Trying to get the span size in meters for an iOS MKCoordinateSpan

Swift implementation for Hanne's solution:

    let span = mapView.region.span
    let center = mapView.region.center
    
    let loc1 = CLLocation(latitude: center.latitude - span.latitudeDelta * 0.5, longitude: center.longitude)
    let loc2 = CLLocation(latitude: center.latitude + span.latitudeDelta * 0.5, longitude: center.longitude)
    let loc3 = CLLocation(latitude: center.latitude, longitude: center.longitude - span.longitudeDelta * 0.5)
    let loc4 = CLLocation(latitude: center.latitude, longitude: center.longitude + span.longitudeDelta * 0.5)
    
    let metersInLatitude = loc1.distanceFromLocation(loc2)
    let metersInLongitude = loc3.distanceFromLocation(loc4)

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EDIT:

For Swift 5 distanceFromLocation(_:) has been renamed to distance(from:) meaning that the two last lines now read

   let metersInLatitude = loc1.distance(from: loc2)
   let metersInLongitude = loc3.distance(from: loc4)

As I can see you already have the region of the map. It doesn't only contain the lat & long deltas but also the center point of the region. You can calculate the distances in meters as illustrated in the picture:

1: Get the region span (how big the region is in lat/long degrees)

MKCoordinateSpan span = region.span;

2: Get the region center (lat/long coordinates)

CLLocationCoordinate2D center = region.center;

3: Create two locations (loc1 & loc2, north - south) based on the center location and calculate the distance inbetween (in meters)

//get latitude in meters
CLLocation *loc1 = [[CLLocation alloc] initWithLatitude:(center.latitude - span.latitudeDelta * 0.5) longitude:center.longitude];
CLLocation *loc2 = [[CLLocation alloc] initWithLatitude:(center.latitude + span.latitudeDelta * 0.5) longitude:center.longitude];
int metersLatitude = [loc1 distanceFromLocation:loc2];

4: Create two locations (loc3 & loc4, west - east) based on the center location and calculate the distance inbetween (in meters)

//get longitude in meters
CLLocation *loc3 = [[CLLocation alloc] initWithLatitude:center.latitude longitude:(center.longitude - span.longitudeDelta * 0.5)];
CLLocation *loc4 = [[CLLocation alloc] initWithLatitude:center.latitude longitude:(center.longitude + span.longitudeDelta * 0.5)];
int metersLongitude = [loc3 distanceFromLocation:loc4];

Based on the above, here's a useful extension I use in my mapping projects:

extension MKCoordinateRegion {
    public var radius: CLLocationDistance {
        let loc1 = CLLocation(latitude: center.latitude - span.latitudeDelta * 0.5, longitude: center.longitude)
        let loc2 = CLLocation(latitude: center.latitude + span.latitudeDelta * 0.5, longitude: center.longitude)
        let loc3 = CLLocation(latitude: center.latitude, longitude: center.longitude - span.longitudeDelta * 0.5)
        let loc4 = CLLocation(latitude: center.latitude, longitude: center.longitude + span.longitudeDelta * 0.5)
    
        let metersInLatitude = loc1.distance(from: loc2)
        let metersInLongitude = loc3.distance(from: loc4)
        let radius = max(metersInLatitude, metersInLongitude) / 2.0
        return radius
    }
}