The hour hand moves between hour marks
An analog hour hand does not remain fixed on the numbered hour while minutes pass. This clock angle calculator includes 0.5° of hour-hand motion per minute and 1/120° per second. The minute hand advances 6° per minute plus 0.1° per second. Both positions use 12 o'clock as 0° and increase clockwise.
Choose 12-hour or 24-hour input, enter hour, minute, and optional seconds, then calculate. The smaller angle is in [0°, 180°]. This page defines the larger/reflex result as 360° minus the smaller result, so coincident hands display a 360° full turn. Directional results remain useful when both magnitudes are not interchangeable.
Calculate a fixed or live clock angle
- Select 12-hour input for hours 1–12 or 24-hour input for hours 0–23. Both normalize to the same 12-hour dial.
- Enter minutes and seconds from 0 up to but not including 60. Seconds are optional and default to zero.
- Select Calculate to commit a fixed result, then read the hand positions and subtraction steps next to the analog SVG.
- Use a preset for a known case, or explicitly start Live clock to use the current device time. Location and timezone are not requested.
- Stop live mode before editing a fixed example. Reduced-motion preferences prevent continuous hand transitions even when time updates.
Clock-hand formulas and direction definitions
- Normalize h modulo 12. The hour hand position is H = 30h + 0.5m + s/120 degrees clockwise from 12.
- The minute hand position is M = 6m + 0.1s. Seconds therefore affect both the minute hand and the continuously moving hour hand.
- Let D = |H − M|. The smaller angle is min(D, 360 − D), while this page's larger/reflex value is 360 − smaller.
- Clockwise from hour to minute is (M − H + 360) mod 360. Counterclockwise is (H − M + 360) mod 360.
- The calculations use the entered numeric time, not a rounded pixel location on the SVG face. Display precision does not alter the underlying result.
Worked clock-angle examples
- At 3:00, H = 90° and M = 0°, so the smaller angle is 90° and the reflex angle is 270°.
- At 12:30, H = 15° because the hour hand has moved halfway toward 1, while M = 180°. The smaller angle is 165°.
- At 3:15, H = 97.5° and M = 90°, so the angle between clock hands is 7.5° rather than zero.
- At 5:20, H = 160° and M = 120°. The smaller separation is 40°, clockwise hour-to-minute is 320°, and counterclockwise is 40°.
Why common shortcuts fail
Subtracting hour-number × 30 from minute × 6 incorrectly freezes the hour hand. At 3:15 that shortcut returns 0° instead of 7.5°. Omitting seconds can also matter in a precision example because 30 seconds advances the minute hand 3° and the hour hand 0.25°.
Twelve-hour and twenty-four-hour input
Times 03:15 and 15:15 point to the same analog positions. Twenty-four-hour mode changes input validation and notation, not the dial formula. The hour is reduced modulo 12 before H is calculated.
What the clock drawing represents
The display models an ideal continuously moving analog clock. Real mechanisms may step, drift, pause, or have hand alignment error. A fixed time needs no timezone and this is not a timezone converter. Live mode reads the device clock only after activation; it cannot verify whether the device time is correct.
Fixed calculations run locally and share URLs contain only mode, hour, minute, and second. Live mode reads the device time without requesting location.