Rule of thumb · MathematicsNº 98 / 102

The hour hand keeps moving

Angle = |30H − 5.5M|. At 3:30 that is 75°, not 90° — the hour hand has already drifted halfway to the 4.

Why it works

The hour hand covers 30° an hour, so it moves 0.5° for every minute that passes. Leaving it parked on the hour mark is the classic error. The same 5.5° per minute closing speed answers every clock-hand question, including why the hands overlap 11 times in 12 hours rather than 12.

Do it exactly

Estimate with the rule, then check it against the calculator that models it properly.

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What is the angle between clock hands at 3:30?

Angle = |30H − 5.5M|. At 3:30 that is 75°, not 90° — the hour hand has already drifted halfway to the 4. The hour hand covers 30° an hour, so it moves 0.5° for every minute that passes.

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