Calculating Historical Intercapital Distances

Last updated 10 January 2018. Lightly edited for reproducibility 14 September 2025.

Military power degrades with distance. Fighting a war on another continent is, for most militaries, more difficult than fighting at home. Studies of conflict frequently employ capital-to-capital distance (or some transformation of this metric) as one proxy for this loss of strength from power projection (see, for example, (Gartzke and Braithwaite (2011)). Combined with data on territorial contiguity, these metrics can provide us with a picture of the geographic constraints facing countries contemplating war with one another.

Historical intercapital distance data proved difficult to find however. Most researchers appear to rely on EuGene to generate this data. I wasn’t able to track down any documentation on exactly how EuGene does this, however.¹ Gleditsch and Ward (2001) generated a minimum interstate distance dataset, but their data only covers the post-1875 period. For researchers using Correlates of War data, distance data would ideally cover 1816 to the present.

It turns out that it’s not too difficult to build intercapital distance data from scratch, however. All that is required is data on the names of capital cities for each state system member for every year between 1816 and the present. Paul Hensel’s ICOW Historical State Names dataset provides this information. We can then use Google’s Geocoding API through the ggmap R package to get the coordinates of each historical capital, which can then be used to generate intercapital distance matrices.

Here, I show how to conduct this exercise in R. A clean version of Hensel’s historical capital dataset is available here. I’ve included all of the data and software necessary to generate this data on Github. Feel free to send along questions, comments, or suggestions for improvement to [email protected].

Capital City Coordinates

Start by loading up the packages we’ll need for analysis:

# Install missing packages automatically
required_packages <- c('readr', 'dplyr', 'tidyr', 'geosphere', 'ggplot2', 'maps', 'knitr')
missing_packages <- required_packages[!required_packages %in% installed.packages()[,"Package"]]
if(length(missing_packages) > 0) {
  install.packages(missing_packages, repos = "https://cran.rstudio.com/")
}

# Load all required libraries
library(readr)
library(dplyr)
library(tidyr)
library(geosphere)
library(ggplot2)
library(maps)
library(knitr)

I started by cleaning up Hensel’s data a bit in excel. Each capital city is listed as its own observation, along with the country, its COW code, and the first and last year the city served as a capital. Because the Hensel data is coded annually, I take the country’s capital at the start of any given year to be its capital for that entire year. For countries that no longer exist (e.g. Mecklenburg-Schwerin) I provide a contemporary alternative country name (aName) to help Google locate the city’s coordinates. The assumption underlying this procedure is that the cities that served as capitals historically have not moved from their historical location (if I’m missing any instances where this occured please let me know). We can take a look at the data below:

# Load data directly from GitHub repository
capitals_url <- "https://raw.githubusercontent.com/brendancooley/intercapital-distances/master/capitals.csv"
dists <- read_csv(capitals_url, show_col_types = FALSE)

# Hensel's data run from 1800-2016, set bounds
dists$startDate <- ifelse(is.na(dists$startDate), 1800, dists$startDate)
dists$endDate <- ifelse(is.na(dists$endDate), 2016, dists$endDate)

head(dists)

## # A tibble: 6 × 6
##   ccode Name                     aName startDate endDate Capital        
##   <dbl> <chr>                    <chr>     <dbl>   <dbl> <chr>          
## 1     2 United States of America <NA>       1800    2016 Washington D.C.
## 2    20 Canada                   <NA>       1800    1841 Ottawa         
## 3    20 Canada                   <NA>       1841    1843 Kingston       
## 4    20 Canada                   <NA>       1843    1849 Montreal       
## 5    20 Canada                   <NA>       1849    1859 Toronto        
## 6    20 Canada                   <NA>       1859    1865 Quebec City

For this tutorial, I’ll use the pre-geocoded dataset that already contains latitude and longitude coordinates for all capital cities. This saves time and avoids the need for Google API keys. In practice, you would use ggmap’s geocode function to get coordinates, but that requires API setup and rate limiting.

# Load the pre-geocoded dataset with coordinates
geocoded_url <- "https://raw.githubusercontent.com/brendancooley/intercapital-distances/master/dists.csv"
dists <- read_csv(geocoded_url, show_col_types = FALSE)

# Clean up any missing values
dists$startDate <- ifelse(is.na(dists$startDate), 1800, dists$startDate)
dists$endDate <- ifelse(is.na(dists$endDate), 2016, dists$endDate)

# Check that all cities have coordinates
cat("Number of cities with missing coordinates:", sum(is.na(dists$lat)), "\n")

## Number of cities with missing coordinates: 0

cat("Total number of capital city records:", nrow(dists), "\n")

## Total number of capital city records: 253

We can verify the geocoding worked correctly by visualizing all capital cities on a world map:

The geocoded capitals are available as the dists dataset we just loaded. You can find the original data here.

Intercapital Distances

Remember that the point of all this was to generate intercapital distance data for all countries in the COW data. To do this, we want to convert our geocoded capital city data into a dyadic time series that gives the distance between any two countries’ capitals for a given year. If there are $N$ countries in the system in a given year $t$, we want to be able to generate an $N \times N$ matrix for that year where each entry is the distance between countries $i$ and $j$.

I start by loading up COW’s state system membership data, so we know which countries were members of the system for each year. The field “styear” denotes the year the country entered the system, and the field “endyear” gives the year it exited. I then append this data to the distance data. The output is shown below.

# get state system membership (COW)
sysMemUrl <- "https://correlatesofwar.org/wp-content/uploads/states2016.csv"

sysMem <- read_csv(sysMemUrl, show_col_types = FALSE) %>% select(ccode, styear, endyear)
dists <- left_join(dists, sysMem, by="ccode")

head(dists)

## # A tibble: 6 × 10
##   ccode Name          aName startDate endDate Capital   lat   lng styear endyear
##   <dbl> <chr>         <chr>     <dbl>   <dbl> <chr>   <dbl> <dbl>  <dbl>   <dbl>
## 1     2 United State… <NA>       1800    2016 Washin…  38.9 -77.0   1816    2016
## 2    20 Canada        <NA>       1800    1841 Ottawa   45.4 -75.7   1920    2016
## 3    20 Canada        <NA>       1841    1843 Kingst…  44.2 -76.5   1920    2016
## 4    20 Canada        <NA>       1843    1849 Montre…  45.5 -73.6   1920    2016
## 5    20 Canada        <NA>       1849    1859 Toronto  43.7 -79.4   1920    2016
## 6    20 Canada        <NA>       1859    1865 Quebec…  46.8 -71.2   1920    2016

From this dataframe, I can build the $N \times N$ intercapital distance matrix for any year. I wrap this in a function coord2DistM, which takes the desired year and the dists dataframe as arguments. It filters the distance data to include only states that were active in that year. It then feeds the latitude and longitude coordinates to the distm function from the geosphere package, which retuns the desired distance matrix. I convert all distances to kilometers.

The function distM2dydist takes this distance matrix and a pair of COW country codes and returns the dyadic distance. Below, I show how to use these functions to build the intercapital distance matrix for the year 1816 and get the distance between Britain and Saxony.

# Note: assigns capital to city that was capital at beginning of year

coord2DistM <- function(dists, year) {
  # filter by system membership, then relevant capital
  distsY <- dists %>% filter(styear <= year, endyear >= year) %>% filter(startDate < year & endDate >= year)
  # check that one capital returned per country
  if (length(unique(distsY$Capital)) != length(unique(distsY$Name))) {
    print('error: nCountries != nCapitals, check underlying coordinate data')
  }
  else {
    # get distance matrix for selected year
    latlng <- distsY %>% select('lng', 'lat') %>% as.matrix()
    distsYmatrix <- distm(latlng, latlng, fun=distVincentySphere)
    distsYmatrix <- distsYmatrix / 1000  # convert to km
    rownames(distsYmatrix) <- colnames(distsYmatrix) <- distsY$ccode
    return(distsYmatrix)
  }
}

# get distance between i and j
distM2dydist <- function(distM, ccode1, ccode2) {
  return(distM[ccode1, ccode2])
}

# application
year <- 1816
Britain <- "200"
Saxony <- "269"

distM1816 <- coord2DistM(dists, year)
distM2dydist(distM1816, Britain, Saxony)

## [1] 965.3628

These functions can be used in tandem to grab intercapital distances for arbitrary year, dyad pairings.

Merge with COW War Data

Conflict researchers often want this data to analyze wars. Now I show how to merge intercapital distance data with COW’s inter-state-war data. I clean up the COW war data a bit, which you can see below post-cleaning. In the most basic leve, the data give information about the belligerents in every war and how long each war lasted.

# append to COW wars data
warUrl <- "https://correlatesofwar.org/wp-content/uploads/Inter-StateWarData_v4.0.csv"
cowWars <- read_csv(warUrl, show_col_types = FALSE)

# for simplicity, ignore armistices
cowWars$StartYear <- cowWars$StartYear1
cowWars$EndYear <- ifelse(cowWars$EndYear2 == -8, cowWars$EndYear1, cowWars$EndYear2)
cowWars <- cowWars %>% select(WarName, ccode, StateName, Side, StartYear, EndYear)

head(cowWars)

## # A tibble: 6 × 6
##   WarName             ccode StateName                 Side StartYear EndYear
##   <chr>               <dbl> <chr>                    <dbl>     <dbl>   <dbl>
## 1 Franco-Spanish War    230 Spain                        2      1823    1823
## 2 Franco-Spanish War    220 France                       1      1823    1823
## 3 First Russo-Turkish   640 Ottoman Empire               2      1828    1829
## 4 First Russo-Turkish   365 Russia                       1      1828    1829
## 5 Mexican-American       70 Mexico                       2      1846    1847
## 6 Mexican-American        2 United States of America     1      1846    1847

We want to know the intercapital distance between each pair of belligerents between 1816 and the present. We could use the coord2DistM and distM2dydist but this would require calculating the intercapital distance matrix for every year in which there was a war. A simpler solution is to build a dataframe of capital-years, along with their coordinates, merge this with the war data, and calculate the distance between belligerents, given their capitals’ coordinates.

I used the procedure in this stackoverflow post to create the capital-year dataframe. Once merged, I use geosphere’s distVicentySphere function to calculate the distances. The resulting data is shown below the code.

# convert capital data to yearly observations
# https://stackoverflow.com/questions/28553762/expand-year-range-in-r
distsYear <- dists
distsYear$year <- mapply(seq, distsYear$startDate, distsYear$endDate, SIMPLIFY=FALSE)
distsYear <- distsYear %>%
  unnest(year) %>%
  select(ccode, year, lat, lng)

# get capital in start year
cowWars$year <- cowWars$StartYear

# append coords for each side
cowWars1 <- cowWars %>% filter(Side == 1) %>% left_join(distsYear, by=c("ccode", "year")) %>% rename(State1 = StateName, ccode1 = ccode, lat1 = lat, lng1 = lng) %>% select(-Side)
cowWars2 <- cowWars %>% filter(Side == 2) %>% left_join(distsYear, by=c("ccode", "year")) %>% rename(State2 = StateName, ccode2 = ccode, lat2 = lat, lng2 = lng) %>% select(WarName, State2, ccode2, lat2, lng2)

cowWarsDyadic <- left_join(cowWars1, cowWars2, by="WarName") %>% select(WarName, ccode1, State1, ccode2, State2, year, lng1, lat1, lng2, lat2)

# calculate distance
latlng1 <- cowWarsDyadic %>% select(lng1, lat1)
latlng2 <- cowWarsDyadic %>% select(lng2, lat2)
cowWarsDyadic$distance <- distVincentySphere(latlng1, latlng2) / 1000  # convert to km

cowWarsDyadic %>% select(WarName, ccode1, State1, ccode2, State2, distance)

## # A tibble: 813 × 6
##    WarName                  ccode1 State1                 ccode2 State2 distance
##    <chr>                     <dbl> <chr>                   <dbl> <chr>     <dbl>
##  1 Franco-Spanish War          220 France                    230 Spain     1054.
##  2 Franco-Spanish War          220 France                    230 Spain     1054.
##  3 First Russo-Turkish         365 Russia                    640 Ottom…    2233.
##  4 Mexican-American              2 United States of Amer…     70 Mexico    3035.
##  5 Austro-Sardinian            300 Austria                   337 Tusca…     632.
##  6 Austro-Sardinian            300 Austria                   325 Italy      765.
##  7 Austro-Sardinian            300 Austria                   332 Modena     575.
##  8 First Schleswig-Holstein    255 Prussia                   390 Denma…     356.
##  9 First Schleswig-Holstein    255 Prussia                   390 Denma…     356.
## 10 First Schleswig-Holstein    255 Prussia                   390 Denma…     356.
## # ℹ 803 more rows

The resulting data can be found here.

R Packages

Wickham H, Hester J and Francois R (2017). readr: Read Rectangular Text Data. R package version 1.1.1, <URL: https://CRAN.R-project.org/package=readr>.

Wickham H, Francois R, Henry L and Müller K (2017). dplyr: A Grammar of Data Manipulation. R package version 0.7.4, <URL: https://CRAN.R-project.org/package=dplyr>.

Wickham H and Henry L (2017). tidyr: Easily Tidy Data with ‘spread()’ and ‘gather()’ Functions. R package version 0.7.2, <URL: https://CRAN.R-project.org/package=tidyr>.

Kahle D and Wickham H (2013). “ggmap: Spatial Visualization with ggplot2.” The R Journal, 5(1), pp. 144-161. <URL: http://journal.r-project.org/archive/2013-1/kahle-wickham.pdf>.

Hijmans RJ (2016). geosphere: Spherical Trigonometry. R package version 1.5-5, <URL: https://CRAN.R-project.org/package=geosphere>.

Cheng J, Karambelkar B and Xie Y (2017). leaflet: Create Interactive Web Maps with the JavaScript ‘Leaflet’ Library. R package version 1.1.0, <URL: https://CRAN.R-project.org/package=leaflet>.

Xie Y (2017). knitr: A General-Purpose Package for Dynamic Report Generation in R. R package version 1.18, <URL: https://yihui.name/knitr/>.

Xie Y (2015). Dynamic Documents with R and knitr, 2nd edition. Chapman and Hall/CRC, Boca Raton, Florida. ISBN 978-1498716963, <URL: https://yihui.name/knitr/>.

Xie Y (2014). “knitr: A Comprehensive Tool for Reproducible Research in R.” In Stodden V, Leisch F and Peng RD (eds.), Implementing Reproducible Computational Research. Chapman and Hall/CRC. ISBN 978-1466561595, <URL: http://www.crcpress.com/product/isbn/9781466561595>.

Francois R (2017). bibtex: Bibtex Parser. R package version 0.4.2, <URL: https://CRAN.R-project.org/package=bibtex>.

Boettiger C (2017). knitcitations: Citations for ‘Knitr’ Markdown Files. R package version 1.0.8, <URL: https://CRAN.R-project.org/package=knitcitations>.

References

Gartzke, Erik, and Alex Braithwaite. 2011. “Power, Parity and Proximity.”

Gleditsch, Kristian S, and Michael D Ward. 2001. “Measuring space: A minimum-distance database and applications to international studies.” Journal of Peace Research 38 (6).