Clock Angle Calculator
Clock hand angles small and large for any hour and minute.
What it does
Clock hands sweep steady circles at different speeds. The gap between them follows one absolute formula with a 360 complement.
The tool above runs the math. At 3:15 the hour hand sits at 97.5 degrees with the minute at 90, for 7.5 degrees small and 352.5 large. Time is universal, so no unit toggle is needed.
Hour hands move thirty degrees per hour plus half a degree per minute. Minute hands jump six degrees per minute flat.
Feel tags read closeness. Under five degrees nearly overlaps, over 175 nearly opposes, and the middle reads separated.
Contest clocks love this problem. Whole hours, quarters, and trick minutes all fall to the same line.
How to use
- Enter hour: 3 suits the default.
- Enter minutes: 15 suits the default.
- Read small angle first.
- Read large angle next.
- Read feel tag.
Formula
- H
- Hour 1 to 12.
- M
- Minutes 0 to 59.
Hour hand moves 30 degrees per hour plus half a degree per minute. Times use 12 hour format.
Worked example
Example: 3:15
Defaults: 3:15. These are also the default values, so the page opens on this answer.
- Time: 3:15.
- Hour hand: 3 x 30 + 15 x 0.5 = 97.5 degrees.
- Minute hand: 15 x 6 = 90 degrees.
- Small: |97.5 - 90| = 7.5 degrees.
- Large: 360 - 7.5 = 352.5 degrees.
- Tool shows 7.5 degrees, 352.5 degrees, Separated.
Reference table
| Time | Small | Large |
|---|---|---|
| 12:00 | 0 degrees | 360 degrees |
| 3:00 | 90 degrees | 270 degrees |
| 3:15 | 7.5 degrees | 352.5 degrees |
| 6:00 | 180 degrees | 180 degrees |
Limits
- Analog math only. Digital needs none.
- Twelve hour format assumed.
- Feel tags are rough guides.
- Seconds hands ignored.
Common mistakes
- Forgetting hour hand creeps per minute.
- Reading only the large angle.
- Twelve as zero versus twelve.
- Radians expected instead.
- Skipping the 360 complement.
Try it yourself
Quick checks. Answers sit tucked under each question.
12:00?
|30 x 12 - 0| = 0, min(0, 360) = 0 degrees. Large is 360 degrees, shown as 360 degrees.
6:00?
|30 x 6 - 0| = 180, min(180, 180) = 180 degrees. Large matches at 180 degrees.
Questions
Angle at 3:15?
Take |30H - 5.5M| and the 360 complement. Here |90 - 82.5| = 7.5 degrees.
When zero?
Twelve o five past: hands nearly overlap near 2.5 degrees? At 12:00 exactly 0 degrees.
When opposite?
Opposite near 6:00 with 180 degrees between hands.
Feel tags?
Under 5 reads nearly overlapping, over 175 nearly opposite, else separated.
Hand speeds?
Yes. Each minute moves the minute hand 6 degrees and the hour hand half a degree.
Digital too?
No. Digital clocks need no math.