map(value, fromLow, fromHigh, toLow, toHigh)

Re-maps a number from one range to another. That is, a value of fromLow would get mapped to toLow, a value of fromHigh to toHigh, values in-between to values in-between, etc.

Does not constrain values to within the range, because out-of-range values are sometimes intended and useful. The constrain() function may be used either before or after this function, if limits to the ranges are desired.

Note that the “lower bounds” of either range may be larger or smaller than the “upper bounds” so the map() function may be used to reverse a range of numbers, for example

 y = map(x, 1, 50, 50, 1); 

The function also handles negative numbers well, so that this example

 y = map(x, 1, 50, 50, -100); 

is also valid and works well.

The map() function uses integer math so will not generate fractions, when the math might indicate that it should do so. Fractional remainders are truncated, and are not rounded or averaged.

value: the number to map

fromLow: the lower bound of the value's current range

fromHigh: the upper bound of the value's current range

toLow: the lower bound of the value's target range

toHigh: the upper bound of the value's target range

The mapped value.

/* Map an analog value to 8 bits (0 to 255) */
void setup() {}
 
void loop()
{
  int val = analogRead(0);
  val = map(val, 0, 1023, 0, 255);
  analogWrite(9, val);
}

For the mathematically inclined, here's the whole function

long map(long x, long in_min, long in_max, long out_min, long out_max)
{
  return (x - in_min) * (out_max - out_min) / (in_max - in_min) + out_min;
}

* Constrain

Source: arduino.cc