Compare the Dimensions

First:

( Units or Expression )

Second:

( Units or Expression )

Result:

( Consistency Report )

 

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Help Information

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)

100 yd

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

This calculator determines if the "First" and "Second" entries have consistent units, i.e., have matching dimensions. Note that the entries are treated 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.

The "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.

Expression Features

Feature

Example

Interpretation

Abbreviations are supported (see the name index).

ft

foot

m

meter

Standard metric power prefixes are supported.

millisecond

0.001 seconds

kilometer

1000 meters

Scientific notation is supported

4.2 * 10^-3

0.0042

4.2e-3

0.0042

2 * 10^3

2000

2e3

2000

"^" is the power operator.

4^2

16

mile^2

mile mile

second^-1

1 / second

sqrt is the square root function.

sqrt(4 m^2)

2 meters

sqrt(-37)

(not supported)

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 such as deg with function arguments.

cos(pi/3)

0.5

cos((pi/3) rad)

0.5

cos(60 deg)

0.5

sin(100 grad)

1.0

tan(800 mil)

1.0

"*" 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 (which is common with written expressions).

(4 * 5) grams

20 grams

3 newtons * 2 meters

6 newton meters

5ft 45lbf

225 foot pounds-force

6ft 4in

6 feet + 4 inches

2hr 37min

2 hours + 37 minutes

Modifiers square, sq, squared, cubic, cu, cubed, and reciprocal have their normal meaning.

square meter

meter^2

sq yard

yard^2

second squared

second^2

cubic inch

inch^3

cu yd

yard^3

cm cubed

centimeter^3

reciprocal second

1 / second

In general, a "-" connecting names is treated the same as a space. If you need a subtraction operator or negative sign involving just unit names, put at least one space around the "-".

kilogram-meter/second^2

kilogram meter/second^2

kg - lb

(subtraction)

cubic-yard

yard^3

cubic -yard

(-yard)^3

Sometimes a "-" is used to distinguish a unit name from an expression with the same words.

kilogram-calorie

the unit kilocalorie

kilogram calorie

a mass times an energy