Distance Between Two Points Calculator - step by step calculation, formula & solved example to find the exact length between 2 co-ordinates (x_{1}, y_{1}) & (x_{2}, y_{2}) in the XY plane or two dimensional geographical co-ordinate system, by applying pythagoras theorem. According to the rule of right triangle, squared hypotenuse is equal to the sum of the squares of the other two sides. The same formula is applied in this distance calculator to find the length between the two given coordinates (x_{1}, y_{1}) and (x_{2}, y_{2}) in the XY plane. The distance between two point formula, example & calculator helps user to understand, practice and verify such calculations.
Formula
Based on the Pythagorean theorem, the formula to find the distance between two points is
where
d is the distance
Solved Example
The below solved example let users to understand how the example values are being used to calculate the length between two locations.
Problem:
The longitude and latitude for San Francisco are 37.7833 & 122.4167 degrees respectively and the longitude and latitude for Los Angeles are 34.0500 & 118.2500 degrees respectively. What is the distance between the two locations?
Solution:
Let's x_{1} be the longitude & y_{1} be the latitude of San Francisco
x_{1} = 37.7833 & y_{1} = 122.4167
Let's x_{2} be the longitude & y_{2} be the latitude of Los Angeles
x_{2} = 34.0500 & x_{2} = 118.2500
Apply the above values in the formula
= √((x_{2} - x_{1})^{2} + (y_{2} - y_{1})^{2})
= √((34.05 - 37.7833)^{2} + (118.25 - 122.4167)^{2})
= √(13.93752889 + 17.36138889000005)
= √(31.29891778000005)
= 5.594543572088795
Distance in degrees = 5.5945
The respective conversion factor should be multiplied with 5.5945 to convert it into miles or kilometers or any other distance measurement units.
It's an analytical geometry calculator which provides the complete step by step calculation to find the length between two points on the XY plane, thus users also determine the distance between the countries or places or locations on the two dimensional map or geographic coordinate system. For calculating the linear length or distance between two locations on geographic coordinate system, first user have to find the distance based on the longitude & latitude points, then the answer should be multiplied with the respective weighing or conversion factor to measure it in miles or kilometers or any other units. It's a featured online geometry tool provides the step by step calculation for each calculation done by using this calculator.
The linear distance between 2 points or location calculation is being used in various applications such as finding the length of a fence, distance between countries or planning a trip or creating a 2 dimensional projected map etc. When it comes to online to verify or perform such calculations, this distance between two points calculator, formula & example calculation may assist users to understand, perform & verify such calculations.