Hiking: The prediction of the spent time

Published by gbal, 13 November 2010, 23h27. This page has been displayed 2879 times.

This is a topic with which I measured myself several times and in many ways because, as you can imagine, it is very important to leave on a trip provided with the appropriate technical equipment: backpack, boots, shoes, clothing, food, compass, maps, etc.. but also with an idea as precise as possible, about the time it takes. Unfortunately, the daylight hours are often limited, especially in winter, our forces are not inexhaustible and often return to our home is looked forward to our relatives. So, it is important to have a criterion for estimating at home the time our tour takes.
Really, there are several criteria and the first in which I came across was based on the simple difference in altitude assuming to climb up to 300-400 m / hour and go down to 500 m / hour; this is useful but it does not consider the path length. You understand that the same drop of 1000m results differently if we walk for 2 km (gradient 50%) or if we have to walk for 10 km (10% slope) for which it is useful to associate to the simple drop also a parameter that takes into account the distance traveled.

Some time ago, inquiring about this, I found a useful feedback in a couple of Web pages published by friends UpTheHill and giorgio59m that gave this interesting information: to bind together drop and route length they reached the concept of linear equivalent effort (SLE) adding up the kilometers  to go and further kilometers obtained by dividing the difference in altitude by 100.

For example, on a trip, which we know the length of 12 km and drop of 800 m we can determine the linear equivalent effort SLE by using the simple rules:

SLE = 12 km + (800/100) km = 12 km + 8 km = 20 km

 Needless to say, we speak of an empirical formula that relates a real mountain tour to a hypothetical trip that takes place on a plane road but of different length (greater).


Already obtained this value (SLE), each of us should know and apply their traveling speed to the trail so calculated to determine the time needed to complete it. In this practical case, if we know we can walk the SLE at a speed of 4 km / hour in the example above we actually will spend:


Time = 20 km / 4 km/h = 5 hours

At this point I asked to me a further question: "How to calculate the forward and back part as well as you often have to climb down?". I replied, imagining to use two SLE : the first for the part up (SLEup) and the second to be used for downhill (SLEdw). Now let's take a more concrete example. Imagine that you go up 800 m in 12 km and then descend from another way for 14 km.


Then we have a linear equivalent effort up:

SLEup = 12 km + (800/100) km = 12 km + 8 km = 20 km

 and a linear equivalent effort for the descent:

dw = 14 km + (800/100) km = 14 km + 8 km = 22 km

Now, to know the total time to be spent we have to apply two different speeds of travel, one for the climb (we imagine is 4 km / hour) and one for the descent (suppose to be 6 km / hour) and the game is made:

Time = SLEup / Velup + SLEdw / Veldw              (a)



Time = (20 km / 4 km/hour) + (22 km / 6 km/hour) = 5h + 3h40' = 8h40'


The third question I have asked to me is: "What if there are any ups and downs involved?". The answer is simple: reduce our path to a series of segments up or down and use the formula (a) as a sum of as many terms as are the segments we considered applying for each term the speed of climb up or down as appropriate.

The formula
(a) become more generalized as follows:

Time =  SLE
up1 / Velup + SLEup2 / Velup + …..+ SLEupN / Velup + SLEdw1 / Veldw + SLEdw2 / Veldw + …. + SLEdwN / Veldw

 It sounds complicated but it is not; let's do the usual example.

We have to climb 1000 m in 12 km, 300 m down in 2 km, climb 200 m in 1 km and then 900 m down in 11 km. Then the segments are:


SLEup1 = 12 + (1000/100) = 22 km

SLEdw1 = 2 + (300/100) = 5 km

SLEup2 = 1 + (200/100) = 3 km

SLEdw2 = 11 + (900/100) = 20 km

Now we will apply the up or down speed for each segment depending on whether it is going up or down and therefore:

Time = SLEup1/Velup + SLEdw1/Veldw + SLEup2/Velup + SLEdw2/Veldw

 which in numbers means:

Time = ( 22 / 4 ) + ( 5 / 6) + ( 3 / 4 ) + (20 / 6) = 10,41 hours

 who converted to sexagesimal (just divide the centesimal minutes by 1.6) are:

Time = 10h25'  (I must say….a tiring hike!)


What about now? What is the accuracy of this method?

Please note that:

I tried this method only on a hiking on "summer"; the use of snowshoes / ski / crampons can greatly changing the rate of ascent and descent. The method is applicable only in the hiking; vie ferrate and climbing in the strict sense should be considered with other parameters (eg, for climbing in two person out of  IV / V rank I consider 15'-20 ' each rope length) and then go beyond what has been said here.

The methodology used is entirely empirical and somewhat individual, the speed of ascent and descent must be determined by personal experience.

In my case I checked in a number of trips that my climb speed is 5 km per hour and my down speed is  7 km / hour. I recommend: keep in mind that these speeds are "virtual" and they have value just applied to the "virtual" distances that are the SLE (linear equivalent effort).

The predictions that I do for a new hike, applying the above, are slightly large than the time actually used and include the time to take the pictures, to have my short stops, eating small snacks, excluding only the time for the main meal (one ½ hour).

The method is much better as good is the approximation with which we are able to determine altitude and length of each segment. They range from measurements made directly on the map with the aid of the wheel (not reliable) to data gathered by tools like Google Earth, Swiss Map, BaseCamp, Map Source or other cartographic good software (good reliability ).

When we speak of the "up" or "down" segment  we mean the prevalence of ascent or descent; there will always be a bit  of approximation but this allows us to reduce a trail to 2, 4 or up to 6 segments (very rare ).

In any case, to make life easier, you can arrange with an Excel spreadsheet in which to place the above formulas. For those interested, I will be able to provide the model for the Excel spreadsheet that I use regularly.



Comments (16)

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Lone Ranger says: Excellent post
Sent 14 November 2010, 21h19
Thanks for sharing these insights. I can vouch that the SLE formula as stated above has proven to be remarkably accurate in my experience of a few mountain running races and hikes (didn't apply to T4 and above because skill and courage/risk come in play and alter the equation; but your formula for climbing seems reasonable). Did you know the famous UTMB ultra-race uses the same formula to estimate difficulty of the various mounain marathons in the world?

I think it is more accurate for uphills than downhills (e.g. some people avoid hiking fast or running downhill to "save the knees", for others it is no problem).

It is a very useful formula to estimate the effort/time of a planned hike. However in my personal case, when I go hiking alone, I simply turn back at my predetermined turn-back time, usually 1 pm in perfect weather, irrespective of how much distance I have covered.

Please send me a copy of your Excel sheet to niranjantt@gmail.com

gbal says: RE:Excellent post
Sent 14 November 2010, 22h57
Thank you for your compliment. I just put a lot of previous ideas in order developing some detail.
But I am happy for your positive feedback and for reporting your similar personal experience. No, I didn't know that the UTMB runners use a formula like this but we can say that "many roads lead to Rome"!
Yes, the method is as more accurate as you can determine (by your personal past experience) the speed values to apply in your case.
Surely I will send you the Excel sheet; please wait just a little time because I am gathering the requests to prepare the material and decide if sending it directly to everyone or if put the documentation on some server where you could download it.

kopfsalat says: we use the following
Sent 15 November 2010, 07h17
take the longer of distance or ascent/descent plus half of the other.

a) distance 10km
b) ascent 300m

our speeds
a) on flat ground: 5 km/h
b) ascent: 300m/h, descent: 600m/h

a) 10km : 5km/h = 2h
b) 300m : 300m/h = 1h

a) is longer than b) therefore: a + b : 2
or 2h + 1h : 2 = 2.5h

this formula has proven quite accurate on our various multi-week 3-season trekkings through jura, alps and pyrenees. we use it both for planing at home (with the assistance of an excel spread-sheet) as en-route during the so-called "rollende planung".

we haven't applied this to any outings in the snow yet, since we neither do high alps skiing, nor have we done any multi-day winter trips yet. there is no need for it on one-day cross-country skiing or snowshoeing trips in the jura, since there is enough public transport to get you home in time.


the SAC-publication "karten lesen" suggests the following speeds:

by foot
- on flat ground: 4km/h
- for ascent: add 15min per 100m (or multiply the hight-gain by 10 and add it to the distance)
- moderate descent: minus 10%
- middle to steep descent: 800m-600m/h

on ski
- on flat ground: 6km/h
- ascent: as by foot
- descent: depends on the snow, as a rule of thumb 1/6th of the time of the ascent

by bike
depending on training, material, wind on average between 12km/h and 20km/h with tops at 40km/h

refer to the respective route guides

gbal says: RE:we use the following
Sent 15 November 2010, 10h23
Hi kopfsalat,
thank you for your contribution. Now we have another way to calculate the time for our trip.
I did not know this but it seems easy to use, too. I think that the best method is the one that everyone uses with trust and success.

gbal says: Conclusion....
Sent 15 November 2010, 22h39
Following the previous discussion I give to those who want the links to reach the documents:

Model of Excel file to use freely:

Directions to use the above:
I just ask you to send me a private message at the end of your testing to give me your result and opinions.

Thank you to all

Madrus says:
Sent 19 November 2010, 07h23
Thank you gbal and kopfsalat. I will try your calculations next year. It is very important to be able to make realistic estimate of the hiking time. What I did up to now was comparing the real time of the group with the time from the guide the first day and then calculated the ratio. E.g. the guide said 4 hours and it took the group 5 hours. Then we would use the ratio of 1,2 on the times from the guide on other days. I would like to try your methods as they seem to be more accurate as estimations.

gbal says: Hi Madrus!
Sent 19 November 2010, 19h49
I'm very happy for your words because I believe the presented method is either "incredible" and "reliable". I spent most of my professional life on technical work and this is why I know it is an empirical method, not scientific. But it works, maybe just for me (?)
Today I hiked from Cabbio (CH-Tessin) to Sasso Gordona and back. The time I estimated with my method was 4h46'.....the time really spent was 4h44' ! Is it a strange coincidence? I don't think. I believe, instead, I set up the involved parameters based on many data previously collected. How many more you have the more accurate is the method.
So, thank you and good testing.

gbal says: RE:Calculations
Sent 19 November 2010, 22h22
Thank you Tom.
Ok I would try your links; I saw they concern many trip data but.... I don't understand German and I could translate statements, labels and so on in Italian or English. Before to do this I would like to know the subject of them. In other words what do you mean with those two links ? Are they another way to make prevision of spent time? Or are they some trip data collection you processed by a similar or alternative method and you want compare the results? Could you kindly add some clarification or explanation ?
Thank you

neutrino Pro says: RE:Calculations
Sent 20 November 2010, 11h56
ciao Giulio:
the same in italian (but only as pdf):
(some instructions on the second page)

TomClancy says: RE:Calculations
Sent 21 November 2010, 22h19
Hi Giulio!

My english is very poor, but I try to explain what the excel-sheets are for. Both sheets calculate the time for a planned hike. You just have to fill in the hights and the distances of your waypoints and the sheets will calculate the time and even a profile of the hike in a seperate sheet. I use these tools often an like their precision. Personally I prefer the first link. I hope I could help you with my explanations.

The next link is the sheet in italian language, This may help you to translate.




gbal says: RE:Calculations
Sent 21 November 2010, 23h31
Thank you very much Tom for your explanation. Neutrino already send me the link to the Italian document and I promised to myself to use all those documents (sewed together) to estimate this method compared with my one. My first impression is that the method you follow could be more complete of mine and keeps into account many other parameters; on the other hand my method seems more simple. Ok, we will talk about this topic again in the future.
Thank you very much and...compliments for your English; it is as good (or bad) as mine.

gbal says: RE:Calculations
Sent 22 November 2010, 22h23
Hi Tom,
I compared all the data you linked me with my method. You and the interested people can see the results on tthe following links.




It is better to use Chrome or Firefox as browser but IE is good enough.

MicheleK says: Great post
Sent 20 November 2010, 03h44
Ciao Giulio,
great post indeed.

Interesting model - I think you could finetune it by translating a GPS trace onto excel, calculate distance and drop for each step - this would give you very small segments and finetune the result.

Anyone knows what algorithm Swissmap is using when they indicate times?

I use something much more empiric but it has served well so far as it seems to average out some of the errors - or maybe I just always adapt my speed to what I foresee unconsciously (provided I dont take unplanned breaks or conditions are unexpected?
to answer this I would have to do a small experiment and check accurancy in a planned vs unplanned situation :-)

I use 4 Km/h for distance in general and 400 m/h for ascent and 600 m/h for descent - I then add 1h or 1.5h for breaks. I am normally happy with accuracy 1h - thats of course different for mountain runs. I think its important to calculate enough safety margins and a point of no return that gives you some flexibility - Conditions play a big role, too.

Cari Saluti.

gbal says: RE:Great post
Sent 20 November 2010, 10h07
Hi Michele,
I thank you for appreciating my work. About a more accurate finetuning by directly transfer the data from GPS to Excel I am agree with you; it will be the best way but I also think it would require a big programming effort compared with a slight improvement.
I don't know how Swissmap works in estimating the walk times, sorry.
I suppose that my method works fine in that it's based on a lot of old collected data that refer to averaging situations and this is why it takes into account the unforeseen situations, some stops, some error in following the tour and so on.
Your system is as good as my method if you are confident about it (this is the key!)
Un caro saluto anche a te.

MicheleK says: RE:Great post
Sent 5 December 2010, 14h58
...if you are confident in it (this is the key...)... AGREE COMPLETELY and a very accurate observation indeed: we of course have a behaviour which tries to stick to our plan and the more we believe into it the better it will work....

cari saluti

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