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I need a sight range for a ship at sea in 5e.

This is important because I'm using a virtual tabletop and using fog of war. This seems like a stat that would be part of the ship's stat block, but such a stat is nowhere to be found.

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    \$\begingroup\$ Is this a magical ship that can see? Or do you mean whether being on a ship has any effect on how far someone on it can see? \$\endgroup\$ – Szega Jul 2 at 8:24
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As far as the people on it can

5e doesn't offer any rules for how far a ship can "see"; however, the DMG does have some default rules about visibility outdoors. According to these rules, characters can normally see about 2 miles out from ground (or sea) level, and 40 miles out if looking from a vantage point such as a hill or mountain "or are otherwise able to look down on the area around them from a height", though rain or fog can significantly reduce visibility (down to 1 mile in heavy rain, or merely a couple hundred feet in fog).

Applied directly, that would suggest that the crew of a ship in clear weather should be able to see about 2 miles (land, not nautical) to the horizon from the deck or 40 miles to the horizon from the crow's nest atop a mast. These rules don't offer any kind of middle ground between those extremes, and a viewing distance of 40 miles is not realistic for an actual ship, on which the crow's nest will be at best a few tens of meters above sea level - but it is all that the rules have to say about how far characters on a ship might be able to see.

Luckily, the formula for estimating horizon distance based on vantage height is simple and, if you assume the planet you're on has earthlike dimensions, there are online calculators which will do it for you. The world of Oerth from the Greyhawk campaign setting (in which Ghosts of Saltmarsh is set) is almost exactly Earth-sized, according to the 2e sourcebook The Adventure Begins (p.9):

Careful mathematical measurements and magical divinations reveal that the circumference of Oerth is 25,200 miles. Thus, the diameter of Oerth is about 8,021.5 miles...

The actual Earth's circumference is is about 24,900 miles, so the values determined by an Earth-based calculator will be near as makes no difference to Oerth. Popular alternative campaign setting the Forgotten Realms' default planet, (Abeir-)Toril, hasn't been specified with such precision so far as I can find, but the the 2e A Grand Tour of the Realms (p.4) does state it is "Earth-sized", so Earth-based vision measurements should also be valid there.

So, using such a calculator, we can easily figure out some more realistic vision distances for your ships. Using the heights of masts given for sample ships in Ghosts of Saltmarsh Appendix A (and assuming, possibly inaccurately, that the given mast height is measured from sea level rather than the deck), we get the following vision distances:

  • Galley. One 120ft mast. 13.4 miles to horizon.
  • Keelboat. One 10ft mast. 3.9 miles to horizon.
  • Longship. One 20ft mast. 5.5 miles to horizon.
  • Sailing ship or warship. Three 80ft masts. 11 miles to horizon.

Larger ships with taller masts have an advantage in being able to spot other ships from further away. Of course, larger ships should also be easier to spot from a distance as their masts will be visible at much greater distance than the body of the ship... but observers from the top of a mast on a large ship would be able to see the body of a smaller vessel while only the tip of their mast is over the horizon, so would almost certainly spot the other ship first and could probably skirt it without being noticed.

In any event, ships that are close enough to meaningfully interact with each other would be able to see each other from their decks - barring unusual weather such as extremely heavy fog, in which case the vision range is up to the DM's determination of the weather.

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The maximum sight range without obstructions, weather, or darkness depends on the height of the eyes over the ground.

This is explained in this Wikipedia article (it is in German): https://de.wikipedia.org/wiki/Sichtweite

Most of the same information is explained in the following English article: https://en.wikipedia.org/wiki/Horizon#Distance_to_the_horizon

The sight range is given by:

$$S = \sqrt{2R} \times \sqrt{h}$$

Where S is the sight range, R the radius of the planet, and h the height of the eyes. The sight is influenced by atmospheric refractive index.

Eye height of 2 meters (7 feet) makes 5 kilometers sight (about 3 statute miles), which would be reasonable for a person on deck of a small ship. 30 meters (100 feet) makes for 19 kilometers (12 statute miles), reasonable for a person in the crow’s nest, maybe.

Now, obviously, these values are for the real world earth, not for the forgotten realms, so R may need to be adjusted and the results recalculated. For a disc (which the Forgotten Realms aren't on) completely different rules apply.

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  • \$\begingroup\$ Great point about the influence of R, since the fantasy setting can take you to many different places. For infinite R (a flat world), sight distance is theoretically unlimited, so atmospheric clarity and eye anatomy will be among the few limiting factors. \$\endgroup\$ – Nuclear Hoagie Jul 2 at 18:27
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Assuming a clear day, you can actually see another ship breach the horizon about 12 miles away (19.3 kilometres or 10.4 nautical miles). Sneaking up on a ship tends be rather tricky!

Adverse weather such as actual fog (as opposed to "fog of war") or obstructions such as islands will obviously affect this. But generally you can see a long way in either direction at sea during the day, which is probably why they didn't bother with sight range. At night you will obviously be limited by the ambient brightness of the moon and stars or darkvision (which only tends to be out to 60').

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