Clock Angle Problem Calculator
Find the angle between the hour and minute hands at any time, or the time when the hands overlap, form a straight line, or make a right angle.
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Input
Enter a time to find the angle between the hands, or pick a base hour and condition to find when the hands overlap, align, or form a right angle.
h
min
sec
Result
Angle between the hands
90deg
Minute hand angle
0 deg
Hour hand angle
90 deg
Reflex angle
270 deg
Calculation steps
1
The minute hand angle for 0 min 0 sec is 0 deg.
2
The hour hand angle at 3 h 0 min is 90 deg.
3
Reducing the difference between 0 deg and 90 deg to 0 to 180, the angle is 90 deg.
How it works
- The minute hand moves 6 degrees per minute and the hour hand moves 0.5 degrees per minute. The 12 position is taken as 0 degrees (straight up).
- The minute hand angle comes from the minutes and seconds, the hour hand angle from the hours, minutes and seconds. The angle between them is their difference reduced to a value from 0 to 180 degrees.
- To find when the hands overlap, align, or form a right angle, we use that the minute hand gains 5.5 degrees per minute on the hour hand, then compute the elapsed minutes to reach the target gap.
- Results follow exact formulas and fractional parts are shown as decimals. Use this as a study and checking aid.
Frequently asked questions
- How is the angle between the hands calculated?
- The minute hand moves 6 degrees per minute and the hour hand 0.5 degrees per minute, with 12 o'clock as 0 degrees (straight up). The angle of each hand is computed for the given time, and the difference is folded into the 0-to-180-degree range.
- How does it find when the hands overlap, align, or make a right angle?
- The minute hand gains on the hour hand by 5.5 degrees every minute. Using that rate, the tool finds the minutes needed to reach the target separation โ 0 degrees to overlap, 180 for a straight line, or 90 for a right angle.
- Why do the results show decimals?
- The values come from exact formulas, so times and angles that do not divide evenly are shown as decimals. Use them as a reference for study and for checking your own answers.
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