Find Clock Times from Hand Angle
Find every continuous hour-and-minute hand solution for a chosen smaller angle in a 12-hour cycle, with precise seconds and hand-position reports.
Ready. Explore the example or use the input controls to begin.
Scope and practical limits
Angles 0–180 degrees. Uses continuously moving hands over one half-open 12-hour cycle. Displayed seconds are rounded to 0–3 decimal places; precise seconds-after-12 and hand angles remain available in the report.
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Using Find Clock Times from Hand Angle
Find every continuous hour-and-minute hand solution for a chosen smaller angle in a 12-hour cycle, with precise seconds and hand-position reports.
- Start with the example and set the relevant dates, range or clock settings.
- Review validation messages and the calculated results, including calendar conventions and day offsets.
- Download JSON or CSV; where available, export all-day calendar events. Save a project to retain your inputs.
Example
A 90-degree smaller angle has 22 solutions in one 12-hour cycle. Coincident hands and opposite hands each have 11 distinct solutions in that cycle.
Questions & answers
Are these times restricted to whole seconds?
No. The mathematical solutions can fall between seconds. Display rounding can introduce a small apparent angle difference.
Why does the list not repeat 12:00 at the end?
The cycle includes its beginning and excludes the next 12:00, avoiding a duplicate endpoint.
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