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Compare the Dimensions
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 | |||
