Clock Angle Calculator
Angle between the hour and minute hands of a clock at any time, and how long until they next overlap.
Results
Angle between the hands (smaller)
7.50
°
The other angle
352.50
°
Minutes until the hands next overlap
1.36
min
What this tool does
The minute hand turns 6° a minute, but the hour hand also moves — half a degree a minute — which is the detail most people miss: at 3:15 the hands are not on top of each other but 7.5° apart. That is why the angle is |30 h − 5.5 m|. The hands overlap 11 times in twelve hours, every 65 min 27 s, not every hour.
Formula
θ = |30 × h − 5.5 × m| · smaller angle = min(θ, 360° − θ)
Variables
| Symbol | Meaning | Unit |
|---|---|---|
h | Hour | h |
m | Minutes | min |
A | Angle between the hands (smaller) | ° |
B | The other angle | ° |
NX | Minutes until the hands next overlap | min |
Worked example
- Hour3 h
- Minutes15 min
- Angle between the hands (smaller)7.50 °
- The other angle352.50 °
- Minutes until the hands next overlap1.36 min
Limitations
- The calculation runs at full precision and only the display is rounded. If you copy an intermediate value and retype it, small differences can appear.
- Mixing units is the most common source of error. Convert every input to the units shown next to each field before calculating.