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Get the Dimensions
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 | |||
