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Monday, July 29, 2019

New: Units Calculator

Units Calculator is a Web interface to the GNU Units utility which allows conversion among thousands of physical units, constants, and currencies. Units Calculator may be used to perform complex scientific and engineering calculations involving physical units and guards against common errors due to dimensional incompatibility. Units Calculator is 100% compatible with GNU Units, but as a Web application can be used from any platform with a Web browser. Currency exchange rates and precious metal prices are updated daily. See the Introduction for a tutorial, or proceed directly to the Expert page, which contains a click-to-copy table of common units.

Units Calculator can be used as a simple units conversion tool, but is much more powerful than that. Suppose you wish to calculate the power emitted as gravitational radiation as the Earth orbits the Sun. This is given by the following equation, where G is the Newtonian gravitational constant, c is the speed of light, R is the radius of the orbit (which we'll assume here to be circular), and m₁ and m₂ are the masses of the two bodies. (You don't often see an equation in physics with an exponent greater than three, but this one has two fives and a four, and that's the fifth power of the speed of light in the denominator!)

{\frac{dE}{dt}}= - {{32 G^4}\over{5c^5R^5}} (m_1 m_2)^2(m_1+m_2)

Since Units Calculator already “knows” all of the quantities which figure in this equation, we can immediately calculate as follows.

Convert ((32 G^4)/(5 c^5 astronomicalunit^5)) ((sunmass earthmass)^2) (sunmass + earthmass)
To watt
((32 G^4)/(5 c^5 astronomicalunit^5)) ((sunmass earthmass)^2) (sunmass + earthmass) = 196.27068 watt

So, around 200 watts!

Units Calculator supports, as of this writing, 3460 linear units, 109 nonlinear units, and 109 prefixes, plus 171 currencies and 3 precious metal (gold, silver, and platinum) prices. See the Unit Definition database (taken directly from the GNU Units utility) for a complete list.

Posted at 13:50 Permalink