Dimensional analysis

Dimensional analysis allows you to verify that your calculations are dimensionally correct. The following paragraphs explain how to switch on dimensional analysis, and detail the dimensions of variables that can be used with mathematical operators or functions.

Switch on dimensional analysis (the Tedds Application)

On the Home tab, click Options.

The Options - Default dialog appears.
In the side pane, click Calculating.
Select the Perform dimensional checks option.

Switch on dimensional analysis (Tedds for Word)

In the Tedds ribbon group, click More > Tedds Options.

The Options - Default dialog appears.
In the side pane, click Calculating.
Select the Perform dimensional checks option.

Operators

Tip:

For Tedds for Word users:

You can access most of the operators in the Library Access System. Go to Writing your own custom calculations > Calculation writing documentation > Math symbols.


Dimensional analysis operators
Function	Input dimensions	Result dimensions	Example
x + y = z x - y = z	x and y must have identical dimensions	z has the same dimensions as x and y	(1m) + (1m) = 2m
x × y = z x ÷ y = z	x and y may have any dimensions	Dimensions of z result from those of x and y being multiplied and divided according to × or ÷ function	(1m) * (1m) = 1m²
(((...)))	Any	No change to dimensions	None
y^x = Z 10^x	x has to be dimensionless, y may have any dimension	z's dimension exponent is y's dimension altered by exponent x	(1m)⁵ = 1m⁵

Functions

Tip:

For Tedds for Word users:

You can access most of the operators in the Library Access System. Go to Writing your own custom calculations > Calculation writing documentation > Maths functions.


General dimensional analysis functions
Function	Input dimensions	Result dimensions	Example
sqrt(x) = z	x may have any dimension	z's dimension exponent is x's halved	sqrt((1 m)) = 1 m^0.5
abs(x) = z int(x) = z int(x,"unit") = z round(x,y) = z round(x,y,"units") = z mod(x, y) = z quotient(x,y) = z	x may have any dimension, y has to be dimensionless	z has the same dimension as x	abs((-1 m)) = 1 m
sum(x,y,z,…) = z max(x,y,z,…) = z min(x,y,z,…) = z average(x,y,z,…) = z median(x,y,z,…) = z	All items being considered in the list (x,y,…) must have identical dimensions	z has the same dimensions as x and y	sum((1 m),(1 m)) = 2 m
rand() = z	None	z is dimensionless	None


Logarithmic and exponential dimensional analysis functions
Function	Input dimensions	Result dimensions	Example
ln(x) = z log(x) = z exp(x) = z	x has to be dimensionless	z is dimensionless	None


Trigonometric dimensional analysis functions
Function	Input dimensions	Result dimensions	Example
degrees(x,y,z) = a	x, y and z have to be dimensionless. x can be in degrees or radians because those units are dimensionless.	a is dimensionless, but may be in degrees or radians since they are dimensionless	degrees((1,30,0) = 1.5 °
sin(x) = z cos(x) = z tan(x) = z cosec(x) = z sec(x) = z cot(x) = z	x has to be dimensionless because degrees and radians are dimensionless	z is dimensionless	sin (90 °) = 1
asin(x) = z acos(x) = z atan(x) = z	x has to be dimensionless	z is dimensionless - but may be in degrees or radians since they are dimensionless	asin (1) = 90 °


Hyperbolic dimensional analysis functions
Function	Input dimensions	Result dimensions	Example
sinh(x) = z cosh(x) = z tanh(x) = z asinh(x) = z acosh(x) = z atanh(x) = z	x has to be dimensionless	z is dimensionless	None


Logical dimensional analysis functions
Function	Input dimensions	Result dimensions	Example
if(condition,x,y) and(x,y,z,...) (x && y) or (x,y,z,...) (x \|\| y) x > y x >= y, x ≥ y x == y x <> y, x ≠ y x <= y, x ≤ y x < y	All logical comparisons must be between values with identical dimensions	No change to dimensions, true and false are dimensionless	None