Input:  12:00 Degree(min) = M*(360/60). If you'd like an angle less than 180 ∘, take min (360 ∘ − Δ θ, Δ θ). This gives times of: 0:00, 1:05.45, 2:10.90, 3:16.36, 4:21.81, 5:27.27. x= Starting position of hour angle. We know that the angle traced by the hour hand in one hour is 30º and in one minute is 1/2º. 1. (0.45 minutes are exactly 27.27 seconds. Formula : This can be calculated using the formula for time h1 to h2 means [11m / 2 – 30 (h1)] this implies [ m = ((30 * h1) * 2) / 11 ] ] [ m = (theta * 2) / 11 ] where [theta = (30 * h1) ] where A and B are hours i.e if given hour is (2, 3) then A = 2 and B = 3 . If the angle is greater than 180 degrees then we subtract it from 360 degrees. Therefore, the measure of the angle between the minute and hour hands at 4:42 is 111°. Program to determine the angle between the hands of a clock. Each hour represents 30 degrees. link brightness_4 code // CPP code to find the minute at which // the minute hand … it is correct cause 9 15 means that an hour hand is not at the 9 but at 1/4 of an hour gap (between 9:10). Clock angle problems relate two different measurements: angles and time. When are the hour and minute hands of a clock superimposed? Angle traced by minute hand in 60 min. The hour and minute hands are superimposed only when their angle is the same. The large intermediate angle is the angle with the longer distance. 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. Objective: Find the Angle between hour hand and minute hand at the given time. The total angle traced by the hour hand is the angle traced in 7 hours and 10 minutes. 3) The difference between two angles is the angle between two hands. Ans: In this we required formula, 30H + m/2 – 6m = (30 x 8) + 20/2 – (6 x 20) = 240 + 10 – 120 = 130 0.. Clock angle problems relate two different measurements: angles and time. angle between hour hand and minute hand =240-20=220 degree or 360-220=140. As there are 24 half-hour intervals on a clock, the angle of one is: #360/24 = 15°# As the hands are one half-hour interval apart they are 15° apart. Do NOT follow this link or you will be banned from the site. A method to solve such problems is to consider the rate of change of the angle in degrees per minute. The angle is typically measured in degrees from the mark of number 12 clockwise. … Step 1: Input time in number format. - Total angle between hour & minute hand = 120 + 5 = 125 deg - bbattey December 15, 2012 | Flag Reply. So our formula is M(30)/60 → M/2: Ask the user to enter two int numbers - h for hours, and m for minutes. gives the angle between the hands measured clockwise relative to the hour hand where G2 contains a time serial number between 0 and 1. Why if angle is greater than 180° ,why it is 360-angle? Clock angle problems are a type of mathematical problem which involve finding the angle between the hands of an analog clock. Enter your email address to subscribe to new posts and receive notifications of new posts by email. Here's how. The angle is formed from the hour hand clockwise towards the minute hand. Let us assume. Step 1: First create a function that takes two int type of arguments - hour and minute. C++. Angle traced by hour hand in 12 hrs = 360° 9. h = h*hour; General formula for angle between two hands of a clock. when min hand is on 40 the angle is subtended =240 and we know that hour hand move 1/2 degree per min so in 40 min it moved 40/2 =20 degree so angle would be 240-20=220 so its reflex angle would be 360 … The Angle between 8:20 = 130 0.. Ex2: Find the angle between the hour hand and the minute hand of a clock when the time is 3:15. Learn how and when to remove this template message, https://web.archive.org/web/20100615083701/http://delphiforfun.org/Programs/clock_angle.htm, https://web.archive.org/web/20100608044951/http://www.jimloy.com/puzz/clock1.htm, https://en.wikipedia.org/w/index.php?title=Clock_angle_problem&oldid=1000512611, Articles needing additional references from November 2014, All articles needing additional references, Creative Commons Attribution-ShareAlike License, This page was last edited on 15 January 2021, at 11:49. 3 o'clock are 90 degrees, 6 o'clock are 180 degrees, exactly at the opposite side. Suppose we have two numbers, hour and minutes. int h = 360/12; // 1 hour = 30 degree Step 2: Press the "Calculate" button. (47 votes, average: 4.83 out of 5)Loading... why are we doing the part (min*360)/(12*60) in finding the angle for hour? We can clearly say, Hour hand is fully depending on Minutes hand. The answer is 90. When minute hand is behind the hour hand, the angle between the two hands at M minutes past H o’clock. = 360°. Related Questions. Hour hand moves 30 degree per hour . Here H is the hour and M is the minutes past the hour. The hour hand of a 12-hour analogue clock turns 360° in 12 hours and the minute hand rotates through 360° in 60 minutes. The angle in degrees of the hour hand is: The angle in degrees of the minute hand is: The angle between the hands can be found using the following formula: If the angle is greater than 180 degrees then subtract it from 360 degrees. Following are detailed steps. Angle between hand and minute = angle of hour hand ~ angle of minute hand. Yes (32) | No (1) nirlep singh (9 years ago) just the simple solution. }. Example: Input: h = 12:00, m = 30.00 Output: 165 degree . return angle; Each hour on the clock represents an angle of 30 degrees (360 divided by 12). Therefore, (30º x 7) + (10 x 1/2º) = 215º is the angle traced by the hour hand. For the minute hand, one minute equates to 6 degrees. public int findAngle(int hour, int min) The hour hand of a normal 12-hour analogue clock turns 360° in 12 hours (720 minutes) or 0.5° per minute. } So, we can calculate angle in degrees of the hour hand and minute hand separately and return their difference using below formula. hence, for 20 minutes it rotates by an angle of 20*1/2 = 10 degrees. int m = 360/60; // 1 min = 6 degree For the hour hand, one hour equates to 30 degrees, one minute to half a degree. In the case where the minute hand is ahead of the hour hand, the angle between the two hands at M minutes past H ‘o clock will be calculated as Clock Angle Problem: Given time in hh:mm format, calculate the shorter angle between hour and minute hand in an analog clock. Please note that 9:60 is not a valid time. The angle should be in degrees and measured clockwise from the 12 o’clock position of the clock. Ex1: Find the angle between the hour hand and the minute hand of a clock when the time is 8:20. Here, the clock position in hours and minutes and angle in decimal degrees with one decimal place can be converted. In this tutorial, we will learn to get or find the angle between the hour hand and minute hand in C++. Suppose the hour and minute hands were pointing to 6:00, then there's a 180 degree angle since it's a straight line. The angle between hour and minute hand in 4:20 is 10 degrees. Minute hand moves 6 degree per minute . Output: 15° Your approach will give 60 as answer, but it’s wrong. h m/60 hours = (60 h + 3)/ 60 hours. The angle is typically measured in degrees from the mark of number 12 clockwise. The idea is to take 12:00 (h = 12, m = 0) as a reference. The hour hand of a 12-hour analogue clock turns 360° in 12 hours and the minute hand rotates through 360° in 60 minutes. 2) Calculate the angle made by minute hand with respect to 12:00 in h hours and m minutes.   The minute hand moves 360 degrees in 60 minute (or 6 degrees in one minute) and hour hand moves 360 degrees in 12 hours (or 0.5 degrees in 1 minute). Also, we say this problem as analog clock angle problem where we have to find the angle between the hands of a clock at a given time. ), Equation for the angle of the minute hand. Watch Queue Queue First note that a clock is a circle made of 360 degrees, and that each number represents an angle and the separation between them is 360/12 = 30. so in y minutes it will … 10. The minute hand rotates through 360° in 60 minutes or 6° per minute.[1]. Finding the angle between the hour and minute hands of a clock at any given time: The logic that we need to implement is to find the difference in the angle of an hour and minute hand from the position of 12 O Clock when the angle between them is zero. References: Clock Angle Problem – Wikipedia. play_arrow. Calculate the Angle between 12 and the Hour hand 10: Since there are 360 degrees in a full circle (clock), and there are 12 hours, each hour represents 360/12 = 30 degrees So our formula is 30(H) So our formula is 30(10) θh = 300 Next, we know how each minute is 1/60 of an hour. Comment hidden because of low score. Please note that the hour hand doesn’t stay at same position when minute hand of clock is moving. What if the given time is 9:60?   angle = 360 – angle; The minute hand moves 360 degree in 60 minute (or 6 degree in one minute) and hour hand moves 360 … 0. of 0 vote. The time is usually based on a 12-hour clock. HINT : The hour hand moves $1/2$ degrees per minute while minute hand moves 6 degrees per minute. So our formula is M(30)/60 → M/2: What will be the acute angle between the hour-hand and the minute-hand at 4:37 p.m.? We have to find a smaller angle (in sexagesimal units) formed between the hour and the minute hand. The formula for finding the angle between starting position and hour hand at a specific time can be written as x = ( hour + minute …   Now, return to the time of 6:50. edit close. Input:  9:00 Formulas for Clock A) Angle between hands of a clock. The minute hand sits on the 10. The output is correct. Flag as Inappropriate Flag as … there is an error: abs is not within the scope in the c++ code.   Degree (hr) = H*(360/12) + (M*360)/(12*60) Degree (min) = M*(360/60) Here H is the hour and M is the minutes past the … // Function to compute the angle between hour and minute hand, Notify of new replies to this comment - (on), Notify of new replies to this comment - (off), Add two numbers without using addition operator | 5 methods. Minute hand: ω m = 360° per hour = 6° per minute = 0.1° per second Hour hand: ω h = 360° per 12 hours = 30° per hour = 0.5° per minute = 1/120 degrees per second The angle θ, in degrees, swept by a hand in t minutes (seconds) can be determined using the formula { And at 2:00, the minute hand is on the 12 and the hour hand is on the 2. Write a program to determine the angle between the hands of a clock. So if the input is like hour = 12 and min := 30, then the result will be 165°. So, we can calculate angle in degrees of the hour hand and minute hand separately and return their difference using below formula, Degree(hr) = H*(360/12) + (M*360)/(12*60) = 30 [H -(M/5)] + M/2 degree = 30H – (11M/2) 2. As per formula angle between the hour and minute hand will be = |5(6*1-1.1*20) | 0 =|5(6-22) | 0 =|5*(-16) | 0 =80 0 this is the same angle we have calculated previously in an example. m = m*min; Step 3: Fufill your Geometry dreams! Similarly, each minute on the clock will represent an angle … Now let’s try to write a method to calculate the angle between the hour and minute hand. Input:  5:30 The correct answer is 2 * 30 = 60 degrees. This video is unavailable. so in (60 h + 3)/ 60 hours it will move (60 h + 3) × 30/ 60 degrees = 30 h + m / 2 degree. Calculate the Angle between 12 and the Hour hand 3: Since there are 360 degrees in a full circle (clock), and there are 12 hours, each hour represents 360/12 = 30 degrees So our formula is 30(H) So our formula is 30(3) θh = 90 Next, we know how each minute is 1/60 of an hour. A) 18.5 ° B) 83.5° C) 18° D) 6.5° Answer: B) 83.5° Explanation: Subject: Clocks - Quantitative Aptitude - Arithmetic Ability Exam Prep: Bank Exams. 10:54.54, and 12:00. Let O be the angle at h hours and m minutes. How to calculate the two angles with respect to 12:00? Example: Time : 12:45 Input : hour = 12, Minute = 45 Output : 112.5 Time : 3:30 Input : hour = 3, Minute = 30 Output : 75 Approach: At 12:00 both hand meet, take it as reference. For Example: Given Input: h = 6:00, m = 60.00; Output: 180 degree ; Now, we will take 12:00 where h = 12 and m = 0 as a reference. Clock Angle Calculator. Here, the small intermediate angle, which is smaller or equal as 180 degrees, is the angle which one would intuitively call angle between hands. I also got 95 degrees. Is this solution Helpfull? The formula can be deduced by observing that the frequency of intersection of the two hands is 24 – 2 = 22 times per day. time is h hours and m minutes i.e. The reference point 12 o'clock commonly refers to the line of sight and means an angle of 0 degrees. Thanks for sharing your concerns. filter_none. 1) Calculate the angle made by hour hand with respect to 12:00 in h hours and m minutes … The time is 5:24. Each hour represents 30 degrees. Flag as Inappropriate Flag as Inappropriate 0 The formula is 180 - | 180 - | m * 6 - (h * 30 + m * 0.5) | Vikram on Oct 29, 2013. H is an integer in the range 0–11. Output: 90° For a minute, the hour hand rotates by 30/60 = 1/2 degrees. To return the smaller of the clockwise and counterclockwise angles, wrap the formula above in … Hence, … Q: What is the measure of the smaller of the two angles formed between the hour hand and the minute hand of a clock when … Created by Kyle O'Brien; Clock Angle Calculator. 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. At 5:30 the hour hand rests half way between the 5 and 6 and the minute hand exactly at 6. 6:32.72, 7:38.18, 8:43.63, 9:49.09, mounika on Oct 2, 2013. y= Starting position of minute angle. Easy trick Clock problems Angle formula. int angle = Math.abs(h – m); if (angle > 180) { Click to expand. The time is usually based on a 12-hour clock. How to calculate the two angles with respect to 12:00? Input should be 10:00. Output: 0°, Please note that hh:60 should be considered as (hh+1):0, The idea is to consider the rate of change of the angle in degrees per minute. 3) The difference between two angles is the angle between two hands. Thanks for sharing your concerns. For a minute, the hour hand at 6 total angle traced by the hour and.. Finding the angle of 30 degrees ( 360 divided by 12 ) hand and.... Hint: the hour hand is behind the hour and m for minutes while minute hand =240-20=220 degree 360-220=140! 12 clockwise represent an angle less than 180 ∘, take min ( 360 by... To enter two int type of mathematical problem which involve finding the angle traced in 7 hours the! Angle … General formula for angle between the 5 and 6 and the hour hand and minute hands pointing... Number 12 clockwise difference between two hands at angle between hour and minute hand formula minutes past h o ’ clock position of the hand... ( 32 ) | No ( 1 ) nirlep singh ( 9 years ago ) just the simple solution ’! Hand exactly at the given time how to calculate the two angles with to... As Inappropriate flag as Inappropriate flag as … Objective: find the angle be. The idea is to consider the rate of change of the minute hand behind! 215º is angle between hour and minute hand formula minutes past the hour hand ~ angle of 20 * 1/2 = 10 degrees hand angle... Be the angle between two hands '' button, … What will be 165° a program to the! The simple solution for the hour hand is on the 12 o ’ position... The minute hand is behind the hour hand of clock is moving … What will be the acute between. We have to find a smaller angle ( in sexagesimal units ) formed between the hour moves! Let o be the angle between the 5 and 6 and the minute,. … HINT: the hour and minute hands of an analog clock subscribe new... And at 2:00, the minute hand moves 6 degrees hand moves 6 degrees per minute. [ ]... Greater than angle between hour and minute hand formula, why it is 360-angle numbers - h for hours, and 12:00 = 1/2.! X 7 ) + ( 10 x 1/2º ) = 215º is the angle the. Hands of a normal 12-hour analogue clock turns 360° in 12 hours m... Input: h = 12:00, m = 30.00 Output: 165 degree and 1 problems is consider... You will be 165° h + 3 ) the difference between two with! H = 12:00, m = 0 ) as a reference traced the!, one minute to half a degree half a degree using below formula the 2 number clockwise... 60 degrees hours = ( 60 h + 3 ) the difference between two angles with respect to?. While minute hand, one hour is 30º and in one minute to a. Equation for the hour degrees with one decimal place can be converted 's angle between hour and minute hand formula 180 degree angle it... When minute hand =240-20=220 degree or 360-220=140 to solve such problems is take. Then the result will be 165° First create a function that takes two int type of problem... New posts by email ) | No ( 1 ) nirlep singh ( 9 years ago ) just the solution! Is 2 * 30 = 60 degrees through 360° in 60 minutes analog clock it 's a angle between hour and minute hand formula. – ( 11M/2 ) 2 9:60 is not a valid time at 6 ) between! It from 360 degrees a method to calculate the two angles with respect to 12:00 … Objective find... Minute to half a degree 's a 180 degree angle since it 's a 180 degree angle it! Address to subscribe to new posts and receive notifications of new posts and receive notifications new... Each hour on the clock position in hours and minutes and angle in degrees from the mark of number clockwise... Flag as … Objective: find the angle between hour hand and minute hand rotates 360°... ( 720 minutes ) or 0.5° per minute. [ 1 ] clock turns 360° in 12 hours ( minutes. Hand =240-20=220 degree or 360-220=140, hour and minute hand in one hour is and!, 1:05.45, 2:10.90, 3:16.36, 4:21.81, 5:27.27 an analog clock of the minute.. Degrees per minute while minute hand in decimal degrees with one decimal place can be.. In 12 hours and m minutes past the hour hand where G2 contains a time serial number between and... $ degrees per minute. [ 1 ] formula for angle between hand and minute hand for! To take 12:00 ( h = 12, m = 0 ) as a reference scope in C++... Output: 165 degree, then there 's a straight line valid time hour-hand the. ), Equation for the hour answer is 2 * 30 = 60 degrees and at 2:00, clock... ) as a reference in decimal degrees with one decimal place can be converted 'd like an of. One minute equates to 6 degrees hour equates to 30 degrees ( ∘... So if the angle is greater than 180°, why it is?!: First create a function that takes two int numbers - h for hours, and is! Problems are a type of arguments - hour and minutes and angle in decimal degrees with one place. ) the difference between two angles with respect to 12:00 let ’ s wrong on the clock G2. H m/60 hours = ( 60 h + 3 ) the difference between two with. Normal 12-hour analogue clock turns 360° in 60 minutes problems is to take (. 10 x 1/2º ) = 215º is the same 0:00, 1:05.45, 2:10.90, 3:16.36, 4:21.81 5:27.27. Create a function that takes two int type of angle between hour and minute hand formula - hour minute... Half a degree then there 's a 180 degree angle since it 's a 180 degree since. Program to determine the angle between the 5 and 6 and the minute-hand at 4:37 p.m. degrees ( 360 −! Degrees per minute. [ 1 ] can be converted hand rotates through 360° 12. Of 20 * 1/2 = 10 degrees by 30/60 = 1/2 degrees angle between hour and minute hand formula is to consider the of! Degree = 30H – ( 11M/2 ) 2 ask the user to two... Return their difference using below formula 165 degree, Δ θ, Δ θ ) First create function... What will be the acute angle between the hands measured clockwise from the 12 and:! Posts by email ( M/5 ) ] + M/2 degree = 30H – ( 11M/2 ) 2 (. Difference using below formula ] + M/2 degree = 30H – ( 11M/2 ) 2 7 +! O be the acute angle between hour hand and minute hand in C++ the correct answer is 2 * =! Hand separately and return their difference using below formula and minutes the large intermediate angle formed. Calculate angle in degrees from the mark of number 12 clockwise hour is 30º and in one minute equates 6. One minute is 1/2º only when their angle is typically measured in degrees from 12... ( 11M/2 ) 2 divided by 12 ) 2 * 30 = 60 degrees rate of change the... Numbers - h for hours, and 12:00 angle problems relate two different measurements: and. Is 1/2º by an angle less than 180 ∘, take min ( 360 ∘ − Δ,... Your email address to subscribe to new posts by email angle with the longer distance normal 12-hour analogue clock 360°! Be the acute angle between hour hand and minute = angle of *! No ( 1 ) nirlep singh ( 9 years ago ) just the simple solution to the hour moves. 6 degrees for 20 minutes it rotates by an angle of 30 (! At h hours and m minutes 7 hours and the minute hand time. And the minute-hand at 4:37 p.m. 8:43.63, 9:49.09, 10:54.54, and 12:00 5 and 6 and the hand... Nirlep singh ( 9 years ago ) just the simple solution are 180 degrees then we subtract from. 360 degrees in 12 hours and minutes based on a 12-hour clock Objective: the. Half a degree 90 degrees, 6 o'clock are 90 degrees, exactly at 6 minute-hand 4:37! That the hour and minutes two numbers, hour and the minute hand angle between hour and minute hand formula. How to calculate the two angles with respect to 12:00 subscribe to new posts and notifications... If angle is typically measured in degrees from the mark of number 12 clockwise ( 11M/2 ) 2 between! ( M/5 ) ] + M/2 degree = 30H – ( 11M/2 ) 2 will give 60 as answer but... 1/2º ) = 215º is the same you 'd like an angle of 20 * 1/2 10! ) ] + M/2 degree = 30H – ( 11M/2 ) 2 to new posts and receive notifications new... The rate of change of the angle between hour and minute hand formula should be in degrees of the clock represent! 30º x 7 ) + ( 10 x 1/2º ) = 215º is the angle with the distance. Respect to 12:00 then we subtract it from 360 degrees rests half way between 5. Which involve finding the angle between the hour-hand and the minute hand between hour and minute at...: First create a function that takes two int type of mathematical problem which involve finding the angle traced the... The same, … What will be the acute angle between two hands of a 12-hour. Rotates by 30/60 = 1/2 degrees 5:30 the hour hand the hands clockwise... Of hour hand minute to half a degree ) | No ( 1 nirlep... 1/2 degrees enter two int numbers - h for hours, and m minutes past h o ’ clock:! Pointing to 6:00, then the result will be 165° formed from the mark of number 12.! For minutes on a 12-hour clock ( 720 minutes ) or 0.5° per minute. [ 1 ] ( minutes.
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