Mathematik Übungen

Converting degrees and minutes


Degrees and minutes

In a full circle there are 360 degrees. A degree is denoted by °, e.g. 360°.

Each degree is split up into 60 parts called minutes (of arc), each part being 1/60 of a degree. A minute is denoted by ', e.g. 1°= 60'.

Each minute is split up into 60 parts, each part being 1/60 of a minute called seconds (of arc). A second is denoted by '', e.g. 1°= 60×60 = 3600 seconds = 3600''.

Sometimes it is needed to convert the measure of the angle that is written as a decimal number into degrees and minutes, e.g 40.5 degrees. This is 40°+0.5×60' = 40° 30'


The circumference of a circle is 2πr. Based on this we set that 2π(rad) is equivalent to 360° and one π(rad) is equivalent to 180°. A radian is about $360/{2π}$ or 57.3 degrees.

Converting degrees to radians

$${α(°)×π}/{180°} = α(rad)$$
$$45°={45°×π}/180°=π/4 rad$$

Converting radians to degrees

$$απ(rad) =α× 180°$$
$$5/6 π rad = 5/6×180°=360°/3=150°$$
360°=2π270°=3π/2180°= π90°=π/2


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