I know that is not a technical question, but I don't know where else to ask.
Is there a way to get the marked speed limit of a road from google or bing maps? or any other web service?
The speed limit is shown on the bottom left corner of the map while navigating, just above the bar that shows the estimated time of arrival (ETA) along with other information. Google Maps first made the on-screen speedometer available to users in 2019.
Open Google Maps and tap on your profile icon in the upper right corner. Tap on Settings. Tap on Navigation. Tap on the toggle switch next to Show speed Limits.
On UK roads, maximum speed limits are indicated by roadside signs which show the number on a circular sign with a red border. These signs are shown as you enter a new limit and may be displayed at intervals along the road – either on lamp posts or free-standing poles for single carriageway or dual carriageways.
You cannot obtain this information from Bing Maps or Google Maps. Nor am I aware of any other webservices that provide this information (certainly not any free ones).
Open Street Map (http://osm.org) has the ability for ways to be recorded with the maxspeed tag. You could download the OSM planet dataset and host it in a spatial database such as SQL Server 2012, then create your own web service to query the database and return the maxspeed of the closest way, but this value is not always reliably filled in. However, even when the maxspeed tag is missing, you can derive an approximate max speed limit by looking at the national speed limit for the type of road in the country of interest, as documented at http://wiki.openstreetmap.org/wiki/OSM_tags_for_routing/Maxspeed
OSM data varies in quality quite a lot by country. Here in the UK it's really very good - more up-to-date, accurate, and complete than Google Maps or Bing Maps in many respects. However, in other countries it's not so reliable. Alternatively, there are providers that will sell you commercial datasets of road networks containing this information, but they tend to be at the national level and can be very expensive. (What country(s) are you interested in? You don't mention..)
Finally, be aware that this information is fairly dynamic and time-dependent - if you do download a dataset of max road speed information (either from OSM or a commercial source) expect to have to update it frequently to keep up-to-date with highway changes.
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