

η

Stress: damage ratio

θ

angle (degrees)

κ

Electrical: conductivity

λ

Engineering: thermal conductivity

λ

Physics: wave length

μ (or ƒ)

Engineering: friction coefficient
Note: ƒ is used where formulas also include dynamic viscosity

μ

Fluids: dynamic viscosity
Note: also known as absolute viscosity

ν

Fluids: kinematic viscosity

ν

Stress: Poisson's ratio

ρ

Materials: density

ρᴹ

Chemical: molecular density

ρᴿ

Electrical: resistivity

ϵ

Engineering: surface roughness

σ

Fluids: surface tension

σ

Stress: equivalent and general stress

τ

Stress: shear stress

φ

angle (degrees)

φ

Engineering: phase angle

ω

angular frequency

Datum:

e.g. Ṯᴰ

A datum value is defined by a superscript capital 'D'. The example shown here is for temperature.

Prefixes:

 

δ

variation or range

y

yocto (1E-24)

z

zepto (1E-21)

ɑ

atto (1E-18)

f

femto (1E-15)

p

pico (1E-12)

n

nano (1E-09)

μ

micro (1E-06)

m

milli (0.001)

c

centi (0.01)

d

deci (0.1)

da

deka (10)

h

hecto (100)

k

kilo (1000)

M

mega (1E+06)

G

giga (1E+09)

T

tera (1E+12)

P

peta (1E+15)

E

exa (1E+18)

Z

zetta (1E+21)

Y

yotta (1E+24)

Suffixes:

 

Fluids: in

Fluids: out

to

Engineering: sequencing

a

Engineering: anchor

ᵅᵛᵉ or

average

note a bar above a letter (e.g. v̅) is sometimes used as an abbreviation for average in the calculators

a

Hydrodynamics: added mass

A, B, etc.

Engineering: end or position

Maths: angle in radians

Stress: equivalent

Engineering: fluid

h

Stress: hoop

h

Engineering: horizontal direction

Engineering: internal

Stress: index

l

Stress: longitudinal

or min

minimum

A 'ʌ' above any letter indicates a minimum value

or max

maximum

A 'v' above any letter indicates a maximum value

mm

Engineering: … about weak/strong axis

n

Stress: nominal

nn

Engineering: … about strong/weak axis

ᴺᵒ

Number (as in Reynolds, Euler, Mach, etc.)

Engineering: outside / external

o

Stress: total

%

Engineering: packing

p

Stress: primary

P

Stress: principal

r

Stress: radial

t

Engineering: terminal

total

u

Stress: ultimate tensile stress

v

Engineering: vertical direction

w

Engineering: wall

x, y, z, etc.

Engineering: horizontal, vertical, etc. position or direction

xx, yy, zz, etc.

Engineering: … (about) fundamental axes (xx, yy, etc.)

xy, xz, etc.

Engineering: … (about) compound axes (xy, xz, etc.)

Stress: minimum yield

Derivative Symolism

Hydrodynamics & Engineering: velocity and acceleration

In addition to the conventional symbols used for velocity ('v') and acceleration ('a'), CalQlata occasionally adopt the following mathematical symbols where improved recognition is assumed for groupings ('x' is provided as an example character, any character is equally valid):

velocity = ẋ
(i.e. the first derivative of displacement x)

acceleration = ẍ
(i.e. the second derivative of displacement x)

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