Which idiot came up with percentage-based gradient signs

Rant warning: the contents of this post could sound like something produced by UKIP. I wish to make it clear that I do not in any way support or endorse that political party. In fact it gives me the creeps.

Once upon a time, the signs for a steep hill on British roads displayed the gradient in a simple, easy-to-understand form. If the hill went up, say, one yard for every three yards forward it said '1 in 3'. Then some bureaucrat came along and decided that it would be a good idea to state the slope as a percentage. So now the sign for (say) a 1 in 10 slope says 10% (I think).

That 'I think' is because the percentage-based slope is so unnatural. There are two ways we conventionally measure slopes. Either on X/Y coordiates (as in 1 in 4) or using degrees - say at a 15° angle. We don't measure them in percentages. It's easy to visualize a 1 in 3 slope, or a 30 degree angle. Much less obvious what a 33.333 recurring percent slope is. And what's a 100% slope? It sounds like it should be straight up vertically, but I assume it's really 1 in 1 or 45 degrees.

It's widely reported that the general public is very bad at understanding percentages. That is sad, and ought to be rectified - but it's true. So why, in heavens name, make a street sign, something that a driver is supposed to pick up and react to in seconds, in a format that most people struggle with, and a format that is never conventionally used to measure an amount of slope? It's madness. Madness, I say!

{Retires gibbering.}

Photo from Freefoto.com


  1. I was once told that the gradient on a road sign is not arctan but rather arcsin - i.e. 10% is 1m up for 10m on the slope. You imply this with the word "forward" but then in the next paragraph say X/Y coordinates.

    I can't corroborate this anywhere on the internet, except for this page which says it's true for rail slopes but offers no reference.

    Do you know any better?

    1. This is exactly what we were taught in geography at school in the 1950s.
      1 ft rise for every 3ft travelled as measured on the road was a 1 in 3 gradient.

  2. What's it matter? You going to compute how much pressure to put on the brake pedal from the number on the sign or what? All you really need to know is there's some slope comin, watch out. And if you really need to know more, there's probably an iPhone app that allows you to take a picture and submit it somewhere and then you get an explanation in Swahili, or whatever you desire.

  3. Adam - No I don't know. By forward I meant horizontally forward, I had assumed it was literally X/Y, but that was pure assumption. 10% meaning 1m up for 10m on the slope is even more confusing.

    Bee - I agree to an extent - for most practical reasons 'gentle hill', 'moderate hill', or 'panic' would be sufficient. The moan is mostly that they bothered to spend money changing it from the old style to the new style, presumably to meet some European directive (hence the disassociation from UKIP). But the % basis does seem an odd and unnatural one.

  4. Googling (I hope the html comes out right): Wikipedia has
    http://en.wikipedia.org/wiki/Grade_(slope) with a useful "Illustration of grades in percent and angles in degrees".

    A couple of clicks from there is this page:
    http://www.direct.gov.uk/prod_consum_dg/groups/dg_digitalassets/@dg/@en/documents/digitalasset/dg_070569.pdf. There are pictures of warning signs with a helpful note under the "Steep hill downwards" and Steep hill upwards" signs that "Gradients may be shown as a ratio i.e. 20% = 1:5" - I'd need to get out my slide rule to figure out how close that is to "1 in 5".

  5. Well, I'm half with you in the confusion/frustration(/fear about dumb British motorists), but the other half is saying 'what's the problem' - and why not let units go and just consider ratios as being a fine (if not British) thing.

    P.S. You b' I wanted to use a few single inverted commas in that, but couldn't bring myself to - but now I've got to work out how to compensate!
    P.P.S. I wish I had track changes on here, so that you could see how many edits I have done, and how much conferring with Harriet, not to fall into the trap of using 'the wrong quotation marks'! How did I do?

  6. Thanks, John. As far as I can tell, this contradicts Adam's version where the percentage is rise to slope length, rather than rise to run.

    Peet - but ratios is what has been removed and replaced with percentages! As for the quotations marks, you did fine (apart from putting the exclamation mark outside them).

  7. Brian

    Does this help? p26 - from the Department of Transport Traffic Signs Manual, chapter 4.

    Not being up on mathematics, I'm not sure whether this is detailed enough. There doesn't appear to be a worked example.

  8. And this time, with the link:


  9. Thanks Anon! According to that official manual it's the tangent - i.e. using distance vertically and distance horizontally to calculate the percentage, not distance up the actual slope. (Though it does say it doesn't really matter if you use the sine.)

  10. Carl said...

    You have a point, Brian. For sure, they did use government resources to put up the altered road signs. They had to do extra painting/printing, purchase additional steel strapping and steel strapping seals, pay the laborers, etc. But for me, if the projects aims to adhere to global/regional standards, then I think it's only fair to use government resources for that. I guess they should just spend a little more on an information campaign to educate motorists about the change.

    (Carl - I have re-input your comment without the sales links. If you would like sales links, please contact me to discuss rates.)

  11. Couldn't disagree more.

    Who said the public don't understand percentages? Percentages are something we see in everyday usage, unlike '1 in 3' (or were they displayed '1:3', even worse )would mean absolutely nothing to most people, which is absolutely the reason the format was ditched.

    Of course the Average Joe is more likely to understand that a 90% slope ahead is something he should be worried about rather than arcane combination of numbers and punctuation

  12. Look, I'm sitting here typing this on my laptop. It has 90% battery remaining (quite a lot) and a 20% signal strength (not great). I've just turned down my TV volume from 45% to 5%, which I bought from Currys with 10% off.

    I understand percentages.

    Idiot masses like myself can quickly read what a percentage is trying to convey. I know 50% is more than 0%. I don't need to know precise technical measurements. Showing my wifi signal in dBm would be meaningless, I'm not a telecommunications engineer - and even if I was I think i'd prefer a simple friendly view rather than technical information. Likewise most of us aren't cartographers, or go around graphing inclines by the roadside.

    'x in y' requires you to understand that is shorthand for 1 unit in height for each unit in length. It is not immediately obvious to some that '1 in 3' is steeper than '1 in 5', but 33% is clearly more than 20%.

    Roads are pretty dangerous places it's imperative that information is conveyed quickly and in a manner easily understood. Percentages do this extremely well.

    1. For you 100 percent volume is full volume or maximum.
      but in this case of slope 100% is not maximum slope its just 45degree
      We all know maximum slope is 90 degree it means a vertical line
      Here to express the maximum slope in percent its around 1000000percent
      I hope you are confused .
      PS he pointed out a good thought.

  13. I've finally decided, after years of wondering what the hell 10% gradient actually means, to work it out, which I finally have. BUT, but, but, but I could not agree more that this convention is awkward, to say the least. I had previously assumed 100% would mean 90 deg, but I discover 100% is 45 deg, derived from a 1 to 1 ratio of rise over run. Well, this makes sense but one has to have been educated as to how this % is derived. I guess, once a person has a "feel" for a 10% slope then a 5% or 15% slope will, by comparison, have the appropriate feel. BUT, again I say BUT, we were all educated such that we understand slopes using either ANGLES or RISE/RUN. It is FAR more sensible and easy to understand. Brian, I am with you.....damn those bureaucrats with nothing better to do than unsimplify the simple....oh yeah, that's their job.

  14. Absolutely agree. 1 in 3 is easily visualised. Go along 3ft go up 1ft. Simples. 30% means nothing. Contrary to the above it was abandoned to bring us into line with the EU.

  15. My quibble is that there are slopes greater than 45 degrees and then you have to go into percentages greater than 100%. and a vertical slope is infinity %. The mind boggles and I have had arguments about slopes > 100%. What about an overhang?

  16. Dan

    Very good :D

    As for the EU? - not long now.


  17. I too thought the change silly (probably due to the EU?) It was an awful long time ago it changed now wasn't it?

    I'd assumed the figure was 'gradians' - I've only ever seen them used on calculators otherwise. 100 gradians is 90 degrees. However it seems that % is not the symbol for grad -so that's almost certainly wrong.

    Gradients do not lend themselves to percentages in my opinion - the concept of a 100% gradient and then a 50% gradient only being half that does not seem to work well.

  18. In real life, no actual public road requiring a sign exceeds a slope of 1 in 2.67, 37.45%, so the sign would say 37%.

  19. If percentages were a rational means to express a gradient, then (as mentioned) 100% would mean vertical. Even if we accept that 100% actually means 45 degrees, then it would be reasoable for 50% to be half that (i.e. 22.5 degrees). But - if my maths is correct - 50% actually means 26.5 degrees. So, hardly intuative - as ratios or degrees are - or an intelligent choice for a warning sign that needs to be understood rapidly.
    As we are now out of the EU, perhaps as new signs are rolled out they could once again show ratios (with or without the percentages, as well).


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