Enter Time or Angle in Degrees


  

Calculate the angle between the hands of the clock

If the time is 9:20

Break out time components

H = 9

M = 20

Calculate ∠ between 12 and 9

There are 360° in a full circle (clock)

There are 12 hours

Each hour = 360/12 = 30°

Hour Formula

Hours = 30(H)

Hours = 30(9)

θh = 270

Minute Formula

Each minute is 1/60 of an hour.
Each hour represents 30 degrees.

Minutes Angle = M(30)/60 → M/2:

θm  =  M
  2

θm  =  20
  2

θm = 10

Calculate ∠ between the clock: Δθ

Δθ = |θh + θm|

Δθ = |270 + 10|

Δθ = |280|

Hands in opposite direction:

Clockwise + counter-clockwise = 360°

Subtract our clockwise angle from 360°

Angle 2 = 360 - 280°

Final Answer


Δθ = 280°
Angle 2 = 80°


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What is the Answer?
Δθ = 280°
Angle 2 = 80°
How does the Clock Angle Calculator work?
Free Clock Angle Calculator - Calculate the angle on a clock between the hour and minute hands or how many times on the clock form an angle of (x°) between the minute and hour hand (backwards and forwards). Clock Angle Calculator
This calculator has 1 input.

What 3 formulas are used for the Clock Angle Calculator?

θh = ½(60H + M)
θm = 6M
Δθ = |θh - θm|

For more math formulas, check out our Formula Dossier

What 5 concepts are covered in the Clock Angle Calculator?

angle
the figure formed by two rays, called the sides of the angle, sharing a common endpoint, called the vertex of the angle.
clock angle
degree
A unit of angle measurement, or a unit of temperature measurement
hour
Unit of time equal to 60 minutes
minute
Unit of time equal to 60 seconds
Example calculations for the Clock Angle Calculator
Clock Angle Calculator Video

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