# Compare the Dimensions

## Examples

### 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

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.

ft

foot

m

meter

millisecond

0.001 seconds

kilometer

1000 meters

4.2 * 10^-3

0.0042

4.2e-3

0.0042

2 * 10^3

2000

2e3

2000

4^2

16

mile^2

mile mile

second^-1

1 / second

sqrt(4 m^2)

2 meters

sqrt(-37)

(not supported)

cos(pi/3)

0.5

0.5

cos(60 deg)

0.5

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