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Essential Math

Unit Conversions and Useful Constants

This page contains several useful conversion factors and constants.  In addition, at the end of this page is a short tutorial on how to perform unit conversions.

Conversion Factors

Distance

1 kilometer (km) = 0.6214 miles

1 Astronomical Unit (AU) = 149.6 X 106 km

1 light year (ly) = 9.461 X 1012 km

1 parsec (pc) = 3.262 ly

Angles

360° = 2pi radians

Temperature

K = °C + 273

°C = 0.555 X (°F - 32)

 °F = (1.8 X °C) + 32

Useful Constants

Speed of Light 3 X 108 m/s
Hubble Constant (best current estimate) 70 km/s per megaparsec

Unit Conversions Tutorial

Unit conversions are easiest, I think, when considered from the point of view of dimensional analysis.  A few examples should serve to make this clear.

Example 1:  Your friend's house is 4 miles away.  How many kilometers is that?

Start with the 4 miles, then choose from the conversion factors above and express them in a ratio so that the mile units cancel out leaving only the kilometer units.

Example 2:  The nearest star is 4.2 light years away.  How many miles is that?

The procedure is the same as above but this time there are two conversion factors.  Start with the 4.2 light years.  Use the light year to kilometer conversion factor to "cancel" the light years.  Then use the kilometer to miles conversion factor to "cancel" the kilometers.  Note that in example 1 we needed to cancel miles but in example 2 we need to cancel kilometers, so the conversion factor is "up-side-down".