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).

simplest? looking it up on wiki! : en.wikipedia.org/wiki/Clock_angle_problem'; — Mitch Wheat, May 1 '10 at 5:12
I think that this is a purely mathematical problem, and also fairly trivial. I do not see how this question can get four up-votes... — Andreas Rejbrand, May 1 '10 at 12:06

polygenelubricants · Accepted Answer · 2010-05-01 11:34:34Z

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.

This is not quite correct for h >= 12. – starblue May 1 '10 at 11:03
@starblue: I've clarified that it's a 12-hour analog clock. – polygenelubricants May 1 '10 at 11:34
@starblue Can analog clock be ever 24hr? – AksharRoop Sep 3 '12 at 8:20

EdChum · Answer 2 · 2012-06-22 22:23:33Z

up vote4down vote

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

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

edited Jun 22 '12 at 22:23

EdChum
6,481102134

answered Mar 9 '12 at 14:01

Suwaru Ram
411

This works great. Thanks for the answer!! – gabhi Nov 3 '13 at 18:46

Missing absolute value ? – Hunter McMillen Dec 17 '13 at 14:27

add comment

Victor Hugo · Answer 3 · 2012-11-05 13:54:11Z

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.

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

Imane Fateh · Answer 4 · 2013-08-16 08:45:25Z

Try this code :

import java.util.Scanner;

class Clock{

    public static void main(String args[]){
        int hours,mins;

    System.out.println("Enter the Time(hours) : ");
        Scanner dx = new Scanner(System.in);
        hours = dx.nextInt();

    System.out.println("Enter the time(mins) : ");
        Scanner fx = new Scanner(System.in);
        mins = fx.nextInt();

    if(hours>=0 && hours<=12){

        if(mins>=0 && mins<=59){
            double hDegrees = (hours * 30) + (mins * 0.5);
                    double mDegrees = mins * 6;
                    double diff  = Math.abs(hDegrees - mDegrees);

        System.out.println("The angle between sticks is (degrees) : "+diff);
                if (diff > 180){ 

                diff = 360 - diff;
        System.out.println("The angle between sticks is (degrees) : "+diff);
                }

        }

    }

    else{
        System.out.println("Wrong input ");
    }


}

}

Sim · Answer 5 · 2014-03-09 17:13:45Z

for finding the angle between the hour hand and the minute hand is

angle=(hour*5-min)*6

bodacydo · Answer 6 · 2013-08-17 19:58:40Z

I tried to solve this problem but I don't think it can be solved mathematics.

Gabe · Answer 7 · 2010-05-01 08:19:52Z

up vote-2down vote

I do not know if it's right, .something like this?

//m*360/60 - (h*360/24)+(m*360/(24*60)) ->
t = abs(25*m - 60*h)/4
t = min(t,360-t)

edited May 1 '10 at 8:19

Gabe
47.5k454110

answered May 1 '10 at 5:14

Anycorn
18.9k874166

Well it can't be right if you're missing an end parenthesis :D – Wallacoloo May 1 '10 at 5:17

For h=3, m=0, I get 45. It should be 90. – polygenelubricants May 1 '10 at 5:37

@poly okay, I forgot regular clock is 12, not 24 hours. if you replace division by 24 with 12, you should get correct – Anycorn May 1 '10 at 5:42

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javascript - Find angle between hour and minute hands in an analog clock

javascript - Find angle between hour and minute hands in an analog clock

Find angle between hour and minute hands in an analog clock

7 Answers