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Degrees on A Clock Calculator

Reviewed by Calculator Editorial Team

This degrees on a clock calculator helps you determine the angle between the hour and minute hands at any given time. Whether you're solving a math puzzle or just curious about clock mechanics, this tool provides an accurate calculation.

How to Use This Calculator

Using the degrees on a clock calculator is simple:

  1. Enter the hour (1-12)
  2. Enter the minutes (0-59)
  3. Click "Calculate" to see the angle between the hour and minute hands
  4. View the result and optional clock visualization

The calculator will show you the smallest angle between the two hands, which is always between 0° and 180°.

Formula Explained

The angle θ between the hour and minute hands can be calculated using this formula:

θ = |30H - 5.5M|

Where:

  • H = hour (1-12)
  • M = minutes (0-59)

If the calculated angle is greater than 180°, subtract 360° to get the smallest angle.

The formula accounts for:

  • The hour hand moves 30° per hour (360°/12 hours)
  • The minute hand moves 360° per hour (6° per minute)
  • The hour hand also moves 0.5° per minute (30° per hour ÷ 60 minutes)

Worked Examples

Example 1: 3:00

At 3:00, the hour hand is at 90° and the minute hand is at 0°. The angle is:

θ = |30×3 - 5.5×0| = |90 - 0| = 90°

Example 2: 6:30

At 6:30, the hour hand is at 180° + (0.5×30) = 195°, and the minute hand is at 180°. The angle is:

θ = |195 - 180| = 15°

Example 3: 12:00

At 12:00, both hands are at 0°. The angle is:

θ = |30×12 - 5.5×0| = |360 - 0| = 360°

Since 360° is a full circle, the actual angle is 0°.

Frequently Asked Questions

What is the maximum angle between clock hands?

The maximum angle between clock hands is 180°. This occurs at times like 6:00 when the hands are directly opposite each other.

Can the angle be greater than 180°?

No, the calculator always shows the smallest angle between the two hands, which is never greater than 180°.

How does the hour hand move?

The hour hand moves 30° per hour (360°/12 hours) and 0.5° per minute (30° per hour ÷ 60 minutes).

Is there a time when the hands overlap?

Yes, the hands overlap 11 times every 12 hours (about every 1 hour and 5 minutes).