Get the Dimensions

From:

( Units or Expression )

Result:

( Metric Dimensions )

 

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Help Information

Examples

From

Result

foot

length

83 deg-F

temperature

(6 * 18) mile^2

length2

70.4 kg + 115 lb

mass

(20ft + 2in) * (15ft - 8in)

length2

-16.2 + sqrt(16.2^2 - 4 * 3.1 * 0.7)

[dimensionless]

(5 qt + 2 gal)/ 4.751 seconds

length3 × time-1

pi (4.7 cm)^2 sin(41 deg)

length2

50 meters * 25 meters * 10 ft

length3

(2000 V/m) * 35 cm * 2 elementary-charges

length2 × mass × time-2

This calculator returns the dimensions of the "From" entry in the International System of Units (SI units) which is commonly called the metric system. 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 calculator also reports the plane-angle (radian) and solid-angle (steradian) dimensions for clarity.

The "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.

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