How do I initialize a final class property in a constructor?

You cannot instantiate final fields in the constructor body. There is a special syntax for that:

class Point {
  final num x;
  final num y;
  final num distanceFromOrigin;

  // Old syntax
  // Point(x, y) :
  //   x = x,
  //   y = y,
  //   distanceFromOrigin = sqrt(pow(x, 2) + pow(y, 2));

  // New syntax
  Point(this.x, this.y) :
    distanceFromOrigin = sqrt(pow(x, 2) + pow(y, 2));
}

You can make it even shorter with this. syntax in the constructor (described in https://www.dartlang.org/guides/language/language-tour#constructors):

class Point {
  final num x;
  final num y;
  final num distanceFromOrigin;

  Point(this.x, this.y)
      : distanceFromOrigin = sqrt(pow(x, 2) + pow(y, 2));
}

If you have some more complicated initialization you should use factory constructor, and the code become:

class Point {
  final num x;
  final num y;
  final num distanceFromOrigin;

  Point._(this.x, this.y, this.distanceFromOrigin);

  factory Point(num x, num y) {
    num distance = distanceFromOrigin = sqrt(pow(x, 2) + pow(y, 2));
    return new Point._(x, y, distance);
  }
}

Here is a simplified summary of the ways to initialize a final class variable.

class MyClass {
  final int x; //     <-- initialize this
}

Initializer value

class MyClass {
  final int x = 'hello'.length;
}

You'd only use final if the initialization could only be done at runtime. Otherwise, static const is better:

class MyClass {
  static const int x = 0;
}

Initializer formal

class MyClass {
  MyClass(this.x);
  final int x;
}

This is the most common approach.

Initializer list

class MyClass {
  MyClass(int x) 
    : _x = x;
  final int _x;
}

This is useful when you want to keep a field private.

Default parameter value

You can surround the parameter with square brackets ([]) for an unnamed parameter or curly braces ({}) for a named parameter and then give it a default value.

class MyClass {
  MyClass({this.x = 0});
  final int x;
}

This is useful if you want to make the parameter optional.

You could accomplish the same thing with an initializer list as well:

class MyClass {
  MyClass({int? x}) 
    : _x = x ?? 0;
  final int _x;
}

Late initialization

class MyClass {
  MyClass(String? a) {
    x = a?.length ?? 0;
  }
  late final int x;
}

This is useful if you need to do more complex initialization than is allowed in the initializer list. For example, I've done this when initializing a gesture recognizer in Flutter.

Lazy initialization

Another advantage of using late is that it doesn't initialize a value until you access the value.

class MyClass {
  late final int x = _doHeavyTask();
  int _doHeavyTask() {
    var sum = 0;
    for (var i = 0; i < 100000000; i++) {
      sum += 1;
    }
    return sum;
  }
}

This is useful if you have a heavy calculation that you only want call if you absolutely need it.

This doesn't initialize x:

final myClass = MyClass();

But this does initialize x:

final myClass = MyClass();
final value = myClass.x;

I've had a similar problem: I was trying to initialise a final field from the constructor, while simultaneously calling a super constructor. You could think of the following example

class Point2d {
  final int x;
  final int y;

  Point2d.fromCoordinates(Coordinates coordinates)
      : this.x = coordinates.x,
        this.y = coordinates.y;
}

class Point3d extends Point2d {
  final int z;

  Point3d.fromCoordinates(Coordinates coordinates)
      :this.z = coordinates.z,
        super.fromCoordinates(coordinates);
}

/// Demo class, to simulate constructing an object
/// from another object.
class Coordinates {
  final int x;
  final int y;
  final int z;
}

Well apparently this works. You can initialise your final fields by using the above syntax (check Point3d's constructor) and it works just fine!

Run a small program like this to check:

void main() {
  var coordinates = Coordinates(1, 2, 3);
  var point3d = Point3d.fromCoordinates(coordinates);
  print("x: ${point3d.x}, y: ${point3d.y}, z: ${point3d.z}");
}

It should prin x: 1, y: 2, z: 3