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Clock Angle Calculator

Find the angle between a clock's hour and minute hands at any time, using the standard hands-position formula.

Angle between hands
7.5°
Reflex angle (other way around)
352.5°
Hour hand position
97.5° from 12
Minute hand position
90° from 12

How it works

The minute hand sweeps the full 360° face in 60 minutes, so it sits at 6° × minutes from the 12. The hour hand sweeps 360° in 12 hours (30° per hour) but also creeps forward as minutes pass — 0.5° per minute — so it sits at 30° × (hour mod 12) + 0.5° × minutes.

The angle between the hands is the absolute difference of those two positions. If that raw difference is more than 180°, the shorter way around the clock face is 360° minus it — a clock's two hands always form two angles that add up to 360°, and this calculator reports both: the smaller one and its reflex.

Entering an hour of 13-23 is treated the same as the matching hour on a 12-hour face (e.g. 15 behaves like 3), since a clock's hands don't distinguish AM from PM.

FAQ

Why isn't the hour hand angle just 30° × hour?

Because the hour hand moves continuously, not in discrete jumps on the hour. At 3:30, for example, it's already halfway between the 3 and the 4 — at 30° × 3 + 0.5° × 30 = 105°, not sitting exactly on 90°. Ignoring the minute drift is a common source of error in clock-angle problems.

When are the hands exactly overlapping or exactly opposite?

The hands overlap (0°) eleven times every 12 hours — not exactly on the hour, except at 12:00, since the hour hand keeps drifting forward. They're exactly opposite (180°) eleven times every 12 hours too, for the same reason.

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