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Distance, often assigned the variable d, is a measure of the space contained by a straight line between two points.^{[1] X Research source } Distance can refer to the space between two stationary points (for instance, a person's height is the distance from the bottom of his or her feet to the top of his or her head) or can refer to the space between the current position of a moving object and its starting location. Most distance problems can be solved with the equations d = s_{avg} × t where d is distance, s_{avg} is average speed, and t is time, or using d = √((x_{2}  x_{1})^{2} + (y_{2}  y_{1})^{2}), where (x_{1}, y_{1}) and (x_{2}, y_{2}) are the x and y coordinates of two points.
Steps
Method 1
Method 1 of 2:Finding Distance with Average Speed and Time

1Find values for average speed and time. When you try to find the distance a moving object has traveled, two pieces of information are vital for making this calculation: its speed (or velocity magnitude) and the time that it has been moving.^{[2] X Research source } With this information, it's possible to find the distance the object has traveled using the formula d = s_{avg} × t.
 To better understand the process of using the distance formula, let's solve an example problem in this section. Let's say that we're barreling down the road at 120 miles per hour (about 193 km per hour) and we want to know how far we will travel in half an hour. Using 120 mph as our value for average speed and 0.5 hours as our value for time, we'll solve this problem in the next step.

2Multiply average speed by time. Once you know the average speed of a moving object and the time it's been traveling, finding the distance it has traveled is relatively straightforward. Simply multiply these two quantities to find your answer.^{[3] X Research source }
 Note, however, that if the units of time used in your average speed value are different than those used in your time value, you'll need to convert one or the other so that they are compatible. For instance, if we have an average speed value that's measured in km per hour and a time value that's measured in minutes, you would need to divide the time value by 60 to convert it to hours.
 Let's solve our example problem. 120 miles/hour × 0.5 hours = 60 miles. Note that the units in the time value (hours) cancel with the units in the denominator of the average speed (hours) to leave only distance units (miles).
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3Manipulate the equation to solve for other variables. The simplicity of the basic distance equation (d = s_{avg} × t) makes it quite easy to use the equation for finding the values of variables besides distance. Simply isolate the variable you want to solve for according to the basic rules of algebra, then insert values for your other two variables to find the value for the third. In other words, to find your object's average speed, use the equation s_{avg} = d/t and to find to find the time an object has been traveling, use the equation t = d/s_{avg}.
 For instance, let's say that we know that a car has driven 60 miles in 50 minutes, but we don't have a value for the average speed while traveling. In this case, we might isolate the s_{avg} variable in the basic distance equation to get s_{avg} = d/t, then simply divide 60 miles / 50 minutes to get an answer of 1.2 miles/minute.
 Note that in our example, our answer for speed has an uncommon units (miles/minute). To get your answer in the more common form of miles/hour, multiply it by 60 minutes/hour to get 72 miles/hour.

4Note that the "s_{avg}" variable in the distance formula refers to average speed. It's important to understand that the basic distance formula offers a simplified view of the movement of an object. The distance formula assumes that the moving object has constant speed — in other words, it assumes that the object in motion is moving at a single, unchanging rate of speed. For abstract math problems, such as the ones you may encounter in an academic setting, sometimes it's still possible to model an object's motion using this assumption. In real life, however, this model often doesn't accurately reflect the motion of moving objects, which can, in reality, speed up, slow down, stop, and reverse over time.
 For instance, in the example problem above, we concluded that to travel 60 miles in 50 minutes, we'd need to travel at 72 miles/hour. However, this is only true if travel at one speed for the entire trip. For instance, by traveling at 80 miles/hr for half of the trip and 64 miles/hour for the other half, we will still travel 60 miles in 50 minutes — 72 miles/hour = 60 miles/50 min = ?????
 Calculusbased solutions using derivatives are often a better choice than the distance formula for defining an object's speed in realworld situations because changes in speed are likely.
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Method 2
Method 2 of 2:Finding the Distance between Two Points

1Find two points spatial coordinates. What if, rather than finding the distance that a moving object has traveled, you need to find the distance between two stationary objects? In cases like this, the speedbased distance formula described above won't be of any use. Luckily, a separate distance formula^{[4] X Research source } can be used to easily find the straightline distance between two points. However, to use this formula, you'll need to know the coordinates of your two points. If you're dealing with onedimensional distance (such as on a number line), your coordinates will be two numbers, x_{1} and x_{2}. If you're dealing with distance in two dimensions, you'll need values for two (x,y) points, (x_{1},y_{1}) and (x_{2},y_{2}). Finally, for three dimensions, you'll need values for (x_{1},y_{1},z_{1}) and (x_{2},y_{2},z_{2}).

2Find 1D distance by subtracting the value of the coordinates for the two points. Calculating onedimensional distance between two points when you know the value for each is a cinch. Simply use the formula d = x_{2}  x_{1}. In this formula, you subtract x_{1} from x_{2}, then take the absolute value of your answer to find the distance between x_{1} and x_{2}. Typically, you'll want to use the onedimensional distance formula when your two points lie on a number line or axis.
 Note that this formula uses absolute values (the " " symbols). Absolute values simply mean that the terms contained within the symbols become positive if they are negative.
 For example, let's say that we're stopped by the side of the road on a perfectly straight stretch of highway. If there is a small town 5 miles ahead of us and a town 1 mile behind us, how far apart are the two towns? If we set town 1 as x_{1} = 5 and town 2 as x_{1} = 1, we can find d, the distance between the two towns, as follows:
 d = x_{2}  x_{1}
 = 1  5
 = 6 = 6 miles.

3Find 2D distance by using the Pythagorean theorem.^{[5] X Research source } Finding distance between two points in twodimensional space is more complicated than in one dimension, but is not difficult. Simply use the formula d = √((x_{2}  x_{1})^{2} + (y_{2}  y_{1})^{2}). In this formula, you subtract the two x coordinates, square the result, subtract the y coordinates, square the result, then add the two intermediate results together and take the square root to find the distance between your two points. This formula works in the twodimensional plane — for example, on basic x/y graphs.
 The 2D distance formula takes advantage of the Pythagorean theorem, which dictates that the hypotenuse of a right triangle is equal to the square root of the squares of the other two sides.
 For example, let's say that we have two points in the xy plane: (3, 10) and (11, 7) that represent the center of a circle and a point on the circle, respectively. To find the straightline distance between these two points, we can solve as follows:
 d = √((x_{2}  x_{1})^{2} + (y_{2}  y_{1})^{2})
 d = √((11  3)^{2} + (7  10)^{2})
 d = √(64 + 289)
 d = √(353) = 18.79

4Find 3D distance by modifying the 2D formula. In three dimensions, points have a z coordinate in addition to their x and y coordinates. To find the distance between two points in threedimensional space, use d = √((x_{2}  x_{1})^{2} + (y_{2}  y_{1})^{2} + (z_{2}  z_{1})^{2}). This is a modified form of the twodimensional distance formula described above that takes the z coordinates into account. Subtracting the two z coordinates, squaring them, and proceeding through the rest of the formula as above will ensure your final answer represents the threedimensional distance between your two points.
 For example, let's say that we're an astronaut floating in space near two asteroids. One is about 8 kilometers in front of us, 2 km to the right of us, and 5 miles below us, while the other is 3 km behind us, 3 km to the left of us, and 4 km above us. If we represent the positions of these asteroids with the coordinates (8,2,5) and (3,3,4), we can find the distance between the two as follows:
 d = √((3  8)^{2} + (3  2)^{2} + (4  5)^{2})
 d = √((11)^{2} + (5)^{2} + (9)^{2})
 d = √(121 + 25 + 81)
 d = √(227) = 15.07 km
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Community Q&A

QuestionWhat is the formula for finding the distance traveled of a moving object?DonaganTop AnswererDistance traveled = rate (velocity) multiplied by time elapsed. D = (v)(t).

QuestionHow do I calculate distance on a map?DonaganTop AnswererMaps typically have a scale of miles. Compare a distance shown on a map with its scale.

QuestionHow do I calculate the distance traveled by a courier service truck on 20 trips?DonaganTop AnswererAdd together the distance traveled on each of the 20 trips. If all the trips are the same, just multiply the distance of one trip by 20.

QuestionA woman standing before cliff claps her hands, and 2.8 seconds later she hears the echo. How far away is the cliff?DonaganTop AnswererIt takes 1.4 seconds for sound to travel one way from her hands to the cliff. Therefore, multiply the speed of sound by 1.4 seconds. The speed of sound is 343 meters per second or 1,125 feet per second.

QuestionHow do I find distance and average speed from a to b if the duration of a journey is 2 minutes?Community AnswerCrossmultiply the duration out of an hour and the amount of distance traveled in the duration.

QuestionHow can I calculate how long it will take me to walk 0.1 mile?Community AnswerYou have to know how fast you walk. Divide the distance by your speed. For example, if you walk four miles an hour (a brisk pace), divide (in this case) 0.1 mile by 4 miles/hour. That equals 1/40 of an hour, which is 1½ minutes.

QuestionHow do I check the speed of a vehicle by counting the time between lampposts?DonaganTop AnswererIf you know both the distance between lampposts and the time it takes to travel from one post to the next, divide the distance by the elapsed time. That will give you a speed in feet per second, meters per second, or whatever units you're using. You may want to convert that to other units such as miles per hour or kilometers per hour.

QuestionIf a field is 875 meters long, how many full laps must I run to complete 100 kilometers?DonaganTop AnswererA full lap would consist of 1,750 meters. 100 kilometers is 100,000 meters. 100,000 divided by 1,750 equals slightly more than 57 full laps.

QuestionHow can I calculate hours into distance?DonaganTop AnswererYou would need to know the speed (distance per time consumed). Multiply the speed by the hours to get the total distance traveled.

QuestionAn aircraft covers 3519 km from P to Q and 10,948 km from Q to R on the earth's surface. How do I calculate the time taken by the aircraft to cover the distances PQ and QR at an average speed of 800 km/h?DonaganTop AnswererAdd the two distances together to find the total distance traveled. Then divide by the average speed to calculate the time elapsed (in hours).
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Tips
References
 ↑ https://www.khanacademy.org/math/basicgeo/basicgeometrypythagoreantheorem/pythagoreantheoremdistance/v/distanceformula
 ↑ http://www.softschools.com/formulas/physics/distance_speed_time_formula/75/
 ↑ https://www.geeksforgeeks.org/timespeeddistance
 ↑ https://www.purplemath.com/modules/distform.htm
 ↑ https://www.khanacademy.org/math/basicgeo/basicgeometrypythagoreantheorem/pythagoreantheoremdistance/v/examplefindingdistancewithpythagoreantheorem
About This Article
To calculate distance, start by finding the average speed the object traveled and the amount of time it was traveling for. Make sure you're using the same units for the average speed and time or else your calculation won't be accurate. For example, if you're using miles per hour for the speed, you would need to use hours, not minutes or seconds, for the time. Once you have your 2 values, just multiply them together to get the distance the object traveled. To learn how to calculate the distance between 2 points, scroll down!