Average hiking speed over level ground is often reckoned around twenty miles per day, assuming hikers in good shape who know what they are doing and where they’re going. (As a rough approximation, which is fine, I’m just looking for rough approximations here.)
But I think that assumes either fairly open ground, or a trail through forest. What would a corresponding figure be in the absence of a trail? To be specific, say primeval deciduous forest, as would’ve been found in northern Europe or parts of North America before the arrival of humans? Assuming the hikers know what they are doing, how to handle the terrain, it will still be at least somewhat slower, right?
As a CDT through hiker, off-trail ultramarathon runner, and general fan of cross-country travel, I feel somewhat qualified to speak to this question.
Moving off trail tends to be slower than moving on trail. Exactly how much slower depends on many factors.
- I generally walk 3 mph (~5 km/h) on a well maintained trail with reasonable (less than 1000 ft/mile or 200 m/km) elevation change
- I generally walk 2-3 mph (~3-5 km/h) off trail in the absence of thick brush, with reasonable elevation change, and easy navigation (obvious landmarks to follow).
- I generally walk 1 mph (~1.6 km/h) or slower off trail in moderate brush, with extreme elevation change, and difficult navigation.
- I have moved as slowly as 0.2 mph (~0.3 km/h) in extreme conditions.
Your mileage may vary!
While I love @Lucas Wojciechowski’s answer, I’d also like to answer this from a different direction, as OP is asking about the distance covered in a single day.
I think here the estimate of roughly 20-30 km per day (13-20 miles) is a reasonable base-line assumption given:
- you know you’ll be on decent trails without excessive elevation
- you won’t waste time on navigation (because of obvious landmarks or good trail signage)
- your goal is to cover ground (i.e. no hours spent fishing, landscape painting, sightseeing, etc…)
This will be sustainable for longer multi-day treks even with reasonable pack weight (15-25kg) and with mediocre stamina & training. Also this assumes that you need to spend time to break camp in the morning, setup camp at night, spend time cooking, collecting/purifying water, getting stuff out of and into your backpacks – in short on an 8-10 hour day you’ll hardly do 8-10 hours of actual walking.
–> But, all of this considered, in my experience (of many months and hundreds of kilometers of treks) the 20-30 km/day can be a reasonable assumption to base any route planning on if you want to plan a trek on a well-mainained long-distance hiking trail (e.g. Kungsleden, Appalachian, CDT, Camino de Santiago, …).
If you ever go off-trail, then all bets are off: as Lucas outlined in his answer, depending on various factors your speed can slow to a crawl. In such situations you either need good beta on the planned route (e.g. from locals, a good guide book, etc.) or you need to plan with very conservative speeds, to ensure they will be sustainable for you and your group.
 This is especially true because over multi-day hikes any daily deviations tend to even out over multiple days.