Clock Angle Calculator

Publish date: 2024-06-10

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Calculate the angle between the hands of the clock

If the time is 5:28

Break out time components

H = 5

M = 28

Calculate ∠ between 12 and 5

There are 360° in a full circle (clock)

There are 12 hours

Each hour = 360/12 = 30°

Hour Formula

Hours = 30(H)

Hours = 30(5)

θh = 150

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 =	28
	2

θm = 14

Calculate ∠ between the clock: Δθ

Δθ = |θh + θm|

Δθ = |150 + 14|

Δθ = |164|

Hands in opposite direction:

Clockwise + counter-clockwise = 360°

Subtract our clockwise angle from 360°

Angle 2 = 360 - 164°

Final Answer

Δθ = 164°
Angle 2 = 196°

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What is the Answer?

Δθ = 164°
Angle 2 = 196°

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?

anglethe figure formed by two rays, called the sides of the angle, sharing a common endpoint, called the vertex of the angle. clock angledegreeA unit of angle measurement, or a unit of temperature measurementhourUnit of time equal to 60 minutesminuteUnit of time equal to 60 seconds

Example calculations for the Clock Angle Calculator