Clock Angle Calculator — Angle Between Clock Hands
Calculate the exact angle between the hour and minute hands of an analogue clock at any given time — with a live clock face showing the result.
Smaller angle between the hour and minute hands
- 1
Hour hand position
(3 × 30) + (0 × 0.5) = 90 - 2
Minute hand position
0 × 6 = 0 - 3
Raw difference
|90 − 0| = 90 - 4
Smaller angle
90
How does this calculator work?
The hour hand moves 0.5° per minute (30° per hour) and the minute hand moves 6° per minute. The angle between them = |(H × 30 + M × 0.5) − (M × 6)|, reduced to at most 180°. Enter the hour and minute to get both the smaller angle and the reflex angle.
Formula
How this is calculated
An analogue clock face is a full circle of 360°. The minute hand completes one revolution every 60 minutes, so it sweeps 360 ÷ 60 = 6° per minute. The hour hand completes one revolution every 12 hours (720 minutes), so it moves 360 ÷ 720 = 0.5° per minute — or 30° per hour. Neither hand snaps to tick marks; both move continuously.
To find the angle at H hours and M minutes, compute each hand's position in degrees measured clockwise from the 12 o'clock mark: hour hand = (H mod 12) × 30 + M × 0.5, minute hand = M × 6. Subtract one from the other and take the absolute value. If this raw difference exceeds 180°, subtract it from 360° to obtain the smaller of the two angles formed. The reflex angle is 360° minus the smaller angle.
For example, at 3:00 the hour hand is at 90° (3 × 30) and the minute hand is at 0° (0 × 6), giving |90 − 0| = 90°. At 3:30 the hour hand has moved to 3 × 30 + 30 × 0.5 = 105°, and the minute hand is at 30 × 6 = 180°, giving |105 − 180| = 75°.
Frequently asked questions
The minute hand gains 5.5° per minute on the hour hand. Starting from an overlap, 90° ÷ 5.5 ≈ 16.36 minutes later the hands are 90° apart, and another 16.36 minutes after that they are 90° apart again on the other side. This repeats 44 times per 24 hours.
The hands coincide approximately every 65.45 minutes (= 720 ÷ 11). They overlap at 12:00:00, then again at about 1:05:27, 2:10:55, 3:16:22 … — 22 times in 24 hours.
The reflex angle is the larger of the two angles formed by the two hands. It is always 360° minus the smaller angle. If the smaller angle is 60°, the reflex angle is 300°.
TG we-Calculate Editorial Team. (2026). Clock Angle Calculator — Angle Between Clock Hands [Online calculator]. TG we-Calculate. https://we-calculate.com/calculator/clock-angle-calculator
TG we-Calculate Editorial Team. "Clock Angle Calculator — Angle Between Clock Hands." TG we-Calculate. 2026. https://we-calculate.com/calculator/clock-angle-calculator.
TG we-Calculate Editorial Team, "Clock Angle Calculator — Angle Between Clock Hands," TG we-Calculate, 2026. [Online]. Available: https://we-calculate.com/calculator/clock-angle-calculator
@misc{wecalculate_clock_angle_calculator, title = {Clock Angle Calculator — Angle Between Clock Hands}, author = {{TG we-Calculate Editorial Team}}, howpublished = {\url{https://we-calculate.com/calculator/clock-angle-calculator}}, year = {2026}, note = {TG we-Calculate} }
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