# Clock Formulas

## Formula and Basic Concepts of Clock

A Clock a circle having 360 degrees . It is divided into 12 equal parts numbered from 1 to 12 .Each part is 360/12 = 30°.  When the minute hand takes a complete round i.e covers 360° known as one hour. A Clock has two hands that is the hour hand and the minute hand. Both hands move around the circular dial. The hour hand is smaller than the minute hand and the hour hand is slower than the minute hand.  shows time in hours and the minute hand shows time in minutes. On this page we’ll look for some of the basic Formulas for Clocks.

A) Angle between hands of a clock

1. When minute hand is behind the hour hand, the angle between the two hands at M minutes past H o’clock.

= 30 [H -(M/5)] + M/2 degree

= 30H – (11M/2)

2. In the case where the minute hand is ahead of the hour hand, the angle between the two hands at M minutes past H ‘o clock will be calculated as

= 30 (M/5-H ) -M/2  degree

= 11/2M – 30H

B) To calculate x minute space gain by the minute hand over the hour hand,

= x$\frac{60}{55}$

= x$\frac{12}{11}$

C) Both the two hands of the clock will be at the right angles between H and (H+1) o’clock at (5H ± 15)  minutes H<’o clock.

D) If the minute hand of a clock overtakes the hour hand at the interval of M minutes when the time is correct, the clock gains or loses a day by

=$\frac{720}{11} – M [(60×24)/M] minutes$

E) Between H and H+1 o’clock, the two hands of the clock are M minutes apart at (5H ± M)12/11  minutes past H o’ clock.

### Clocks Formulas & Properties

• The dial of the clock is circular in shape and is divided into 60 equal minute spaces.
•  60-minute spaces traces an angle of 3600. Therefore, one minute space traverses an angle of 60.
• The hands of a clock are perpendicular when they are 15-minute space apart.
• Hands of a clock are in straight line and are opposite to one another when they are 30 minutes space apart.
• Hands of a clock are perpendicular to each other 22 times in 12 hours and 44 times in 24 hours.
• Hands of the clock are opposite to each other for 11 times in 12 hours and 22 times in a day.
• The minute hand gains 55 minutes over hour hand every hour.

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