Calculate the angle between hour hand and minute hand

This problem is know as Clock angle problem where we need to find angle between hands of an analog clock at a given time.


Input:  h = 12:00, m = 30.00
Output: 165 degree

Input:  h = 3.00, m = 30.00
Output: 75 degree

The idea is to take 12:00 (h = 12, m = 0) as a reference. Following are detailed steps.

1) Calculate the angle made by hour hand with respect to 12:00 in h hours and m minutes.
2) Calculate the angle made by minute hand with respect to 12:00 in h hours and m minutes.
3) The difference between two angles is the angle between two hands.

How to calculate the two angles with respect to 12:00?
The minute hand moves 360 degree in 60 minute(or 6 degree in one minute) and hour hand moves 360 degree in 12 hours(or 0.5 degree in 1 minute). In h hours and m minutes, the minute hand would move (h*60 + m)*6 and hour hand would move (h*60 + m)*0.5.

// C program to find angle between hour and minute hands
#include <stdio.h>
#include <stdlib.h>

// Utility function to find minimum of two integers
int min(int x, int y) { return (x < y)? x: y; }

int calcAngle(double h, double m)
    // validate the input
    if (h <0 || m < 0 || h >12 || m > 60)
        printf("Wrong input");

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

    // Calculate the angles moved by hour and minute hands
    // with reference to 12:00
    int hour_angle = 0.5 * (h*60 + m);
    int minute_angle = 6*m;

    // Find the difference between two angles
    int angle = abs(hour_angle - minute_angle);

    // Return the smaller angle of two possible angles
    angle = min(360-angle, angle);

    return angle;

// Driver program to test above function
int main()
    printf("%d \n", calcAngle(9, 60));
    printf("%d \n", calcAngle(3, 30));
    return 0;



Exercise: Find all times when hour and minute hands get superimposed.

This article is contributed by Ashish Bansal. Please write comments if you find anything incorrect, or you want to share more information about the topic discussed above

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