Find angle between hour and minute hands in an analog clock

Question

I was given this interview question recently:

Given a 12-hour analog clock, compute in degree the smaller angle between the hour and minute hands. Be as precise as you can.

I'm wondering what's the simplest, most readable, most precise algorithm is. Solution in any language is welcome (but do explain it a bit if you think it's necessary).

Solution 1

It turns out that Wikipedia does have the best answer:

// h = 1..12, m = 0..59
static double angle(int h, int m) {
    double hAngle = 0.5D * (h * 60 + m);
    double mAngle = 6 * m;
    double angle = Math.abs(hAngle - mAngle);
    angle = Math.min(angle, 360 - angle);
    return angle;
}

Basically:

• The hour hand moves at the rate of 0.5 degrees per minute
• The minute hand moves at the rate of of 6 degrees per minute

Problem solved.

---

And precision isn't a concern because the fractional part is either .0 or .5, and in the range of 0..360, all of these values are exactly representable in double.

Solution 2

For finding the angle between the hands of a clock is ,

30 * [HRS - (MIN/5)] + (MIN/2) 

Solution 3

The java code that polygenlubricants is similar than mine. Let's assume that the clock is 12 hour instead of 24.

If it's 24 hours, then that's a different story. Also, another assumption, assume if the clock is stopped while we calculate this.

One clock cycle is 360 degree.

1. How many degree can the minute hand run per minute? 360 / 60 = 6 degree per minute.

2. How many degree can the hour hand run per hour? 360/12 = 30 degree per hour (since hour hand run slower than minute)

Since it's easier to calculate in the unit, "minute", let's get

"how many degree can the hour hand run per minute"?

30 / 60 = 0.5 degree per minute.

So, if you know how to get those numbers, the problem is pretty much done with solution.

Solution 4

Minute angle (from 12 o’clock): 360 * minutes / 60

Hour angle (from 12 o’clock): 360 * (hour % 12) / 12 + 360 * (minutes / 60) * (1 / 12)

Angle between hour and minute: (hour angle - minute angle) % 360 By simple arithmetic, this reduces to 30 * hours - 5.5 * minutes.

Solution 5

    **php code for find angle via time (minutes and hour's)**

    echo calcAngle(3,70);

function calcAngle($h, $m)
{
    // validate the input
    if ($h <0 || $m < 0 || $h >12 || $m > 60)
      {
       return "Wrong input";
      }
      else {

    if ($h == 12) $h = 0;
    if ($m == 60) $m = 0;

    $hour_angle = 0.5 * ($h*60 + $m);
    $minute_angle = 6*$m;
    $angle = abs($hour_angle - $minute_angle);
    $angle = min(360-$angle, $angle);

    return $angle;
}
}

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