There are some examples on the Mozilla Developer Network page:
/**
* Returns a random number between min (inclusive) and max (exclusive)
*/
function getRandomArbitrary(min, max) {
return Math.random() * (max  min) + min;
}
/**
* Returns a random integer between min (inclusive) and max (inclusive).
* The value is no lower than min (or the next integer greater than min
* if min isn't an integer) and no greater than max (or the next integer
* lower than max if max isn't an integer).
* Using Math.round() will give you a nonuniform distribution!
*/
function getRandomInt(min, max) {
min = Math.ceil(min);
max = Math.floor(max);
return Math.floor(Math.random() * (max  min + 1)) + min;
}
Here's the logic behind it. It's a simple rule of three:
Math.random()
returns a Number
between 0 (inclusive) and 1 (exclusive). So we have an interval like this:
[0 .................................... 1)
Now, we'd like a number between min
(inclusive) and max
(exclusive):
[0 .................................... 1)
[min .................................. max)
We can use the Math.random
to get the correspondent in the [min, max) interval. But, first we should factor a little bit the problem by subtracting min
from the second interval:
[0 .................................... 1)
[min  min ............................ max  min)
This gives:
[0 .................................... 1)
[0 .................................... max  min)
We may now apply Math.random
and then calculate the correspondent. Let's choose a random number:
Math.random()

[0 .................................... 1)
[0 .................................... max  min)

x (what we need)
So, in order to find x
, we would do:
x = Math.random() * (max  min);
Don't forget to add min
back, so that we get a number in the [min, max) interval:
x = Math.random() * (max  min) + min;
That was the first function from MDN. The second one, returns an integer between min
and max
, both inclusive.
Now for getting integers, you could use round
, ceil
or floor
.
You could use Math.round(Math.random() * (max  min)) + min
, this however gives a noneven distribution. Both, min
and max
only have approximately half the chance to roll:
min...min+0.5...min+1...min+1.5 ... max0.5....max
└───┬───┘└────────┬───────┘└───── ... ─────┘└───┬──┘ ← Math.round()
min min+1 max
With max
excluded from the interval, it has an even less chance to roll than min
.
With Math.floor(Math.random() * (max  min +1)) + min
you have a perfectly even distribution.
min.... min+1... min+2 ... max1... max.... max+1 (is excluded from interval)
     
└───┬───┘└───┬───┘└─── ... ┘└───┬───┘└───┬───┘ ← Math.floor()
min min+1 max1 max
You can't use ceil()
and 1
in that equation because max
now had a slightly less chance to roll, but you can roll the (unwanted) min1
result too.