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### Formula for Radial Latitudes and Longitudes

```Date: 10/15/2002 at 00:28:44
From: Bill Tait
Subject: Formula for radial latitudes and longitudes

I have a database of places that lists a latitude and longitude for
each place. I want to make a radius search tool that returns all
places based on latitude/longitude within a certain radius (say
5 miles) of a given place. I have already created one that will return
results of a square or rectangle, but I can't figure out how to do
this when it's a radius. Obviously calculating the area is easy, but
to display a list of every lat/lon within that area is the problem.

Any ideas?

Regards,
Bill Tait
```

```
Date: 10/15/2002 at 08:31:37
From: Doctor Rick
Subject: Re: Formula for radial latitudes and longitudes

Hi, Bill.

We get lots of questions like this. Here's what you need to do. For
each point in your database, compute the distance between that point
and the given point. If it's less than the specified distance, add it
to your list of places within the circle. I suggest the following
algorithm for calculating distance:

Haversine Formula
http://mathforum.org/library/drmath/view/51879.html

If you're only considering short distances like 5 miles, you can use
an approximation for short distances in which the earth can be
regarded as flat. It's explained here:

Circle of Radius 1 km around Given Latitude/Longitude
http://mathforum.org/library/drmath/view/61135.html

Using this method, you will convert the longitude (a2) and latitude
(b2) of each point, with a1 and b1 equal to the longitude and
latitude of the given point, to x and y, then calculate

r^2 = x^2 + y^2

If this is less than the given distance squared, add the point to the
list. This approximation requires fewer trig functions, but it still
requires one. It only needs to be computed once for the given point,
however, not for each point in the database.

- Doctor Rick, The Math Forum
http://mathforum.org/dr.math/
```
Associated Topics:
College Euclidean Geometry
College Higher-Dimensional Geometry
High School Euclidean/Plane Geometry
High School Higher-Dimensional Geometry

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