Compare the Dimensions (Unit Conversion » Dimensional Analysis »)

Comparison Tool

First: (Units or Expression)
Second: (Units or Expression)


Result: (Consistency Report)

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

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Examples

First	Second	Result
foot	inch	consistent
83 deg-F	hour	inconsistent
(360 * 160) ft^2	17 acres	consistent
70.4 kg + 115 lb	(3.2 + 7) oz	consistent
(20ft + 2in) * (15ft - 8in)	100yd	inconsistent
-16.2 + sqrt(16.2^2 - 4 * 3.1 * 0.7)	sqrt(67.2)/17	consistent
(1/4) mile / 4.751 seconds	0.3 seconds / mile	inconsistent
pi (4.7 cm)^2 sin(41 deg)	gallon / foot	consistent
3 volts/meter	(40 watts + 1 hp)/(ampere meter)	consistent
(2000 V/m) * 35 cm * 2 elementary-charges	joule/steradian	consistent

The results indicate whether or not the expressions have consistent units, i.e., their dimensions match. Note that this tool treats expressions as consistent even if they differ in the plane-angle or solid-angle dimensions. This is because the plane-angle and solid-angle dimensions are not official metric (SI) dimensions and could be dropped. However, they are still reported for clarity.

"First" and "Second" Entries

Enter the units or the mathematical expressions with units that you want to compare. These can be as simple as unit names or as complex as formulas 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 the expressions as you would normally write them.

As part of the results, the interpretations of your expressions are shown in order to verify that they match 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 comparison.

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