Fabric.js - Free draw a rectangle

Looks like Fabric.js calculates everything from the origin. So, 'Top' and 'Left' are a bit misleading. Check the following link: Canvas Coordinates Have Offset. Also, I've changed a bit of your code:

var canvas = new fabric.Canvas('canvas');
canvas.observe('mouse:down', function(e) { mousedown(e); });
canvas.observe('mouse:move', function(e) { mousemove(e); });
canvas.observe('mouse:up', function(e) { mouseup(e); });

var started = false;
var x = 0;
var y = 0;

/* Mousedown */
function mousedown(e) {
    var mouse = canvas.getPointer(e.memo.e);
    started = true;
    x = mouse.x;
    y = mouse.y;

    var square = new fabric.Rect({ 
        width: 0, 
        height: 0, 
        left: x, 
        top: y, 
        fill: '#000'
    });

    canvas.add(square); 
    canvas.renderAll();
    canvas.setActiveObject(square); 

}


/* Mousemove */
function mousemove(e) {
    if(!started) {
        return false;
    }

    var mouse = canvas.getPointer(e.memo.e);

    var w = Math.abs(mouse.x - x),
    h = Math.abs(mouse.y - y);

    if (!w || !h) {
        return false;
    }

    var square = canvas.getActiveObject(); 
    square.set('width', w).set('height', h);
    canvas.renderAll(); 
}

/* Mouseup */
function mouseup(e) {
    if(started) {
        started = false;
    }

    var square = canvas.getActiveObject();

    canvas.add(square); 
    canvas.renderAll();
 } 

The answer above seems to be deprecated. I changed some things on the code below to fix that. And on the mousedown function I add the if to detect the active object to avoid creating a new rectangle when the user's move a selected object.

var canvas = new fabric.Canvas('canvas');

canvas.on('mouse:down', function(options) {
      if(canvas.getActiveObject()){
        return false;
      }

      started = true;
      x = options.e.clientX;
      y = options.e.clientY;

      var square = new fabric.Rect({ 
          width: 0, 
          height: 0, 
          left: x, 
          top: y, 
          fill: '#000'
      });

      canvas.add(square); 
      canvas.setActiveObject(square); 
  });

  canvas.on('mouse:move', function(options) {
    if(!started) {
        return false;
    }

    var w = Math.abs(options.e.clientX - x),
    h = Math.abs(options.e.clientY - y);

    if (!w || !h) {
        return false;
    }

    var square = canvas.getActiveObject(); 
    square.set('width', w).set('height', h);
  });

  canvas.on('mouse:up', function(options) {
    if(started) {
      started = false;
    }

    var square = canvas.getActiveObject();

    canvas.add(square); 
  });

Here is the detail blog with jsfiddle - https://blog.thirdrocktechkno.com/drawing-a-square-or-rectangle-over-html5-canvas-using-fabricjs-f48beeedb4d3

var Rectangle = (function () {
    function Rectangle(canvas) {
        var inst=this;
        this.canvas = canvas;
        this.className= 'Rectangle';
        this.isDrawing = false;
        this.bindEvents();
    }

	 Rectangle.prototype.bindEvents = function() {
    var inst = this;
    inst.canvas.on('mouse:down', function(o) {
      inst.onMouseDown(o);
    });
    inst.canvas.on('mouse:move', function(o) {
      inst.onMouseMove(o);
    });
    inst.canvas.on('mouse:up', function(o) {
      inst.onMouseUp(o);
    });
    inst.canvas.on('object:moving', function(o) {
      inst.disable();
    })
  }
    Rectangle.prototype.onMouseUp = function (o) {
      var inst = this;
      inst.disable();
    };

    Rectangle.prototype.onMouseMove = function (o) {
      var inst = this;
      

      if(!inst.isEnable()){ return; }
     
      var pointer = inst.canvas.getPointer(o.e);
      var activeObj = inst.canvas.getActiveObject();

      activeObj.stroke= 'red',
      activeObj.strokeWidth= 5;
      activeObj.fill = 'transparent';

      if(origX > pointer.x){
          activeObj.set({ left: Math.abs(pointer.x) }); 
      }
      if(origY > pointer.y){
          activeObj.set({ top: Math.abs(pointer.y) });
      }

      activeObj.set({ width: Math.abs(origX - pointer.x) });
      activeObj.set({ height: Math.abs(origY - pointer.y) });

      activeObj.setCoords();
      inst.canvas.renderAll();

    };

    Rectangle.prototype.onMouseDown = function (o) {
      var inst = this;
      inst.enable();

      var pointer = inst.canvas.getPointer(o.e);
      origX = pointer.x;
      origY = pointer.y;

    	var rect = new fabric.Rect({
          left: origX,
          top: origY,
          originX: 'left',
          originY: 'top',
          width: pointer.x-origX,
          height: pointer.y-origY,
          angle: 0,
          transparentCorners: false,
          hasBorders: false,
          hasControls: false
      });

  	  inst.canvas.add(rect).setActiveObject(rect);
    };

    Rectangle.prototype.isEnable = function(){
      return this.isDrawing;
    }

    Rectangle.prototype.enable = function(){
      this.isDrawing = true;
    }

    Rectangle.prototype.disable = function(){
      this.isDrawing = false;
    }

    return Rectangle;
}());



var canvas = new fabric.Canvas('canvas');
var rect = new Rectangle(canvas);

<script src="https://cdnjs.cloudflare.com/ajax/libs/fabric.js/1.7.17/fabric.min.js"></script>
 Please draw rectangle here

<div id="canvasContainer">
  <canvas id="canvas" width="400" height="400" style="border: solid 1px"></canvas>
</div>

I have written an example for you. Please follow the link below:

http://jsfiddle.net/a7mad24/aPLq5/

var canvas = new fabric.Canvas('canvas', { selection: false });

var rect, isDown, origX, origY;

canvas.on('mouse:down', function(o){
    isDown = true;
    var pointer = canvas.getPointer(o.e);
    origX = pointer.x;
    origY = pointer.y;
    var pointer = canvas.getPointer(o.e);
    rect = new fabric.Rect({
        left: origX,
        top: origY,
        originX: 'left',
        originY: 'top',
        width: pointer.x-origX,
        height: pointer.y-origY,
        angle: 0,
        fill: 'rgba(255,0,0,0.5)',
        transparentCorners: false
    });
    canvas.add(rect);
});

canvas.on('mouse:move', function(o){
    if (!isDown) return;
    var pointer = canvas.getPointer(o.e);

    if(origX>pointer.x){
        rect.set({ left: Math.abs(pointer.x) });
    }
    if(origY>pointer.y){
        rect.set({ top: Math.abs(pointer.y) });
    }

    rect.set({ width: Math.abs(origX - pointer.x) });
    rect.set({ height: Math.abs(origY - pointer.y) });


    canvas.renderAll();
});

canvas.on('mouse:up', function(o){
  isDown = false;
});