Simple calculations for working with lat/lon and km distance?

Is there a simple calculation I can do which will convert km into a value which I can add to a lat or lon float to calculate a bounding box for searches? It doesn't need to be completely accurate.

For instance: if I were given a lat/lon for London, England (51.5001524, -0.1262362) and I wanted calculate what the lat would be 25km east/west from that point, and what the lon would be 25km north/south of that point, what would I need to do to convert the 25km into a decimal to add to the values above?

I'm looking for a general rule-of-thumb, ie: 1km == +/- 0.XXX

Edit:

My original search for "lat lon" didn't return this result:

How to calculate the bounding box for a given lat/lng location?

The accepted answer seems adequate for my requirements.

Solution 1:

The approximate conversions are:

• Latitude: 1 deg = 110.574 km
• Longitude: 1 deg = 111.320*cos(latitude) km

This doesn't fully correct for the Earth's polar flattening - for that you'd probably want a more complicated formula using the WGS84 reference ellipsoid (the model used for GPS). But the error is probably negligible for your purposes.

Source: http://en.wikipedia.org/wiki/Latitude

Caution: Be aware that latlong coordinates are expressed in degrees, while the cos function in most (all?) languages typically accepts radians, therefore a degree to radians conversion is needed.

Solution 2:

If you're using Java, Javascript or PHP, then there's a library that will do these calculations exactly, using some amusingly complicated (but still fast) trigonometry:

http://www.jstott.me.uk/jcoord/

Solution 3:

Thanks Jim Lewis for his great answer and I would like to illustrate this solution by my function in Swift:

func getRandomLocation(forLocation location: CLLocation, withOffsetKM offset: Double) -> CLLocation {
        let latDistance = (Double(arc4random()) / Double(UInt32.max)) * offset * 2.0 - offset
        let longDistanceMax = sqrt(offset * offset - latDistance * latDistance)
        let longDistance = (Double(arc4random()) / Double(UInt32.max)) * longDistanceMax * 2.0 - longDistanceMax

        let lat: CLLocationDegrees = location.coordinate.latitude + latDistance / 110.574
        let lng: CLLocationDegrees = location.coordinate.longitude + longDistance / (111.320 * cos(lat / .pi / 180))
        return CLLocation(latitude: lat, longitude: lng)
    }

In this function to convert distance I use following formulas:

latDistance / 110.574
longDistance / (111.320 * cos(lat / .pi / 180))