Angle between hour and minute hands of analogue clock using C

This is a very interesting clock angle problem where the C program described in this article calculates the angle between the hour-hand and the minute-hand of an analog clock. In this example program if the user enters the hour and minute, then it should output the angle between the hour-hand and the minute-hand.

Example:

Input: hour = 10 and minute = 10

Output: 115 degree

Calculation theory

The hour hand of a 12-hour analog clock turns 360° in (12 x 60) minutes; in other words 0.5° per minute. Similarly, the minute hand would take 60 minutes to turn a complete 360° (which is 6° per minute). The angle between the hour hand and minute hand is obtained by the difference between these angles.

Code

#include <stdio.h>
#include <stdlib.h>
#include <math.h>

int main()
{
    unsigned int hour;
    unsigned int minute;
    float hAngle;
    float mAngle;
    float angle;
    
    printf("Enter hour (12h format): ");
    scanf("%u", &hour);
    
    printf("Enter minute: ");
    scanf("%u", &minute);
    
    if (hour > 12u || minute > 60u)
    {
        printf("Invalid input!\n");
    }
    else
    {
        if (hour == 12u)
        {
            hour = 0;
        }
        
        if (minute == 60u)
        {
            minute = 0;
            hour += 1u;
        }
        
        hAngle = 0.5f * ((hour * 60.0f) + minute);  // Hour hand angle with respect to 12:00
        mAngle = 6.0f * (float)minute;  // Minute hand angle with respect to 12:00
        
        angle = fabsf(hAngle - mAngle);
        
        if (angle > (360.0f - angle))
        {
            angle = 360.0f - angle;  // Getting the smaller angle value
        }
        
        printf("Angle between hour hand and minute hand is %.1f\n", angle);
    }

    return 0;
}

Code walk-through

The code is simple and self explanatory. Angle between the hour hand and the minute hand is calculated at the below lines,

hAngle = 0.5f * ((hour * 60.0f) + minute);  // Hour hand angle with respect to 12:00
mAngle = 6.0f * (float)minute;  // Minute hand angle with respect to 12:00

fabsf() library function (from <math.h>) is used to get the absolute float value of the angle difference in angle = fabsf(hAngle - mAngle);

The below code section selects the smaller angle value from the two possible angle values,

if (angle > (360.0f - angle))
{
    angle = 360.0f - angle;  // Getting the smaller angle value
}