Clock Angle at 9:20

Enter Time on the Clock (3:45) or Angle in Degrees (85):


Calculate the angle between the hands of the clock if the time is 9:20

H = 9
M = 20

Calculate the Angle between 12 and the Hour hand 9:

Since there are 360 degrees in a full circle (clock), and there are 12 hours, each hour represents 360/12 = 30 degrees
So our formula is 30(H)
So our formula is 30(9)
θh = 270

Next, we know how each minute is 1/60 of an hour. Each hour represents 30 degrees. So our formula is M(30)/60 → M/2:
θm  =  M

θm  =  20

θm = 10

Calculate angle between the clock: Δθ

Δθ = |θh + θm|
Δθ = |270 + 10|
Δθ = |280|

Account for hands going in the opposite direction:

We would also consider the angle between the hands of the clock going counter-clockwise
Since the clockwise and counter-clockwise angle add up to 360°, we subtract our clockwise angle from 360°
Angle 2 = 360 - 280°
Δθ = 280°
Angle 2 = 80°

Δθ = 280°
Angle 2 = 80°

What is the Answer?

Δθ = 280°
Angle 2 = 80°

How does the Clock Angle Calculator work?

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?

  1. θh = ½(60H + M)
  2. θm = 6M
  3. Δθ = |θh - θm|

For more math formulas, check out our Formula Dossier

What 5 concepts are covered in the Clock Angle Calculator?

the figure formed by two rays, called the sides of the angle, sharing a common endpoint, called the vertex of the angle.
clock angle
A unit of angle measurement, or a unit of temperature measurement
Unit of time equal to 60 minutes
Unit of time equal to 60 seconds

What are some example calculations for the Clock Angle Calculator?

  1. Clock angle between 2:40
  2. Clock Time with angle of 84

Clock Angle Calculator Video


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