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 |
|---|---|
| Minutes | 40 |
- 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
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This calculator gives estimates for information only. Check important results independently before you rely on them. See our disclaimer.