Get the Dimensions (Unit Conversion » Dimensional Analysis »)

Dimension Tool

From: (Units or Expression)


Result: (Metric Dimensions)

Library of Units and Constants:	Name Index	Quantity Index	Group Index

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Examples

From	Result
foot	length
83 deg-F	temperature
(6 * 18) mile^2	length^2
70.4 kg + 115 lb	mass
(20ft + 2in) * (15ft - 8in)	length^2
-16.2 + sqrt(16.2^2 - 4 * 3.1 * 0.7)	[dimensionless]
(5 qt + 2 gal)/ 4.751 seconds	length^3 × time^-1
pi (4.7 cm)^2 sin(41 deg)	length^2
50 meters * 25 meters * 10 ft	length^3
(2000 V/m) * 35 cm * 2 elementary-charges	length^2 × mass × time^-2

The results are based on the modern metric system called the International System of Units (or SI units). The metric (SI) dimensions are length (meter), mass (kilogram), time (second), temperature (kelvin), electric-current (ampere), amount-of-substance (mole), and luminous-intensity (candela). Although they are not official metric (SI) dimensions, this tool also reports the plane-angle (radian) and solid-angle (steradian) dimensions for clarity.

"From" Entry

Enter the units or the mathematical expression with units for which you want to get the dimensions. This can be as simple as a unit name or as complex as a formula involving additions, subtractions, multiplications, divisions, powers, square roots, and scientific functions (sin, cos, tan, arcsin, arccos, arctan, sinh, cosh, tanh, log, ln, and exp). The expression entry is very flexible; try typing an expression as you would normally write it.

As part of the results, the interpretation of your expression is shown in order to verify that it matches what you intended. Wherever you see a unit or constant in the results, click on it to read a description of it. This helps verify that the correct unit or constant was used in the calculation.

Below are some important expression features:

Expression Features	Examples	Meaning of Examples
Common abbreviations are allowed (see the Name Index)	ft m	foot meter
Standard metric power prefixes are allowed	millisecond kilometer	0.001 seconds 1000 meters
Scientific notation is allowed	4.2e-3 2e3	0.0042 2000
"" or a space between expressions represents the multiply operator. However, if the expressions are simple* and have the same dimensions, a space is treated as an addition (as is common with written expressions).	(4 * 5) grams 3 newtons * 2 meters 5ft 45lbf 5ft 8in (5ft 8in)(4ft 3in) 2hr 37min 14s	20 grams 6 newton meters 225 foot pounds-force 5 feet + 8 inches (5 feet + 8 inches) * (4 feet + 3 inches) 2 hours + 37 minutes + 14 seconds
"^" represents the power operator	4^2 mile^2 second^-1	16 mile mile 1/second
"sqrt" represents the square root function	sqrt(4 m^2) sqrt(-37)	2 meters (error)
"sin", "cos", "tan", "arcsin", "arccos", "arctan", "sinh", "cosh", "tanh", "log", "ln", and "exp" represent their respective scientific functions. A trig function argument without units is considered to be in radians but you can also use units like "deg" with function arguments.	cos(pi/3) cos((pi/3) rad) cos(60 deg) sin(100 grad) tan(800 mil)	0.5 0.5 0.5 1.0 1.0
Modifiers "square", "sq", "squared", "cubic", "cu", "cubed", and "reciprocal" have their normal meaning	square meter sq yard seconds squared cubic inch cu yd cm cubed reciprocal seconds	meter^2 yard^2 seconds^2 inch^3 yd^3 cm^3 1/seconds
In general, a "-" connecting names is treated the same as a space. If you need a subtraction operator or negative sign, put at least one space around the "-".	kilogram-meter/second^2 kg - lb cubic-yard cubic -yard	kilogram meter/second^2 kg - lb (subtraction) yard^3 (-yard)^3
Sometimes a "-" is required to distinguish a unit name from an expression with the same words.	kilogram-calorie kilogram calorie	the unit "kilocalorie" a mass times an energy