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What size are the standard grids in those roll-up mats people use for D&D 5e and thus what radius / diameter should the base of a miniature be for easy usage?

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In the Dungeon Master's Guide, page 250, it states that when playing with a mat the squares or hexes should be 1 inch across and should represent 5 feet. But you can play with the scale of the squares as much as you like.

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    \$\begingroup\$ The 1" squares are by no means mandatory; I've run games at half that scale (with very tiny minis) to allow for large battlefields. The other answer is still better, because it provides some insight into the reason the typical mat is the size it is. \$\endgroup\$ – T.J.L. Jun 21 '17 at 12:22
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Miniatures come in varying sizes and they are all described in metric units. For D&D and most other RPGs the most commonly used scale is 25/28mm - this is a scale of 1:64/1:56-58.

Mats are usually drawn with 1" or 25mm grids which are almost the same (1"=25.4mm). For D&D a square represents 5 feet, a scale of 1:60.

These scales are clearly not the same, however, they are close enough. You should have no trouble fitting the base of a 25/28mm mini into a square of this size.

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    \$\begingroup\$ You might want to add that Miniatures and mats are not strictly required for 5e. \$\endgroup\$ – J. A. Streich Jun 21 '17 at 3:25
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    \$\begingroup\$ Considering that the context of the question is the selection of mats, I don't see the need to specify that they're optional. \$\endgroup\$ – T.J.L. Jun 21 '17 at 12:21
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    \$\begingroup\$ In my experience, it's not actually practical to use 1 inch minis on a 1 inch grid - at least, not if the battlefield ever contains a clump of critters. Many minis have bits that stick out from the base, especially large ones, and it becomes quite impractical to move minis without fiddling with everything else on the battlefield. So, if you have a choice in the matter, I'd add some space. I try to aim for at least 27mm grids, and 30mm is even better, if you have the space. \$\endgroup\$ – Eamon Nerbonne Dec 15 '18 at 19:43

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