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Clock Hand Angle Calculator — result sheet
Calculate the smaller angle between analog clock hands from an hour and minute value.
Inputs used
Results
Visual chart
Breakdown
Calculation steps
Returned data table
Formula and methodology
Formula: Hour-hand angle = 30h+0.5m; minute-hand angle = 6m; smaller difference = min(|difference|,360−|difference|).
The hour hand moves continuously with the minutes, so the calculator does not snap it to an hour mark.
This result follows the calculator's declared inputs, precision, validation boundaries, and model limits.
Input contract
- Hour — minimum 0; maximum 23
- Minute — minimum 0; maximum 59.999999
Worked example
| Input | Value |
|---|---|
| Hour | 3 |
| Minute | 30 |
The smaller hand angle is 75°.
Assumptions and limits
- Hour uses a 24-hour input and is reduced modulo 12; minute is from 0 through 60.
- Angles are measured clockwise from 12 o’clock.
- Digital display conventions, seconds, and clock-mechanism error are not modeled.
Calculator note
Source and methodology
Use the official WorldCalculate methodology policy for the source, formula, precision, and boundary standards behind this calculator.
Planning estimate, not financial, medical, legal, or professional advice. © WorldCalculate — reuse with attribution. Built and curated by Hassan ALRowaie.
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