Find the Angle Between Hour and Minute Hands of a Clock in C#

The calculation of the angle between the hour and minute hands of a clock is a common problem in Logical Reasoning and programming. This calculation is used in various applications, such as analog clock simulations, scheduling software, and time-based animations

In this article, we are going to discuss how we can calculate the angle between the hour and minute hands of a clock in C# using different approaches:

What is the Angle Between the Hour and Minute Hands?

The angle between the hour and minute hands is determined based on the positions of both hands on the clock face. Some of the main key observations are:

• The minute hand moves 360 degrees in 60 minutes, i.e., 6 degrees per minute.
• The hour hand moves 360 degrees in 12 hours, i.e., 30 degrees per hour.
• The hour hand moves an additional 0.5 degrees per minute as time progresses.

Formula for Calculating the Angle

Angle = | (30 * Hours) - ( (11/2) * Minutes) |

If the calculated angle is greater than 180 degrees, then we take the smaller angle by subtracting it from 360 degrees, as 360 degrees makes a complete circle.

We can calculate the angle between the hour and minute hands in C# using different approaches. Some of the approaches are mentioned below:

• Using a Simple Formula
• Using a Mathematical Function

Using a Simple Formula

In this approach, we directly apply the formula to calculate the angle.

• Take input for hours and minutes.
• Convert the hour and minute hands positions into degrees.
• Calculate the absolute difference between the two positions.
• If the angle is greater than 180 degrees, subtract it from 360 to find the smaller angle.
• Output the result.

Example

The following example calculates the angle between hour and minute hands in C# using a simple formula.

using System;

class ClockAngle
{
    static int FindAngle(int hours, int minutes)
    {
        if (hours < 0 || minutes < 0 || hours > 12 || minutes > 60)
            return -1;

        if (hours == 12) 
            hours = 0;

        if (minutes == 60) 
            minutes = 0;

        int hourAngle = (int)(0.5 * (hours * 60 + minutes));
        int minuteAngle = 6 * minutes;

        int angle = Math.Abs(hourAngle - minuteAngle);

        return Math.Min(360 - angle, angle);
    }

    static void Main()
    {
        int hours = 9, minutes = 15;
        Console.WriteLine("The angle between the hour and minute hands is: " + FindAngle(hours, minutes) + " degrees");
    }
}

The output of the above code is:

The angle between the hour and minute hands is: 173 degrees

Using a Mathematical Function

In this approach, we define a function that takes hours and minutes as input, applies the mathematical calculations, and returns the minimum angle.

• Define a Function.
• Take hour and minute as input.
• Apply the mathematical formula inside the function.
• Return the Output.

Example

Here is an example to calculate the angle between hour and minute hands in C# using a mathematical function.

using System;

class ClockAngleCalculator
{
    static double CalculateAngle(int hours, int minutes)
    {
        double hourAngle = (hours % 12) * 30 + (minutes * 0.5);
        double minuteAngle = minutes * 6;

        double angle = Math.Abs(hourAngle - minuteAngle);

        return Math.Min(angle, 360 - angle);
    }

    static void Main()
    {
        int hours = 3, minutes = 30;
        Console.WriteLine("The angle between the hour and minute hands is: " + CalculateAngle(hours, minutes) + " degrees");
    }
}

The output of the above code is:

The angle between the hour and minute hands is: 75 degrees