Calculates the angle between a clock’s hour and minute hands at any given time.
How it works
The minute hand moves 6 degrees per minute while the hour hand moves 0.5 degrees per minute; the difference between their positions gives the angle, taking the smaller of the two possible angles around the clock face.
What this does not include
This does not include the second hand’s position — this calculator specifically finds the angle between the hour and minute hands.
How to use this calculator
- Enter the hour and minute.
A worked example
At 3:00, the angle between the hour and minute hands is 90°.
At 9:30, the angle is 105° — the hour hand has moved halfway toward 10 by the half-hour mark, not sitting exactly on 9.
At 12:00, both hands overlap: angle = 0°.
What the variables mean
| Variable | Meaning |
|---|---|
| Hour | The clock hour, 1 through 12 |
| Minute | Minutes past the hour, 0 through 59 |
Edge cases worth knowing
The hour hand moves continuously, not in jumps. At 9:30 it’s not pointing straight at 9 — it’s crept halfway toward 10, which is exactly why the 9:30 example gives 105° rather than a rounder-looking number.
The result is always the smaller of the two possible angles — between any two clock hands there are two angles (summing to 360°), and this calculator reports the one at or under 180°.
Frequently asked questions
Why does the hour hand move at all between hours?
The hour hand gradually moves toward the next hour as minutes pass, rather than jumping instantly — that’s why an accurate clock-angle calculation needs both the hour and the minute.
What’s the angle at exactly 12:00?
Zero degrees — both hands point in the exact same direction.
What’s the largest possible angle between the hands?
180 degrees, when the hands point in exactly opposite directions.
