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Code Conversion

Convert gradian to radian

Angular measurement systems play a vital role in mathematics, physics, and engineering. One such system is gradians, which divides a right angle into 100 units. Radians, on the other hand, are a more fundamental angular measurement used extensively in mathematics and physics. Converting angles from gradians to radians is an important task that involves understanding these measurement systems and the relationships between them.

Problem Statement and Description

The task is to convert an angle given in gradians to its equivalent value in radians. Radians are a unit of angular measurement that relates the angle to the length of the radius of a circle. The formula to convert from gradians to radians is (gradian * π) / 200, where π (pi) is a mathematical constant approximately equal to 3.14159. This formula takes the given angle in gradians, multiplies it by π, and then divides by 200 to obtain the equivalent angle in radians.

Example

Let's take an example to illustrate the problem. Suppose we have an angle of 60 gradians that we want to convert to radians. Using the formula:

Radian = (Gradian * π) / 200
Radian = (60 * π) / 200
Radian ≈ 0.94248

So, 60 gradians is approximately equal to 0.94248 radians.

Idea to Solve the Problem

To solve this problem, we need to create a program that takes an angle in gradians as input, applies the conversion formula, and then outputs the equivalent angle in radians. We will use a function to perform this conversion, and the main program will call this function for different test cases.

Pseudocode

Here's the pseudocode for the program:

function gradian_to_radian(gradian):
    radian = (gradian * π) / 200
    return radian

Algorithm Explanation

  1. Define the gradian_to_radian function that takes a parameter gradian.
  2. Inside the function, calculate the equivalent radian using the formula (gradian * π) / 200.
  3. Return the calculated radian.
  4. In the main program, call the gradian_to_radian function with different test cases: 1, 50.80, and 70.50.
  5. Print the results.

Program Solution

//C Program 
//Convert gradian to radian
#include <stdio.h>

#include <math.h>

//Find the radian of given gradian
void gradian_to_radian(double gradian)
{
	// Formula : (gradian*π)/200
	// Calculate given gradian to radian 
	double radian = (gradian * M_PI) / 200;
	//Display result
	printf("Gradian : %lf  radian : %lf\n", gradian, radian);
}
int main()
{
	//Simple test
	gradian_to_radian(1);
	gradian_to_radian(50.80);
	gradian_to_radian(70.50);
	return 0;
}

Output

Gradian : 1.000000  radian : 0.015708
Gradian : 50.800000  radian : 0.797965
Gradian : 70.500000  radian : 1.107411
/*
  Java program
  Convert gradian to radian 
*/
class MyMath
{
	//Find the radian of given gradian
	public void gradian_to_radian(double gradian)
	{
		// Formula : (gradian*π)/200
		// Calculate given gradian to radian 
		double radian = (gradian * Math.PI) / 200;
		System.out.print("Gradian : " + gradian + " radian : " + radian + "\n");
	}
	public static void main(String[] args)
	{
		MyMath obj = new MyMath();
		//Simple test
		obj.gradian_to_radian(1);
		obj.gradian_to_radian(50.80);
		obj.gradian_to_radian(70.50);
	}
}

Output

Gradian : 1.0 radian : 0.015707963267948967
Gradian : 50.8 radian : 0.7979645340118074
Gradian : 70.5 radian : 1.107411410390402
/*
  C++ program
  Convert gradian to radian 
*/
#include<iostream>
#include<math.h>
using namespace std;
class MyMath
{
	public:
		//Find the radian of given gradian
		void gradian_to_radian(double gradian)
		{
			// Formula : (gradian*π)/200
			// Calculate given gradian to radian 
			double radian = (gradian * M_PI) / 200;
			cout << "Gradian : " << gradian << " radian : " << radian << "\n";
		}
};
int main()
{
	MyMath obj = MyMath();
	//Simple test
	obj.gradian_to_radian(1);
	obj.gradian_to_radian(50.80);
	obj.gradian_to_radian(70.50);
	return 0;
}

Output

Gradian : 1 radian : 0.015708
Gradian : 50.8 radian : 0.797965
Gradian : 70.5 radian : 1.10741
/*
  C# program
  Convert gradian to radian 
*/
using System;
class MyMath
{
	//Find the radian of given gradian
	public void gradian_to_radian(double gradian)
	{
		// Formula : (gradian*π)/200
		// Calculate given gradian to radian 
		double radian = (gradian * Math.PI) / 200;
		Console.Write("Gradian : " + gradian + " radian : " + radian + "\n");
	}
	public static void Main(String[] args)
	{
		MyMath obj = new MyMath();
		//Simple test
		obj.gradian_to_radian(1);
		obj.gradian_to_radian(50.80);
		obj.gradian_to_radian(70.50);
	}
}

Output

Gradian : 1 radian : 0.015707963267949
Gradian : 50.8 radian : 0.797964534011807
Gradian : 70.5 radian : 1.1074114103904
<?php
/*
  Php program
  Convert gradian to radian 
*/
class MyMath
{
	//Find the radian of given gradian
	public	function gradian_to_radian($gradian)
	{
		// Formula : (gradian*π)/200
		// Calculate given gradian to radian 
		$radian = ($gradian * M_PI) / 200;
		echo "Gradian : ". $gradian ." radian : ". $radian ."\n";
	}
}

function main()
{
	$obj = new MyMath();
	//Simple test
	$obj->gradian_to_radian(1);
	$obj->gradian_to_radian(50.80);
	$obj->gradian_to_radian(70.50);
}
main();

Output

Gradian : 1 radian : 0.015707963267949
Gradian : 50.8 radian : 0.79796453401181
Gradian : 70.5 radian : 1.1074114103904
/*
  Node Js program
  Convert gradian to radian 
*/
class MyMath
{
	//Find the radian of given gradian
	gradian_to_radian(gradian)
	{
		// Formula : (gradian*π)/200
		// Calculate given gradian to radian 
		var radian = (gradian * Math.PI) / 200;
		process.stdout.write("Gradian : " + gradian + " radian : " + radian + "\n");
	}
}

function main()
{
	var obj = new MyMath();
	//Simple test
	obj.gradian_to_radian(1);
	obj.gradian_to_radian(50.80);
	obj.gradian_to_radian(70.50);
}
main();

Output

Gradian : 1 radian : 0.015707963267948967
Gradian : 50.8 radian : 0.7979645340118074
Gradian : 70.5 radian : 1.107411410390402
#   Python 3 program
#   Convert gradian to radian 
import math
class MyMath :
	# Find the radian of given gradian
	def gradian_to_radian(self, gradian) :
		#  Formula : (gradian*π)/200
		#  Calculate given gradian to radian 
		radian = (gradian * math.pi) / 200
		print("Gradian : ", gradian ," radian : ", radian ,"\n", end = "")
	

def main() :
	obj = MyMath()
	# Simple test
	obj.gradian_to_radian(1)
	obj.gradian_to_radian(50.80)
	obj.gradian_to_radian(70.50)

if __name__ == "__main__": main()

Output

Gradian :  1  radian :  0.015707963267948967
Gradian :  50.8  radian :  0.7979645340118074
Gradian :  70.5  radian :  1.107411410390402
#   Ruby program
#   Convert gradian to radian 

class MyMath

	# Find the radian of given gradian
	def gradian_to_radian(gradian)
	
		#  Formula : (gradian*π)/200
		#  Calculate given gradian to radian 
		radian = (gradian * Math::PI) / 200
		print("Gradian : ", gradian ," radian : ", radian ,"\n")
	end
end
def main()

	obj = MyMath.new()
	# Simple test
	obj.gradian_to_radian(1)
	obj.gradian_to_radian(50.80)
	obj.gradian_to_radian(70.50)
end
main()

Output

Gradian : 1 radian : 0.015707963267948967
Gradian : 50.8 radian : 0.7979645340118074
Gradian : 70.5 radian : 1.107411410390402

/*
  Scala program
  Convert gradian to radian 
*/
class MyMath
{
	//Find the radian of given gradian
	def gradian_to_radian(gradian: Double): Unit = {
		// Formula : (gradian*π)/200
		// Calculate given gradian to radian 
		var radian: Double = (gradian * Math.PI) / 200;
		print("Gradian : " + gradian + " radian : " + radian + "\n");
	}
}
object Main
{
	def main(args: Array[String]): Unit = {
		var obj: MyMath = new MyMath();
		//Simple test
		obj.gradian_to_radian(1);
		obj.gradian_to_radian(50.80);
		obj.gradian_to_radian(70.50);
	}
}

Output

Gradian : 1.0 radian : 0.015707963267948967
Gradian : 50.8 radian : 0.7979645340118074
Gradian : 70.5 radian : 1.107411410390402
/*
  Swift program
  Convert gradian to radian 
*/
import Foundation
class MyMath
{
	//Find the radian of given gradian
	func gradian_to_radian(_ gradian: Double)
	{
		// Formula : (gradian*π)/200
		// Calculate given gradian to radian 
		let radian: Double = (gradian * Double.pi) / 200;
		print("Gradian : ", gradian ," radian : ", radian ,"\n", terminator: "");
	}
}
func main()
{
	let obj: MyMath = MyMath();
	//Simple test
	obj.gradian_to_radian(1);
	obj.gradian_to_radian(50.80);
	obj.gradian_to_radian(70.50);
}
main();

Output

Gradian :  1.0  radian :  0.015707963267949
Gradian :  50.8  radian :  0.797964534011807
Gradian :  70.5  radian :  1.1074114103904

Time Complexity

Similar to the previous problem, the time complexity of this program is constant for each conversion. It involves basic arithmetic operations like multiplication and division, and the number of operations remains consistent regardless of the input gradians. Thus, the time complexity is O(1).

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