In the real world, latitude and longitude play an important role in several fields and calculations, but one of their most common uses is measuring distances between points. As a data company, we want to see our customers use this calculation to improve efficiencies in their business.
In fields like logistics, transportation, air travel, and more, these calculations deliver a key component for examining the fastest, shortest, and most efficient routes between two locations. As a data and analytics company, we help companies visualize this information in dashboards, and it is used by managers to make better decisions on delivery times, destinations, and providers.
The distance between two points on a 2D coordinate plane can be found using the following distance formula. D = √ (x2 - x1)2 + (y2 - y1)2. Where (x 1, y 1) and (x 2, y 2) are the coordinates of the two points involved. The order of the points does not matter for the formula as. A minute of arc, arcminute (arcmin), arc minute, or minute arc, denoted by the symbol ′, is a unit of angular measurement equal to 1 / 60 of one degree. Since one degree is 1 / 360 of a turn (or complete rotation), one minute of arc is 1 / 21 600 of a turn. The nautical mile (nmi) was originally defined as a minute of latitude on a spherical Earth, so the actual Earth circumference is very. An online distance calculator is exclusively programmed to calculate the distance between two places with the help of longitudinal and latitude angles, respectively.
Today, the calculation used for this is mostly handled digitally, by programs and algorithms designed specifically to uncover the answer. Even so, understanding the basics behind the concept and comprehending how the math works is vital to ensuring that you understand exactly how to calculate distance using latitude and longitude. In this blog, we want to start with the basics and go through how it works. We’ve included links to some of our customer case studies, and some example dashboards, for those who want more.
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One second of latitude equals 100.39 feet.here is the proof:one degree = 60 Nautical Miles or 69 Statute miles; (conversion factor 69/60 = 1.15)one minute minute = 1 Nautical Mileone second = 1 Nautical Mile / by 60 seconds = 0.01666 of a Nautical Mileuse conversion factor of 1.15 x 0.01666 = 0.019159 x a Statute Mile -equals (5420 ft X 0.019159) = 100.39 feet per second of latitudeRead. Embedded application for modelling the total magnetic field gradient of typical anomalies.Embedded application for modelling the total magnetic field gradient of typical anomalies.Embedded.
Read MoreLatitude and longitude basics
Latitude and longitude are coordinates system that let anyone determine the location of a single point on any part of the earth’s surface. Latitude refers to the angle of a given point measured from the equator and with a vertex at or near the center of the earth (depending on the type of latitude measured). As you move north or south, the latitude will increase from 0° to 90.
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Longitude is a similar measure, although it measures location to the east or west of the prime meridian—the imaginary line that connects the north and south poles and crosses Greenwich, London. The calculation for longitude uses the angle made from a line that goes from the earth’s center to the intersection of the prime meridian and the equator and then extends east or west. Unlike latitude, however, the earth’s longitude at both east and west reaches 180°.
How to calculate distances using longitude and latitude
One of the most common ways to calculate distances using latitude and longitude is the haversine formula, which is used to measure distances on a sphere. This method uses spherical triangles and measures the sides and angles of each to calculate the distance between points. It was traditionally utilized in pre-digital navigation and is based on calculations that take into account the earth’s radius, as well as the fact that on a sphere shapes are different from their flat counterparts. Namely, spheres do not have parallel lines, and lines are considered “great circles” so any two lines will intersect at two points.
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These equations can be carried out manually—with some difficulty—but today, there are several easy ways to calculate distances digitally, assuming you have the correct data, to begin with. This includes knowing the start and end point (they can be the cities, streets, or even smaller distances), as well as the geographical coordinates of each point. For example, if you measured the distance between New York and Tokyo, their respective coordinates would be as follows:
- New York (latitude 40.7128°N, longitude 74.0060°W)
- Tokyo (latitude 35.6895°N, longitude 139.6917°E)
Keep in mind that for calculation purposes, southern latitudes can be expressed as negative numbers, as can western longitudes. With these numbers in hand, you can plug them into the haversine formulae,
a = sin²(Δφ/2) + cos φ1 ⋅ cos φ2 ⋅ sin²(Δλ/2)
c = 2 * atan2( √a, √(1−a) )
d = R * c
Where φ represent the latitudes, and λ represent the longitudes.
Alternatively, you can use a latitude and longitude calculator, which uses an algorithm based on the formula to find the distance.
What is the calculation useful for?
In the pre-GPS and computer days, the haversine formula was a vital aspect of finding the most efficient distance between two points. Today, this calculation is still important, and it plays a major role in several industries.
For logistics, where distance and time can be the difference between profits and losses, finding the shortest possible point between two locations can greatly improve travel times and reduce wasted resources. Skyrim special edition specs. More importantly, it can help calculations that feature several moving parts. For instance, an airline that has to fly between two locations with a layover can find the most efficient path to fly, reducing jet fuel use, time that a single airplane is occupied, and increase the number of flights possible in a day. Even for delivery services, it can assist companies with planning the best possible routes for their teams to travel while reducing overall transit times, improving delivery speeds, and generating revenues.
While pen and paper calculations are time-consuming—and not entirely necessary—understanding how to calculate distances using latitude and longitude can help any company identify better routes to cut down the distances their planes, ships, cars, and teams must travel.
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Read MoreThe Earth is, more or less, a sphere. So, if we are trying to explain a specific location, or an absolute location, how do we do that?
Let's pretend there are no states, no cities, no addresses to make locations easy to find. That shouldn't be too hard, there are several places in the world where that is true. So, how do we find a specific place? Well that's harder. Not only did it take centuries to figure out, but it's complicated to explain. Basically, though, it had to do with figuring out the sun's location in relation to time. It all had to do with angles and since angles are measured in degrees (and minutes and seconds, but we won't get into that, either), we will measure exact locations in degrees as well.
So, things would be so much easier if the Earth was flat. But it's not. But we are going to do our best to make it seem like it. We are going to draw lines on our sphere.
So, things would be so much easier if the Earth was flat. But it's not. But we are going to do our best to make it seem like it. We are going to draw lines on our sphere.
Will that help us locate a place on the Earth? Sure it would, but we have to make some rules:
First, those lines need names.
First, those lines need names.
What are we going to call the lines that go around our FAT earth like a belt?
Lines of Latitude |
Lines of LAT-itude. Latitude, Fatitude.
Lines of Longitude |
What are we going to call the LONG up and down lines?
Lines of LONG-itude. (They are also called Meridians)
So now we have some simple vocabulary, but that's not enough. We need to define zero. That will be the starting line. Or the place where the counting begins.
The line of latitude that goes around the center of the Earth is the equator. It is an equal distance from both the North and South Poles. It's 0°. It separates the Earth into two parts. Into halves. Into half-spheres. The correct term for that is hemispheres.
If you travel 10 ° North of that, the degrees of Latitude are labeled 10° N. If you travel 45° South of the Equator, you are at 45°S.
It sounds simple, right? You travel towards the North Pole (90° N) from the Equator, you are in the Northern Hemisphere and so are labeled North. Don't get confused. Lines of latitude RUN East and West, but are labeled for which hemisphere they are progressing towards a pole in. Lines of latitude are labeled North or South.
So which hemisphere is the US in? Are we closer to the North Pole or the South Pole?
So which hemisphere is the US in? Are we closer to the North Pole or the South Pole?
The Earth can also be divided into Eastern and Western Hemispheres. Hemi means half. So, you can only have two hemispheres at one time.
To divide the Earth into Eastern and Western Hemispheres, we have two important lines of longitude. Since longitudinal lines are also called meridians, that should give you a hint to what the main meridian is called. It's the Prime Meridian!
The Prime Meridian is labeled 0°. As you travel 5 ° West of the Prime Meridian, you are at 5° W. Make sense? So, if you travel 70 degrees East of the Prime Meridian, you are at 70° E. Meridians, or lines of longitude run North and South, but are labeled by which hemisphere they are moving away from the Prime Meridian in. Lines of Longitude are labeled either East or West.
The crazy thing is that unlike the equator, it didn't matter in the least where the Prime Meridian was. The equator, by definition, is equidistant from the North and South Poles, but there is nothing to be half way between as far as longitude. But, at the time when it was decided exactly which meridian would be the Prime Meridian (which sounds like a Transformer), one country had a bigger voice than the rest of the others.
In 1884, it was determined that the Prime Meridian would go through Royal Observatory in Greenwich, England (London). Not every country used this as 0° Longitude right away, but today it is universally recognized.
In 1884, it was determined that the Prime Meridian would go through Royal Observatory in Greenwich, England (London). Not every country used this as 0° Longitude right away, but today it is universally recognized.
Which hemisphere is the US in? Are we West or East of the Prime Meridian?
Prime Meridian |
But the Prime Meridian is only one boundary of the Eastern and Western Hemispheres.
Look at the map. The Prime Meridian doesn't cut through the entire globe.
There is a second line that separates the Eastern and Western Hemispheres!
International Date Line |
It's called the International Date Line!
The International Date Line is labeled 180°. That makes sense. There are 360° in a circle, and half of that is: 180°!
You might wonder: Why is it jagged? It's actually a really important time zone border. Not only would it be frustrating to have a country in two different time zones, but at this specific boundary, the date changes. So, while it could be Friday, August 7th, here, it's very possibly Saturday, August 8th in Japan. (I know that sounds crazy.. just trust me.. it's all about the rotation of the Earth)
Let's look at the Earth in a way that we can see all the hemispheres at once.
These are called quadrants.
Quadrants in the Northern Hemisphere are all labeled N for North.
Quadrants in the Southern Hemisphere are all labeled S for South. The same is true for quadrants in the Western and Eastern Hemispheres. They are labeled W and E.
If we divide the Earth into four pieces, then each piece is in two hemispheres at the same time.
So, let's say we want to find a location in North America. Which quadrant is that in?
If we were trying to find a location in North America using latitude and longitude, we now know that the coordinates are N and W. But let's be more specific.
In 2005, the US suffered through one of the worst hurricane's in it's history. What is the absolute location of Hurricane Katrina?
New Orleans is 30° N of the equator and 90° W of the Prime Meridian. Do you see that on the map? So, our location is 30°N, 90°W.
If you have a city, it seems useless to use latitude and longitude, but let's say that you discovered what must be an alien spaceship only partially visible under the sand in southwestern New Mexico. You are concerned that when you come back, it might be completely buried. So how will you find it again?
You are going to use latitude and longitude.
But what if our location also isn't nicely situated on one of the latitude or longitude lines? Well, we have to estimate.
Our spaceship siting is marked with the X. Let's do latitude first. It's between 30° and 40° N of the equator. Do you see that? Is it half way in between? If that were so, it would be 35°N. Be careful here. Do not confuse the northern border of New Mexico for a line of latitude. Do you see that it seems a little closer to 30° than halfway? It looks like it's at about 34°N. (Remember: North because we are moving towards the North Pole from the Equator.)
What about our longitude? It's between 100°W and 110°W of the Prime Meridian. (That's hard to tell on this map, but if a line isn't labeled, look at some other labeled lines and see by what number the cartographers were counting. Sometimes it's 5°, 10°, 15°.. just make sure you look and don't guess!)
Is the X closer to 100° or 110°? It looks closer to 110°. Is it about halfway? Not really. Let's call that 107° W. Be careful with longitude. I have two suggestions:
Distance Of 1 Second Latitude
- Make sure you follow the curvature of the longitude lines when estimating. The Earth is a sphere, so our lines of longitude show that. You might want to draw a straight line between the lines of longitude to estimate, but you can't. It has to curve.
- Make sure you check to see if the numbers are going up or down. It would have been easy to say that that was 103°, when we started looking at the halfway point. But it's closer to 110° than 100°, so it's about 107°W.
Definitions:
Absolute Location: A point on the earth's surface defined in terms of a coordinate system such as latitude and longitude.
Equator:thegreatcircleoftheearththatisequidistantfromtheNorthPoleandSouthPole.
The0°meridianfromwhichtheothermeridiansorlinesoflongitudearecalculated,usuallytakentopassthroughGreenwich |
International Date Line: Thelineapproximatelyfollowingthe180°meridianfromGreenwichontheeastsideofwhichthedateisonedayearlierthanonthewest.
Latitude: Themeasurement,in degrees, ofaplace'sdistancenorthorsouthofthe equator.
Longitude:Ameasurement,in degrees, ofaplace'sdistanceeastorwestofthe prime meridian, whichrunsthrough Greenwich, England.
Hemisphere: EitherthenorthernorsouthernhalfoftheEarthasdividedbytheequator,ortheeasternorwesternhalfasdividedbyameridian,especiallytheprimemeridian.
Distance 1 Second Latitude &
Here are a couple of good websites for further explanation:
This is a wonderful website for creating maps to use in class or for practice.