Math

Clock Angle Calculator (Angle Between the Hands)

Enter the hour and minutes.

Your numbers

Your results

Smaller angle (degrees)
Smaller angle (degrees)
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Larger angle (degrees)
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Hour hand position (degrees from 12)
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Minute hand position (degrees from 12)
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Next overlap (minutes after the hour)
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Clock Angle Calculator (Angle Between the Hands) by TheCalcTools

How the Clock Angle Calculator (Angle Between the Hands) works

The minute hand moves 6° a minute. The hour hand moves 30° an hour, plus 0.5° a minute. The angle between them is |30H − 5.5M|; if it is over 180°, the smaller angle is 360° minus it.

The hands overlap 11 times in 12 hours, every 65 5/11 minutes.

The formula

θ = |30H − 5.5M|

Worked example

Using the default values shown in the calculator:

Hour (1 to 12)3
Minutes40
  1. At 3:40 the hands are 130.00° apart.

Result:

Smaller angle (degrees)130.00
Larger angle (degrees)230.00
Hour hand position (degrees from 12)110.00
Minute hand position (degrees from 12)240.00
Next overlap (minutes after the hour)16.36

Frequently asked questions

What is the angle at 3:40?

|90 − 220| = 130°.

Sources and further reading

More in Math · All calculators

This calculator gives estimates for information only. Check important results independently before you rely on them. See our disclaimer.