// creates a global "addWheelListener" method
// example: addWheelListener( elem, callback );

(function(window,document) {
 
    var prefix = "", _addEventListener, onwheel, support;
 
    // detect event model
    if ( window.addEventListener ) {
        _addEventListener = "addEventListener";
    } else {
        _addEventListener = "attachEvent";
        prefix = "on";
    }

    // detect available wheel event
    if ( document.onmousewheel !== undefined ) {
        // Webkit and IE support at least "mousewheel"
        support = "mousewheel"
    }
    try {
        // Modern browsers support "wheel"
        WheelEvent("wheel");
        support = "wheel";
    } catch (e) {}
    if ( !support ) {
        // let's assume that remaining browsers are older Firefox
        support = "DOMMouseScroll";
    }
    window.addWheelListener = function( elem, callback, useCapture ) {
        _addWheelListener( elem, support, callback, useCapture );
 
        // handle MozMousePixelScroll in older Firefox
        if( support == "DOMMouseScroll" ) {
            _addWheelListener( elem, "MozMousePixelScroll", callback, useCapture );
        }
    };
 
    function _addWheelListener( elem, eventName, callback, useCapture ) {
        elem[ _addEventListener ]( prefix + eventName, support == "wheel" ? callback : function( originalEvent ) {
            !originalEvent && ( originalEvent = window.event );
 
            // create a normalized event object
            var event = {
                // keep a ref to the original event object
                originalEvent: originalEvent,
                target: originalEvent.target || originalEvent.srcElement,
                type: "wheel",
                deltaMode: originalEvent.type == "MozMousePixelScroll" ? 0 : 1,
                deltaX: 0,
                delatZ: 0,
                preventDefault: function() {
                    originalEvent.preventDefault ?
                        originalEvent.preventDefault() :
                        originalEvent.returnValue = false;
                }
            };
             
            // calculate deltaY (and deltaX) according to the event
            if ( support == "mousewheel" ) {
                event.deltaY = - 1/40 * originalEvent.wheelDelta;
                // Webkit also support wheelDeltaX
                originalEvent.wheelDeltaX && ( event.deltaX = - 1/40 * originalEvent.wheelDeltaX );
            } else {
                event.deltaY = originalEvent.detail;
            }
 
            // it's time to fire the callback
            return callback( event );
 
        }, useCapture || false );
    }
 
})(window,document);

(function(window,document) {
 
    var prefix = "", _addEventListener, onwheel, support;
 
    // detect event model
    if ( window.addEventListener ) {
        _addEventListener = "addEventListener";
    } else {
        _addEventListener = "attachEvent";
        prefix = "on";
    }

    // detect available wheel event
    if ( document.onmousewheel !== undefined ) {
        // Webkit and IE support at least "mousewheel"
        support = "mousewheel"
    }
    try {
        // Modern browsers support "wheel"
        WheelEvent("wheel");
        support = "wheel";
    } catch (e) {}
    if ( !support ) {
        // let's assume that remaining browsers are older Firefox
        support = "DOMMouseScroll";
    }
    window.addWheelListener = function( elem, callback, useCapture ) {
        _addWheelListener( elem, support, callback, useCapture );
 
        // handle MozMousePixelScroll in older Firefox
        if( support == "DOMMouseScroll" ) {
            _addWheelListener( elem, "MozMousePixelScroll", callback, useCapture );
        }
    };
 
    function _addWheelListener( elem, eventName, callback, useCapture ) {
        elem[ _addEventListener ]( prefix + eventName, support == "wheel" ? callback : function( originalEvent ) {
            !originalEvent && ( originalEvent = window.event );
 
            // create a normalized event object
            var event = {
                // keep a ref to the original event object
                originalEvent: originalEvent,
                target: originalEvent.target || originalEvent.srcElement,
                type: "wheel",
                deltaMode: originalEvent.type == "MozMousePixelScroll" ? 0 : 1,
                deltaX: 0,
                delatZ: 0,
                preventDefault: function() {
                    originalEvent.preventDefault ?
                        originalEvent.preventDefault() :
                        originalEvent.returnValue = false;
                }
            };
             
            // calculate deltaY (and deltaX) according to the event
            if ( support == "mousewheel" ) {
                event.deltaY = - 1/40 * originalEvent.wheelDelta;
                // Webkit also support wheelDeltaX
                originalEvent.wheelDeltaX && ( event.deltaX = - 1/40 * originalEvent.wheelDeltaX );
            } else {
                event.deltaY = originalEvent.detail;
            }
 
            // it's time to fire the callback
            return callback( event );
 
        }, useCapture || false );
    }
 
})(window,document);

https://developer.mozilla.org/en-US/docs/DOM/DOM_event_reference/wheel?redirect=no

A nifty event listener for handling wheel events. Listens for the DOM3 Wheel Event first, then falls back to MouseWheel, and finally DOMMouseScroll.

Cross Browser Wheel Event Listener

JavaScript