Clock Angle Calculator
Math
Calculate clock angle with explicit inputs and a worked example.
Formula
d = |30(h mod 12) − 5.5m|; smaller angle = min(d,360−d)
- Use the units shown beside each field.
- Results update automatically whenever you change an input.
- Displayed values use up to four decimal places, or scientific notation for very small or large numbers. Calculations use standard floating-point arithmetic; exact integer and fraction tools identify their own precision rules.
- Ideal continuous hour hand; seconds are zero.
Example Calculation
Example inputs
- Hour: 3
- Minute: 0
At 3:00, the smaller angle between the hands is 90°.
Frequently asked questions
How do I use this calculator?
Enter hour, minute. The result updates automatically. Use Reset to restore the example values.
What method does it use?
d = |30(h mod 12) − 5.5m|; smaller angle = min(d,360−d). Ideal continuous hour hand; seconds are zero.
Why might a rounded result differ?
The calculation keeps full numeric precision internally, then rounds the displayed result. Rounding intermediate steps by hand can produce a slightly different answer.
Are my inputs saved online?
No. This calculator processes your inputs in your browser. A recently used list stores only calculator names on this device, not your entered values.
Check the assumptions and units before using this result. Read about calculation methods.