Without Haste, what Efficiency level does a Pickaxe need to insta-mine Stone?

Question

I am playing on a server that sells Efficiency 8 and Efficiency 10 Pickaxes, which ones out of the two can insta-mine stone and what other harder blocks can they insta-mine?

The server is a Java Edition Server.

Answer 1

The player's digging speed is controlled by three factors:

• the block being broken
• the item the player is currently wielding
• the mining penalties affecting the player [we can omit them for simplicity]

Every block has a hardness value, which determines the base amount of breaking time.

The base time (in seconds), if the player can harvest the block with the current tool, is:

block_hardness x 1.5   //correct tool
block_hardness x 5     //wrong tool 

The right tool increases digging speed by a constant multiplier, given in the following table:

Material	Nothing	Wood	Stone	Iron	Diamond	Netherite	Gold
Tool Speed	1	2	4	6	8	9	12

If a proper tool is used, the tool speed is further increased by the Efficiency enchantment. If the level of Efficiency is not 0, a value is added to the tool speed:

1 + enchantment_level²

Since you're asking for level 8 and 10 you get:

• Efficiency VIII results in 1+8² = 65 bonus speed
• Efficiency X results in 1+10² = 101 bonus speed

It's worth noting that the total time to break a block is always a multiple of 1⁄20 of a second, or 1 game tick; any remainder is rounded up to the next tick.

---

Regarding your insta-mine question:

When breaking a block, a tool and its enchantments do its speed value as "damage" to a block every game tick, and when that value equals or exceeds the block's hardness, the block breaks. If the tool and enchantments immediately equal or exceeds the hardness times 30, the block breaks with no delay.

Hence, we get the formula:

(tool_speed + efficiency_bonus) >= block_hardness * 30

Given the best Pickaxe materials, they can insta-mine up to the following hardness:

	Efficiency VIII	Efficiency X
Diamond	(8+65)/30 = 2.433	(8+101)/30 = 3.633
Netherite	(9+65)/30 = 2.467	(9+101)/30 = 3.667
Gold	(12+65)/30 = 2.567	(12+101)/30 = 3.767

^{(assuming that the broken block can be harvested with the relative tool)}

Here's a list of blocks ordered by their hardness.

EDIT:

Which ones out of the two can insta-mine Stone?

Stone has 1.5 hardness, so the answer is both.

What Efficiency level does a Pickaxe need to insta-mine Stone?

Reversing the formula (tool_speed + efficiency_bonus) >= block_hardness * 30 we get:

tool_speed + (1 + enchantment_level²) >= 1.5 * 30
tool_speed + enchantment_level² >= 44

So Diamond, Netherite and Gold Pickaxe will require at least Efficiency VI to insta-mine Stone, since all of them produce a damage greater or equal than 44.

Source, Minecraft wiki.

Answer 2

I found this website, which has a table about which tools can instant mine which blocks.

It seems an efficiency 5 diamond pickaxe will be able to instant-mine stone if you have haste 2.

It's hard to say which pickaxes other than diamond will be able to instant mine stone, but it seems your pickaxe's "speed" will need to be greater than 45 to instant mine stone.

Efficiency: additional (1+level2) when using the proper tool

This means an Efficiency 6 Diamond, Netherite or gold pickaxe should work. Efficiency 7 should be enough for any pickaxe to break stone.

So to answer your question: Both should be able to instant mine stone.

As for other blocks, that depends on which material the pickaxe is made out of. Take a look at the table on this page. The total speed needs to be at least 30 times the block hardness.

Answer 3

I'll answer

what other, harder blocks can they insta-mine?

Given pinckerman's answer, we have

Since you're asking for level 8 and 10 you get:

• Efficiency VIII gives 65
• Efficiency X gives 101

plus the value given by the material (8 for diamond, 9 for netherite).

Blocks can be insta-mined if the value above (e.g. 110 for an Efficiency X netherite pickaxe) is larger than 30 times the hardness value of the block:

If the tool and enchantments immediately equal or exceeds the hardness times 30, the block breaks with no delay

so (assuming a netherite pickaxe) with Eff X, you'll insta-mine blocks with hardness lower than 110/30 = 3.6666
with Eff VIII instead you'll insta-mine blocks with an hardness lower than 74/30 = 2.4666

Hardness values are listed here. Please do note that you also have to check if the block is optimally broken by a pickaxe, e.g. a wooden door with hardness 3 won't be insta-mined, as you need an axe, not a pickaxe.