Convert coordinates from readShapePoly in R to long-lat coordinates

Question

I'm trying to find some centroids of a shapefile for Danish municipalities and afterwards find the driving time between them. I use R's readShapePoly function from maptools combined with the gCentroidfunction from rgeos, and everything works. However, I get spatialpoints such as

SpatialPoints:
     x       y
1 571860.7 6225016
Coordinate Reference System (CRS) arguments: NA 

Which is clearly not something I can use in Google to grab travel times. I'm looking for a way to convert these numbers to longitude-latitude, but have no idea how.

When I read the data using readOGR from the rgdal library I get the same coordinates but it tells me the following about what I assume is the projection (but the coordinates are the same)

Slot "proj4string":
CRS arguments:
+proj=utm +zone=32 +ellps=intl +units=m +no_defs

Reproducible example: I've put the data for the example here: https://github.com/sebastianbarfort/shapefiles

This should reproduce the problem:

library(maptools)
library(rgdal)
library(rgeos)

map = readShapePoly("~/Downloads/shapefiles-master/kommuner1983.shp")
centroid = gCentroid(map)
centroid

Answer 1

Use spTransform to transform the coordinates to WGS84:

library("rgdal")
library("rgeos")

map <- readOGR(".", "kommuner1983")
map_wgs84 <- spTransform(map, CRS("+proj=longlat +datum=WGS84"))
plot(map_wgs84, axes=TRUE)

gCentroid(map_wgs84)
# SpatialPoints:
#       x     y
# 1 10.05 55.96
# Coordinate Reference System (CRS) arguments: +proj=longlat +datum=WGS84
# +ellps=WGS84 +towgs84=0,0,0 

rgdal::readOGR is capable to read the projection information automatically. maptools functions neither read nor write projection information, leaving it up to you to manage these details manually.