ETA Cal­cu­la­ti­on

How a GPS navi­ga­ti­on soft­ware cal­cu­la­tes the ETA

The artic­le explains, how the esti­ma­ted time of arri­val (ETA) is cal­cu­la­ted, how it takes live traf­fic infor­ma­ti­on into account and how we use big data to impro­ve our calculation.

What is the ETA and how is it cal­cu­la­ted? The esti­ma­ted time of arri­val is the cur­rent time plus the remai­ning dri­ve time. It is the cal­cu­la­ted time when you will most likely arri­ve at your destination.

You are curr­ent­ly vie­w­ing a pla­ce­hol­der con­tent from You­tube. To access the actu­al con­tent, click the but­ton below. Plea­se note that doing so will share data with third-par­ty providers.

More Infor­ma­ti­on

In our pri­va­te lives we see the ETA on the screen of our GPS app. It tells us, when we will arri­ve at our desti­na­ti­on and if we beat it by a cou­ple of minu­tes it makes us a litt­le proud and we feel good. We use it as a rough indi­ca­ti­on of the remai­ning dri­ve time and if it is off by a cou­ple of minu­tes, it is not a big deal.

Cal­cu­la­te your truck dri­ving time here

Enter Start and Desti­na­ti­on — choo­se with or wit­hout Live-traf­fic and cal­cu­la­te your truck dri­ving time:

You are curr­ent­ly vie­w­ing a pla­ce­hol­der con­tent from Default. To access the actu­al con­tent, click the but­ton below. Plea­se note that doing so will share data with third-par­ty providers.

More Infor­ma­ti­on

This exam­p­le was imple­men­ted using the Map­Trip Ser­ver-API.

ETA in Trans­port Planning

In the pro­fes­sio­nal envi­ron­ment howe­ver, the ETA is the second most important fea­ture of a GPS navi­ga­ti­on soft­ware. The most important is obvious­ly to make sure, that the dri­ver rea­ches his desti­na­ti­on. The dri­ve time (or ETA) is the basis for most trans­port plan­ning tasks. Here, errors in the ETA cal­cu­la­ti­on can accrue to signi­fi­cant dimen­si­ons. Pre­cis­e­ly pre­dic­ting the ETA is the­r­e­fo­re extre­me­ly important.

How the ETA cal­cu­la­ti­on works with traf­fic information

Let’s look at an exam­p­le to under­stand how the ETA is calculated.

a basic map to explain how the ETA is calculated
The grey lines repre­sent a basic map on which the ETA will be cal­cu­la­ted. Each seg­ment of the map has a length of 1km.

A cru­cial com­po­nent for the cal­cu­la­ti­on of dri­ve times (and the rou­te its­elf) is obvious­ly live traf­fic infor­ma­ti­on. They tell the navi­ga­ti­on soft­ware how fast traf­fic is moving curr­ent­ly on a seg­ment. In Map­Trip Truck we are using eit­her Tom­Tom or Here for traf­fic information.

Adding traf­fic infor­ma­ti­on to the map

ETA Calculation
Live traf­fic data is being super­im­po­sed on the map. The speed values are used for rou­te cal­cu­la­ti­on and ETA calculation.

Now we have a map that gives us the distance to the desti­na­ti­on and live traf­fic data which tells us the speed that are curr­ent­ly being dri­ven on tho­se seg­ments. Howe­ver, the live traf­fic data is not available for all seg­ments. The­re are still many grey seg­ments in our sketch which have no live data attri­bu­ted. In prac­ti­ce the­se are most­ly resi­den­ti­al and other minor side roads. The soft­ware now assu­mes speed values for tho­se roads to be able to cal­cu­la­te the time requi­red to tra­ver­se tho­se seg­ments. In this exam­p­le we assu­me a speed of 50km/h if we have no live traf­fic data.

Cal­cu­la­ting the route

The rou­ting algo­rithm will now figu­re out the quickest con­nec­tion bet­ween the cur­rent posi­ti­on and the destination. 

The light blue line indi­ca­tes the fastest rou­te cal­cu­la­ted by the rou­ting algorithm.

Now that we know the rou­te, it is easy to cal­cu­la­te the dri­ve time.

Cal­cu­la­ting the dri­ve time

The rou­te con­sists of four “green” seg­ments and three “grey” seg­ments. In our sam­ple map each seg­ment has a length of 1km. To cal­cu­la­te the dri­ve time, the length of the seg­ment has to be devi­ded by the speed at which it can be tra­vel­led on.

Green: 4km / 85km/h = 0.047h = 2,82min ~ 3min

Grey: 3km / 50km/h = 0.06h = 3.6min

The soft­ware will return a total dri­ve time of rough­ly 6.6min. Howe­ver, this con­ta­ins some mar­gin of error. 

How to mini­mi­ze the mar­gin of error in ETA calculation

As we have seen abo­ve the dri­ve time cal­cu­la­ti­on and the ETA cal­cu­la­ti­on reli­es on three types of information:

  1. the length of the rou­te / of the segments
  2. the live traf­fic speeds
  3. the assu­med speeds on seg­ments wit­hout traffic

While the length of the rou­te can be assu­med to be extre­me­ly pre­cise the values of the live traf­fic and the assu­med speeds will ine­vi­ta­b­ly con­tain some error.

Traf­fic data are crea­ted by aver­aging the enti­re traf­fic on a seg­ment. Speed values from Por­sches are aver­a­ged with values from trucks and bus­ses. Our typi­cal user dri­ves a truck. The­r­e­fo­re we can igno­re speed values over 90km/h. But speed data from traf­fic is never 100% accurate.

Com­pa­ring cal­cu­la­ti­on with measurement

In order to impro­ve our ETA cal­cu­la­ti­on, we found, we need to compa­re our cal­cu­la­ti­ons with actu­al mea­su­re­ments. As Map­Trip is a con­nec­ted navi­ga­ti­on we had the pos­si­bi­li­ty to crea­te a test fleet which sends home the cal­cu­la­ted dri­ve time and the actu­al mea­su­red dri­ve time. Ther­eby we accu­mu­la­ted a vast amount of data which we then analyzed.

For each gui­dance we had three values:

  1. length of route
  2. cal­cu­la­ted dri­ve time tc
  3. actu­al mea­su­red dri­ve time tm

From the cal­cu­la­ted dri­ve time and the mea­su­red dri­ve time we cal­cu­la­ted the rela­ti­ve error Er for each route. 

Er = (tc — tm) / tc * 100 [%]

We then plot­ted the fre­quen­cy dis­tri­bu­ti­on for dif­fe­rent inter­valls of rou­te lengths. This is what we got.

Fre­quen­cy dis­tri­bu­ti­on of the error in dri­ve time calculation

ETA Calculation
fre­quen­cy dis­tri­bu­ti­on of the rela­ti­ve error in dri­ve time cal­cu­la­ti­on for rou­tes of length 10km to 30km

The abo­ve graph shows the num­ber of rou­tes with a given rela­ti­ve error Er. The left half of the chart (nega­ti­ve) repres­ents rou­tes whe­re the dri­ver has arri­ved at the desti­na­ti­on later than cal­cu­la­ted. The right half of the chart (posi­ti­ve) repres­ents rou­tes whe­re the dri­ver has arri­ved at the desti­na­ti­on later than calculated. 

The bubbles point out data points whe­re the error is zero (white), ‑10% (oran­ge) and +10% (green).

The influence of traf­fic lights on ETA calculation

ETA Calculation
fre­quen­cy dis­tri­bu­ti­on of the rela­ti­ve error in dri­ve time cal­cu­la­ti­on for rou­tes of length 2km to 5km

In the abo­ve chart you can see the error dis­tri­bu­ti­on for rou­tes which are bet­ween two and five kilo­me­ters long. Plea­se note that the dis­tri­bu­ti­on cur­ve is much more even­ly spread out to both sides. The cur­ve is much less shaped like a peak but rather like a bell.

The rea­son for this shape is easy to under­stand: Ima­gi­ne a short 2km urban rou­te. If you are unlucky and spend just two minu­tes wai­ting in front of a red light, your dri­ve time cal­cu­la­ti­on will alre­a­dy be about 100% off!

Bet­ter ETA pre­dic­tion on long routes

By con­trast the ETA pre­dic­tion beco­mes more relia­ble with lon­ger routes.

ETA Calculation

The dis­tri­bu­ti­on graph for rou­tes with a length of 100km to 200km has a much more peak-like shape. Plea­se note the sharp drop off after about Er = 10%. This means that hard­ly any­bo­dy beat the ETA by more than that mar­gin (in other words, nobo­dy went faster). This is logi­cal as our test fleet con­si­sted of trucks which have a speed limit of about 90km/h.

On the other side of the peak the dis­tri­bu­ti­on is much more spread out. In other words, the­re were quite a few dri­vers whos dri­ve time was lon­ger than cal­cu­la­ted. This can be explai­ned by unex­pec­ted traf­fic jams (which were not pre­dic­ted by the traf­fic infor­ma­ti­on) or, sim­ply, by bra­ke times. Dri­vers take a break and lea­ve the navi­ga­ti­on soft­ware in the gui­dance mode.


The ana­ly­sis of the actu­al dri­ve time com­pared to the cal­cu­la­ted dri­ve time is a good means to fine tune the ETA calculation. 

ETA Calculation
mean error of dri­ve time calculation

In the shown exam­p­le the dri­ve time cal­cu­la­ti­on would need a cor­rec­tion of 9% in order to mini­mi­ze the mean error.

Skip to toolbar