# How do I read 2d10 as a percentage?

I own 2 d10 dice with differently numbered sides (0 through 9, and 00 through 90), although the same applies for two identical 'regular' d10 dice.

How do I read the percentage value if I use both dice?

It's pretty straight-forward if I roll between 11 and 89, but outside this range it becomes slightly confusing:

50, 6 → 56%
8, 9 → 89%
00, 0 → 0% or 10% or 100%?
90, 0 → 90% or 100%?
10, 0 → 10% or 20%?


Note: if I roll with identical d10, I roll sequential, not simultaneous to avoid discussion if the 8 or 9 is the first digit.

I have a hunch that 0% isn't really a thing in most systems that use d100, so that eliminates 00, 0 → 0%.

So is it then true that on the first d10, the 00 counts as zero, but on the second d10, the 0 counts as ten?

You read one die as the 10s place and the other die as the 1s place. Traditionally, (00, 0) means 100 instead of 0. Your set is marked to make forgetting which die is which, intentionally or accidentally, impossible.

10s| 1s | Reads as
00    1      1
00    2      2
10    0     10
30    1     31
50    6     56
80    9     89
90    0     90
90    1     91
90    9     99
00    0    100 (exception)


If you have just two dice numbered 0-9 you can do the same thing by just designating one color as 10s and the other as 1s.

Apparently, there are some new d100 sets that are intended to be added together, so that 90, 10 = 100, but those are not the dice you have described.

• My group uses the houserule that if your d10s are completely identical, you must read them from left to right when they fall. May 20 '15 at 1:31
• @MarcDingena We use the facing of the player making the roll. That said, it doesn't really matter how you determine which is left and which is right as long as it's unambiguous whenever a roll is made. May 20 '15 at 7:11
• @GMJoe: we just forbid people to roll identical d10s together as a d100. If you can't find two different, then roll them one at a time. Saves getting the set square out to adjudicate close cases. May 21 '15 at 12:57
• It might be worth extending "Traditionally, (00, 0) means 100 instead of 0. But some RPG's do differ. Check in the rulebook for your system as to if it is 0-99 or 1-100. Depending on the system rolling (00,0) could be the perfect success, or the most significant failure (or something else entirely)" Jun 30 '16 at 2:31

X|00|10|20|30|40|50|60|70|80|90|
--------------------------------
0|00|10|20|30|40|50|60|70|80|90|
1|01|11|21|31|41|51|61|71|81|91|
2|02|12|22|32|42|52|62|72|82|92|
3|03|13|23|33|43|53|63|73|83|93|
4|04|14|24|34|44|54|64|74|84|94|
5|05|15|25|35|45|55|65|75|85|95|
6|06|16|26|36|46|56|66|76|86|96|
7|07|17|27|37|47|57|67|77|87|97|
8|08|18|28|38|48|58|68|78|88|98|
9|09|19|29|39|49|59|69|79|89|99|


If you need a range of 1%-100% instead of 0%-99%, interpret 0% as 100%

• nfd: alternatively, take the numbers at face value, and add one. (Yes, it's more complicated that way). That makes 00 the lowest roll, and 99 the highest roll, and adding 1 makes the 00+1 = 1, lowest roll, and 99+1 =100, the highest roll. May 20 '15 at 16:05
• This is the best explanation of the conventional method, with the least text. May 21 '15 at 1:28

Starting from scratch: Percentile dice (d%) is meant to get you a number between 1-100. The "classic" way of getting this number is with two d10s, one designated as your "tens digit", the other as your "ones digit". (Some sets will give you a tens-digit dice that's actually labelled that way: instead of 1,2,3,4,5,6,7,8,9,0 it'll have 10,20,30,40,50,60,70,80,90,00. It's purely a help, doesn't change the mechanics at all.)

Before rolling, choose one of the two dice to be your "tens" digit. Roll them, then arrange them in order (just like you were writing it down - tens to the left of ones). Read the number, that's your answer. If you get a 0 in the tens spot, it means you rolled under 10.

The only weirdness is if you get 00. (Zeroes on both dice). That's 100. (Just imagine the little floating hundreds digit "1" there). If you're using a game that goes 0-99 rather than 1-100, then that's a straight up 0.

The important point is that there's no adding involved - you never add one die to the other, because each die is rolling a separate digit.

• "The important point is that there's no adding involved". If your dice are marked in tens (00-90) and ones (0-9), adding them is precisely what you are accomplish "because each die is rolling a separate digit". May 19 '15 at 19:26
• Except that normally a 0 on a d10 is 10, not 0, which was a cause of confusion in the original question. (And it's simpler to just put the two dice together and read the number anyway) May 19 '15 at 21:05
• @AllenGould Putting together 10 and 5 would read 105 then, no? May 20 '15 at 17:08
• I suppose if you have that style of d10 - the majority I've seen have 0 on that side. I wouldn't recommend that one for percentiles. May 20 '15 at 18:18
• @AllenGould I think he means if you have a "tens" dice, numbered 00-90 Sep 16 '15 at 1:30

There is no single right way. The important point is that everybody knows how you do it before you roll. It might also be nicer, if everybody in the group rolls the same way, but it's not something to get into a fight over.

I prefer just adding the tens and ones, and 00+0 is 100. Arguably, it's also nicer when all zeros is the special number 100, instead of being obscure 10.

Some others in my group interpret 0 as 10, so 00+0 is 10, and 90+0 is 100. This might be the most logical choice if the dice actually were 1..10 and 00..90.

The important thing is correct probabilities, of course. As long as any percentage 1..100 can occur with equal probability, the most intuitive way is a matter of how one thinks. With 2 ten-sided dice, there's exactly 100 (10x10) permutations, so as long as every percentage 1..100 can come out of the throw, then each percentage has exactly one permutation, and all is fine.

So is it then true that on the first d10, the 0 counts as zero, but on the second d10, the 0 counts as ten?

That is a mathematically coherent way to do it, but most people just read it as a two-digit number, then translate 00 to 100. This also adds a bit of dramatic tension when rolling sequentially - if you roll a 0 first, then you're probably going to get a low score, but also have a chance of getting the best one.

If I had a die marked 1-10 (they do exist, but are very uncommon), I would probably add them together. Your system reminds me somewhat of the bijective system.

• Depending on the exact system used, "100" may well be the worst possible roll (most everything BRP-derived uses percentile dice for skill checks, with a "roll equal or under", so if your skill is 20%, a first "1" is a guaranteed success, a first "0" gives you 10% chance of failing and 90% chance of succeeding). Jun 30 '16 at 9:50

Before you roll, designate which of your two dice will represent the tens digit, and which die will represent the ones digit. This is easiest if the dice are visually distinct: two different colors, or one solid-color and one metallic, or different sizes or shapes, or whatever. But if you have some other way to keep track of which die is which, that will work too. For example, you could roll 1d10 twice, first for the tens digit and then for the ones digit.

Some companies also make a special "d%": a d10 specifically meant to represent tens digits. Instead of being numbered with the traditional 0-9, a d% is numbered using multiples of 10: 00, 10, 20, 30, 40, 50, 60, 70, 80, and 90. You can also use this as a standard d10 just by using only the tens digit on each face.

In any event, once you've decided which die is which digit, roll them both and combine them to get the result. If you're rolling 2d10, then multiply the tens die's result by 10 and then add them together. If you're rolling a d10 and a d%, then you can just add the numbers, because the die has already done the multiplying by 10 for you.

Lastly, remember that a zero result means 100, not 0. Even though you can roll a 0 on 1d10, you can't roll zero on 1d100.

• In non-percent situations, a 0 on a d10 really means 10, just like how on any other die you can't roll 0 but can roll the max, such as d4(4), d6(6), d8(8), etc. Sep 15 '15 at 19:00

You have a percentile dice (or a d10 you nominate as your percentile dice) and a d10 dice.

There are broadly three ways to read these dice, each with their own conventions. So long as you are consistent with your convention then any of these methods are functionally equivalent.

# Method 1 - read the d10 as 0-9 and the percentile dice as d10*10 (ie 00, 10, 20, ... )

The natural sum of the two dice then gives you values from 0 - 99. This method won't be suitable for games like D&D (which want a range of 1-100)

Example Calculations: Percentile Dice, d10 dice, result 00,0, 0 + 0 = 0 00,5, 0 + 5 = 5 20,0, 20 + 10 = 30 90,1, 90 + 1 = 91 90,0, 90 + 0 = 90

# Method 2 - read the d10 as 0-9 and the percentile dice as d10*10 (ie 00, 10, 20, ... ), with a value of 00, 0 being 100

With this method we've introduced an exception for a roll of 00, 0. In particular, we've removed the lowest value from the previous set of sums.

Aside from the exceptional case we sum values on the dice as in method 1.

So now we get a range of 1-100 on the dice, with the lowest possible roll being 00, 1 giving a value of 1.

Example Calculations: Percentile Dice, d10 dice, result 00,0, 100 00,5, 0 + 5 = 5 20,0, 20 + 0 = 20 90,1, 90 + 1 = 91 90,0, 90 + 0 = 90

# Method 3 - read the d10 as 1-10 (assigning the 10 to 0) and the percentile dice the same way as method 1

In this method we do a straight sum of the two dice to get a read.

This gives us a range of possible values of 1 - 100, with the lowest value being 1 (on a roll of 00,1)

Example Calculations: Percentile Dice, d10 dice, result 00,0, 0 + 10 = 10 00,5, 0 + 5 = 5 20,0, 20 + 10 = 30 90,1, 90 + 1 = 91 90,0, 90 + 10 = 100

(Note: I'll format the example calculations into tables when I'm home later)

The 00 means 00. So 00/1 is 1%, 00/2 is 2% and so on. The 0 counts as nothing. If you get both, and 0% is unacceptable, then that's your 100%.

However, if 0% is acceptable but 100% is not, then it's 0%. If none are acceptable, reroll. If both are acceptable, flip a coin. Heads is 100%, tails is 0%.

• Have you actually seen a game call for a percentile roll that included both or neither 0% and 100%? Did it still call it "percentile"/"percentage", or did it use a name that didn't mean "out of 100"? Dec 23 '15 at 16:18
• I was on board with this answer until "If none are acceptable"; everything from there onward reads as written by someone who's never actually used a ruleset that includes d100 rolls. Jun 29 '16 at 23:17

I have always rolled for percent in a mathematically consistent way. Your double digit die, whether it has double digits or not, goes from 0-90. The single digit die goes from 1-10, just as when rolling for damage. Using this system a 100 is achieved by rolling 90 and 0, 10 is added to 90 making 100. I prefer this since it truly has 100 parts and the value of each die is consistent.

• While it's certainly desirable that a system for turning 2d10 into 1d100 meet the qualifications you list —"truly has 100 parts and the value of each die is consistent"— there are multiple systems that satisfy that in different ways, and this is only one of them. Dec 24 '17 at 3:22

To me it, there is an easy to remember system to use depending on what dice you have available.

I think the problem stems from the fact that ten sided dice come either as 0-9 or 1-10 or 00-90.

From this you can potentially come up with six different combinations of these three different ten sided dice. But most people use one of three of these combinations to generate a number between 1 and 100:

1. 0-9 and 00-90

The result of the 00-90 dice represents the tens place and the 0-9 represents the ones place. The only exception to this rule is if you roll 00 and 0, which represents 100.

00 and 9 is 9

50 and 0 is 50

00 and 0 is 100

1. 1-10 and 00-90

Simply add the two dice results together.

00 and 1 is 1

10 and 10 is 20

90 and 10 is 100

1. 0-9 and 0-9

This one is covered in the PHB. Roll one dice, which represents tens place, roll the other, that represents the ones place. Double 0 is 100.

0 and 8 is 8

5 and 3 is 53

0 and 0 is 100

The other dice combinations get a bit more confusing. I would stick to one of these three.

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