Clock Angle Calculator

Clock angle calculator helps you find the angle between the hour and minute hands of a clock. Find the angle between the hour and minute hands of a clock at any given time.

How to Calculate the Angle Between Clock Hands

Have you ever looked at an analog clock and wondered what the exact angle is between the hour hand and the minute hand? While it might seem like a simple geometry problem, the movement of the hands makes it a bit more interesting. This Clock Angle Calculator helps you find that angle instantly.

Understanding the Clock Face

A clock face is a circle, which consists of 360 degrees. It is divided into 12 hour sections and 60 minute marks.

  • Minute Hand: Moves 360 degrees in 60 minutes, which is 6 degrees per minute.
  • Hour Hand: Moves 360 degrees in 12 hours (720 minutes), which is 0.5 degrees per minute.

The Clock Angle Formula

To find the angle between the hands, we calculate the position of each hand from the 12:00 position (0 degrees) and find the absolute difference. The formula is:

Angle = |(30 × H) - (5.5 × M)|;

Where:

  • H is the Hour (1-12 or 0-23)
  • M is the Minute (0-59)

Note: If the result is greater than 180 degrees, subtract it from 360 degrees to get the smaller angle properly (the reflex angle is usually not the primary answer requested).

Example Calculation

Let's find the angle for 11:20.

  1. Hour Hand Position: 11 hours and 20 minutes.
    Angle = (11 × 30) + (20 × 0.5) = 330 + 10 = 340 degrees.
  2. Minute Hand Position: 20 minutes.
    Angle = 20 × 6 = 120 degrees.
  3. Difference: |340 - 120| = 220 degrees.
  4. Adjust for Smaller Angle: Since 220 > 180, we do 360 - 220 = 140 degrees.

So, the angle at 11:20 is 140°.

Why use this tool?

Calculating this manually can be tedious, especially remembering the 0.5 degrees per minute movement of the hour hand. Our tool does the math instantly for any time of day!