Calculate the angle between hour hand and minute hand
Last Updated :
03 Sep, 2025
Given a string s represents time in 24-hour format ("HH:MM"), determine the minimum angle between the hour and minute hands of an analog clock.
Examples:
Input: s = "06:00"
Output: 180.000
Explanation: When the time is 06:00, the angle between the hour and minute hands of the clock is 180.000 degrees.
Input: s = "03:15"
Output: 7.500
Explanation: When the time is 03:15, the angle between the hour and minute hands of the clock is 7.500 degrees.
Input: s = "00:00"
Output: 0.000
Explanation: When the time is 00:00, the angle between the hour and minute hands of the clock is 0.000 degrees.
[Approach] Using Mathematical Formula - O(1) in Time and O(1) in Space
The minute hand moves 6° per minute, while the hour hand moves 0.5° per minute. Thus, the hour hand's angle is calculated as hrAngle = 30 × H + 0.5 × M, and the minute hand's angle as minAngle = 6 × M. The difference between the two angles is diff = |hrAngle - minAngle|.
Since the clock follows a 12-hour format, any 24-hour input should be converted using H = H % 12. After finding the absolute difference between the two angles, the smaller angle is determined using min(diff, 360 - diff).
C++
#include <iostream>
#include <cmath>
#include <iomanip>
using namespace std;
// Utility function to return the minimum of two double values
double getMin(double x, double y) {
return (x < y) ? x : y;
}
// Function to calculate the minimum angle between
// hour and minute hands
double getAngle(string s) {
// Extract hours and minutes from "HH:MM"
int h = stoi(s.substr(0, 2));
int m = stoi(s.substr(3, 2));
// Convert 24-hour time to 12-hour format
h = h % 12;
// Hour hand moves 0.5 degrees per minute
// (30 degrees per hour)
double hrAngle = 0.5 * (h * 60 + m);
// Minute hand moves 6 degrees per minute
double minAngle = 6 * m;
// Find the absolute difference between the two angles
double angle = fabs(hrAngle - minAngle);
// Return the smaller angle of the two possible angles
return getMin(360.0 - angle, angle);
}
int main() {
string s = "06:00" ;
cout << fixed << setprecision(3);
cout << getAngle(s) << endl;
return 0;
}
import java.text.DecimalFormat;
public class GfG {
// Utility function to return the minimum of two double values
static double getMin(double x, double y) {
return (x < y) ? x : y;
}
// Function to calculate the minimum angle between
// hour and minute hands
static double getAngle(String s) {
// Extract hours and minutes from "HH:MM"
int h = Integer.parseInt(s.substring(0, 2));
int m = Integer.parseInt(s.substring(3, 5));
// Convert 24-hour time to 12-hour format
h = h % 12;
// Hour hand moves 0.5 degrees per minute
// (30 degrees per hour)
double hrAngle = 0.5 * (h * 60 + m);
// Minute hand moves 6 degrees per minute
double minAngle = 6 * m;
// Find the absolute difference between the two angles
double angle = Math.abs(hrAngle - minAngle);
// Return the smaller angle of the two possible angles
return getMin(360 - angle, angle);
}
public static void main(String[] args) {
String s = "06:00";
DecimalFormat df = new DecimalFormat("0.000");
System.out.println(df.format(getAngle(s)));
}
}
# Utility function to return the minimum of two values
def getMin(x, y):
return x if x < y else y
# Function to calculate the minimum angle between
# hour and minute hands
def getAngle(s):
# Extract hours and minutes from "HH:MM"
h = int(s[:2])
m = int(s[3:])
# Convert 24-hour time to 12-hour format
h = h % 12
# Hour hand moves 0.5 degrees per minute
# (30 degrees per hour)
hrAngle = 0.5 * (h * 60 + m)
# Minute hand moves 6 degrees per minute
minAngle = 6 * m
# Find the absolute difference between the two angles
angle = abs(hrAngle - minAngle)
# Return the smaller angle of the two possible angles
return getMin(360 - angle, angle)
if __name__ == "__main__":
s = "06:00"
print(f"{getAngle(s):.3f}")
using System;
class GfG
{
// Utility function to return the minimum of two double values
static double getMin(double x, double y)
{
return (x < y) ? x : y;
}
// Function to calculate the minimum angle between
// hour and minute hands
static double getAngle(string s)
{
// Extract hours and minutes from "HH:MM"
int h = int.Parse(s.Substring(0, 2));
int m = int.Parse(s.Substring(3, 2));
// Convert 24-hour time to 12-hour format
h = h % 12;
// Hour hand moves 0.5 degrees per minute
// (30 degrees per hour)
double hrAngle = 0.5 * (h * 60 + m);
// Minute hand moves 6 degrees per minute
double minAngle = 6 * m;
// Find the absolute difference between the two angles
double angle = Math.Abs(hrAngle - minAngle);
// Return the smaller angle of the two possible angles
return getMin(360 - angle, angle);
}
static void Main()
{
string s = "06:00";
Console.WriteLine($"{getAngle(s):F3}");
}
}
// Utility function to return the minimum of two values
function getMin(x, y) {
return x < y ? x : y;
}
// Function to calculate the minimum angle between
// hour and minute hands
function getAngle(s) {
// Extract hours and minutes from "HH:MM"
let h = parseInt(s.substring(0, 2));
let m = parseInt(s.substring(3, 5));
// Convert 24-hour time to 12-hour format
h = h % 12;
// Hour hand moves 0.5 degrees per minute
// (30 degrees per hour)
let hrAngle = 0.5 * (h * 60 + m);
// Minute hand moves 6 degrees per minute
let minAngle = 6 * m;
// Find the absolute difference between the two angles
let angle = Math.abs(hrAngle - minAngle);
// Return the smaller angle of the two possible angles
return getMin(360 - angle, angle);
}
// Driver code
let s = "06:00";
console.log(getAngle(s).toFixed(3));
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