Clock Angle Calculator

Math

Calculate the angle between the hour and minute hands of a clock at any given time.

Formula

Hour angle = (hours × 60 + minutes) × 0.5°; Minute angle = minutes × 6°
  • Hour hand moves 0.5° per minute (360° ÷ 720 minutes for full rotation).
  • Minute hand moves 6° per minute (360° ÷ 60 minutes).
  • The smaller angle between the hands is reported (≤ 180°).

3:30

Inputs
  • Hours: 3
  • Minutes: 30

Hour hand at 3:30 = (3×60+30)×0.5 = 105°. Minute hand = 30×6 = 180°. Angle = |105-180| = 75°.

Frequently asked questions

At what time are the hands exactly aligned?
Approximately every 65.45 minutes (not every 60 minutes), at 12:00, 1:05.45, 2:10.91, ...
What is the angle at 12:00?
0° — both hands point straight up.
What is the angle at 6:00?
180° — the hands point in opposite directions.
When are the hands perpendicular (90°)?
At approximately 3:00 and 9:00, and about 44 other times during the day.