Which walking trail is the least direct one you can walk?

Published 1 March 2017

Checking the map near Woodhead reservoir

What is the most indirect walking trail? The one where you walk oodles of miles, yet at the end of it, find yourself rather embarrassingly close to where you set off from? It was a question that was on my mind after working out that when you walk the Thames Path, your feet go on a 184 miles/296km journey, but the two trailheads are a mere 90 miles/145km apart.

The question burrowed itself into my mind, and slowly niggled at me until I finally cracked and started to find out.

The methodology

Of course, I couldn’t work how direct every walking route is. There are just too many. The Long Distance Walkers Association, for example, has a directory of 1,500 walking routes in the UK. It would take me years to calculate that lot. So instead I decided to concentrate on main routes:

With 20 trails to look at, the next job was the find latitude and longitude co-ordinates for the start and end positions of each trail. These I found in a variety of ways, including pouring over Ordnance Survey maps, official route websites, Bing Maps and Google Streetview to pinpoint the proper start and end points. With those coordinates, I could calculate the point-to-point distances between the start and end using the distance calculator at doogal.co.uk.

I obviously also needed a distance for the trail itself. I got these from each trail’s official website. For the Coast to Coast you’ll find multiple distances given by different people (thanks, no doubt, to the different options you can take) so I opted for the 190 miles/306km distance given by the Wainwright Society.

With all that done, all that remained was to find out a ‘Directness Value’, simply measured by dividing the point-to-point distance by the official difference. The higher directness value, the more direct the route is. So if a walking trail went in exactly a straight line for its entire length, it would have a directness value of 1. And a circular walking trail, starting and ending in exactly the same place, well that would have zero. (Well actually it wouldn’t, because that would require the ability to divide by zero and that’s impossible. But for the sake of simplicity, we’ll ignore the rules of mathematics just this once. Besides, there are no circular routes in our list.)

And with all that done, it was time to be able to find some answers.

The most direct paths

Crossing a stile on the South Downs, near Brighton

Not surprisingly, there are several walking routes that are quite direct, namely those that run roughly in a straight line. Of course there is no perfectly direct trail – it’s just not possible to walk exactly in a straight line. But there are some fair Directness Values out there.

Our third most direct trail is the South Downs Way, coming in with a Directness Value of 0.73. Walking its 100 miles/160km between Winchester and Eastbourne will take you 72.2 miles/116.2km as the crow flies. Even better is the Hadrian’s Wall Path with a Directness Value of 0.80, an achievement really helped by the obsession of the Romans in building things in incredibly straight lines.

Most direct of all though is the Great Glen Way. Running between Fort William and Inverness, this trail goes in an incredibly straight line by following a canal and the edge of some long, very narrow lochs. With a Directness Value of 0.87, the Great Glen Way is truly the walking route with no faffing around.

Something in the middle

The outskirts of Reading, on the banks of the River Thames

What’s the trail with a middle directness? The one with the Directness Value of 0.5? Well there isn’t one, but there’s two that get very close. Coming in with a Directness Value of 0.52 is the Cotswold Way. Now that’s not bad at all.

But even closer to 0.5 is the trail that sparked off this whole, rather pointless endeavour. Yes, it’s the Thames Path with a Directness Value of 0.49. Good work river walkers!

And finally… the least direct path!

South West Coast Path near St Ives

All the above though is just a sideshow from the ultimate question. Just what is the least direct trail? And what does one look like? The answer is, kind of horseshoe-shaped, and there are certainly a couple of trails that fit into that category; not every major trail goes off in a straight line after all.

Coming in third is one I know very well myself. Those walking it will probably spend nine or ten days walking just to travel a distance of just 22 miles/36km between its two trailheads in Knighton and Welshpool. With a Directness Value of a mere 0.16, yes, it’s the Glyndŵr’s Way, a V-shaped trail that is one of the few not to follow any feature that’s geographic or historical. Yes, it does visit some sites connected to Owain Glyndŵr, the last Welsh Prince of Wales, but the way mostly goes where it does because its creators thought it would be a good idea.

The second least direct path, with a Directness Value of 0.13, is also in Wales. But this time, it is a trail that is far less arbitrary. Indeed this one follows a geographic feature, and it is that feature that causes the indirectness. And it’s the coast. The Pembrokeshire Coast Path may be a 186 mile/300km walk, but when you get to the other end you’ll find yourself just 25 miles/40km from where you set off from. And that’s what happens when you walk on the coast, because coastlines are rarely straight and flat.

That same excuse is the reason for the most indirect path as well. Almost inevitably, that honour falls on the longest National Trail in existence. At 630miles – or the far longer sounding 1014km – the South West Coast Path is an epic undertaking. It will take you about a month and a half to do it all, yet on many days you’ll barely make any progress at all thanks to the many inlets and bays it encounters. And when you finally do get the end, what have you got to show for your progress? You find yourself just 76miles/100km from where you left all that time before. Yes, with a Directness Value of just 0.10, the South West Coast Path is an easy contender for this crown.

So there you go. If you want to actually set off on a walk and actually go places, the Great Glen Way is probably the trail for you. But if your main aim is to arrive reasonably close from where you started from, why not try the South West Coast Path? Although if you haven’t got seven weeks to spare, you might just want to consider other options, such as public transport.

The data

For those interested, here’s a table with

Trail Start coordinates End coordinates Official distance Point-to-point distance Directness Value
miles km miles km
South West Coast Path 51.211092, -3.473884 50.679653, -1.950111 630 1014 75.9 99.8 0.10
Pembrokeshire Coast Path 52.089062, -4.681956 51.733894, -4.652027 186 300 24.6 39.5 0.13
Glyndwr’s Way 52.344261, -3.049674 52.658563, -3.144496 135 217 22.1 35.5 0.16
Cleveland Way 54.246346, -1.061377 54.217696, -0.271974 109 175 30.9 49.8 0.28
Peddar’s Way/Norfolk Coast Path 52.390763, 0.855365 52.932618, 1.300361 93 150 41.2 63.3 0.42
Yorkshire Wolds Way 53.717589, -0.434779 54.217696, -0.271974 79 127 35.5 57.2 0.45
Pennine Bridleway 53.092784, -1.591007 54.412835, -2.403434 205 330 97.2 156.4 0.47
Thames Path 51.694262,-2.029724 51.494995, 0.037451 184 294 89.8 144.6 0.49
Cotswold Way 52.050930, -1.779739 51.381500, -2.358718 102 164 52.5 84.6 0.52
Pennine Way 53.370509, -1.816907 55.547455, -2.275127 268 429 151.7 244.1 0.57
Speyside Way 57.190562, -3.829121 57.676414, -2.964936 80 130 46.5 74.9 0.58
North Downs Way 51.212761, -0.793908 51.122432, 1.315457 153 246 91.7 147.5 0.60
Southern Upland Way 54.841502, -5.119953 55.932687, -2.360358 212 340 132.1 212.6 0.63
Coast to Coast 54.490750, -3.606449 54.430416, -0.532011 190 306 123.6 198.9 0.65
Offa’s Dyke Path 51.632536, -2.648470 53.342625, -3.412604 177 285 122.4 197 0.69
The Ridgeway 51.411506, -1.830571 51.842156, -0.608428 87 139 60.4 97.3 0.70
West Highland Way 55.940606, -4.318159 56.816367, -5.113975 96 154 67.8 109.1 0.71
South Downs Way 51.061038, -1.314666 50.751869, 0.267037 100 160 72.2 116.2 0.73
Hadrian’s Wall Path 54.953928, -3.211641 54.988093, -1.530114 84 135 66.7 107.4 0.80
Great Glen Way 56.816367, -5.113975 57.477290, -4.224846 75 121 56.6 105.8 0.87

Note: Speyside Way distance does not include the Speyside Way Extension, but does include the Tomintoul spur. Coast to Coast distance is that given by the Wainwright Society.

Your Comments

Chris Hunt

1 March 2017 at 1:08 pm

There’s nothing impossible about having a “directness value” of zero, nor does it require dividing by zero. You get it by dividing the point-to-point difference (which would be zero for a circular trail) by the official distance (which wouldn’t). So taking my local trail of the Leicestershire Round, the directness value is 0 / 100 = 0.

The only way to get an infinite directness value would be to have a trail that travelled a non-zero point-to-point distance, but had a zero official distance. Short of travelling through some kind of wormhole, the impossibility of the maths is the least of your problems in such a scenario.

Actually, wormholes aside, the directness value can never exceed 1. To do so, the point-to-point distance would need to be longer than the official distance, which should never happen (if it does, the official distance is wrong!).

The LDWA have a database of 1500 UK routes on their website, it’d be interesting to run your test against all of them.

Andrew Bowden

3 March 2017 at 9:29 am

An interesting idea Chris on an alternative Directness Value. A rather simple way of solving the problem that didn’t occur to me. Although I was just in too much of a rush to get doing the maths!

I would love to do a wider range, but that would require some kind of automation. I did all the above manually, finding all the various start and end points myself. Notably the LDWA does have the map references in its database so it is do-able if I had access to the data.

Chris Hunt

3 March 2017 at 3:44 pm

That’s not an alternative method, it’s your method: “all that remained was to find out a ‘Directness Value’, simply measured by dividing the point-to-point distance by the official difference.” The point-to-point difference can be zero, the official difference can’t.

It might be interesting to come up with an alternative that somehow factors in the magnitude of the distances concerned. If you walk 600 miles to end up 100 miles away, it’s no more or less indirect than walking 6 miles to end up 1 mile away – but maybe it *should* be?

Automation is definitely the way to go with the LDWA database. If I find some time, I’ll explore the idea of scraping all the start and finish map references from their website. As a map reference is essentially a pair of x,y coordinates measured in metres, working out the point-to-point distances becomes a matter of simple trig (it’s WAY more complicated with lat and long).

John Seager

13 March 2017 at 7:18 am

Hi Andrew, how about the ‘Serpent Way’
64 miles long, start and finish is 11 miles a part.

Your Comments

Notify me of followup comments via e-mail. You can also subscribe without commenting.