Units For Measuring Angle

SI Unit for measuring angle – radian

Raidan is the angle subtended at the centre of a circle by an arc along a circumference whose length is equal to that of radius of circle.

In the below picture of a circle, angle AOB will be one radian if length of AB = radius of circle OA/OB

Circle having arc AB

Fact
Number of radians in the circle is equal to 2 \pi r / r or 2 \pi

radian is the official SI unit of angle. There are other non SI units for measuring angle which are widely used in mathematics books. Let’s now discuss what are those other non SI Units for measuring angle.

Non SI Units for measuring angle

Angle can also be measured in terms of degrees(°), minutes(), seconds(). The basic principle behind these units is that 1° is equal to 60′ and 1′ equals to 60”, this means that 1 degree have 60 minutes and 1 minute have 60 seconds.

A circle can have an angle of 360° (full rotation angle) and angle for full rotation of circle is 2π radian. Thus using simple maths it can be found how many radians there in one degree?

1^{\circ}=\left(\frac{2 \pi}{360}\right)=0.017453292520 \mathrm{rad}

Similarly it can be found how many radians are there in one minute and one second.

1^{\prime}=\left(\frac{2 \pi}{60 \times 360}\right)=0.000290888209 \mathrm{rad}

1^{\prime \prime}=\left(\frac{2 \pi}{60 \times 60 \times 360}\right)=0.000004848137 \mathrm{rad}

So 1 degree = 0.017453292510 radians, 1 minute = 0.000290888209 radians, 1 second = 0.000004848137 radians


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