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.

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.

Hour

Minute

min

Second

sec

Angle between the hands

90deg

Minute hand angle

0 deg

Hour hand angle

90 deg

Reflex angle

270 deg

Calculation steps

The minute hand angle for 0 min 0 sec is 0 deg.

The hour hand angle at 3 h 0 min is 90 deg.

Reducing the difference between 0 deg and 90 deg to 0 to 180, the angle is 90 deg.

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.

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