Scroll smoothly to specific element on page

I want to have 4 buttons/links on the beginning of the page, and under them the content.

On the buttons I put this code:

<a href="#idElement1">Scroll to element 1</a>
<a href="#idElement2">Scroll to element 2</a>
<a href="#idElement3">Scroll to element 3</a>
<a href="#idElement4">Scroll to element 4</a>

And under links there will be content:

<h2 id="idElement1">Element1</h2>
content....
<h2 id="idElement2">Element2</h2>
content....
<h2 id="idElement3">Element3</h2>
content....
<h2 id="idElement4">Element4</h2>
content....

It is working now, but cannot make it look more smooth.

I used this code, but cannot get it to work.

$('html, body').animate({
    scrollTop: $("#elementID").offset().top
}, 2000);

Any suggestions? Thank you.

Edit: and the fiddle: http://jsfiddle.net/WxJLx/2/

Super smoothly with requestAnimationFrame

For smoothly rendered scrolling animation one could use window.requestAnimationFrame() which performs better with rendering than regular setTimeout() solutions.

A basic example looks like this. Function step is called for browser's every animation frame and allows for better time management of repaints, and thus increasing performance.

function doScrolling(elementY, duration) { 
  var startingY = window.pageYOffset;
  var diff = elementY - startingY;
  var start;

  // Bootstrap our animation - it will get called right before next frame shall be rendered.
  window.requestAnimationFrame(function step(timestamp) {
    if (!start) start = timestamp;
    // Elapsed milliseconds since start of scrolling.
    var time = timestamp - start;
    // Get percent of completion in range [0, 1].
    var percent = Math.min(time / duration, 1);

    window.scrollTo(0, startingY + diff * percent);

    // Proceed with animation as long as we wanted it to.
    if (time < duration) {
      window.requestAnimationFrame(step);
    }
  })
}

For element's Y position use functions in other answers or the one in my below-mentioned fiddle.

I set up a bit more sophisticated function with easing support and proper scrolling to bottom-most elements: https://jsfiddle.net/s61x7c4e/

Question was asked 5 years ago and I was dealing with smooth scroll and felt giving a simple solution is worth it to those who are looking for. All the answers are good but here you go a simple one.

function smoothScroll(){
    document.querySelector('.your_class or #id here').scrollIntoView({
        behavior: 'smooth'
    });
}

just call the smoothScroll function on onClick event on your source element.

DOCS: https://developer.mozilla.org/en-US/docs/Web/API/Element/scrollIntoView

Note: Please check compatibility here

3rd Party edit

Support for Element.scrollIntoView() in 2020 is this:

Region            full   + partial = sum full+partial Support
Asia              73.24% + 22.75%  = 95.98%
North America     56.15% + 42.09%  = 98.25%
India             71.01% + 20.13%  = 91.14%
Europe            68.58% + 27.76%  = 96.35%

Just made this javascript only solution below.

Simple usage:

EPPZScrollTo.scrollVerticalToElementById('signup_form', 20);

Engine object (you can fiddle with filter, fps values):

/**
 *
 * Created by Borbás Geri on 12/17/13
 * Copyright (c) 2013 eppz! development, LLC.
 *
 * Permission is hereby granted, free of charge, to any person obtaining a copy of this software and associated documentation files (the "Software"), to deal in the Software without restriction, including without limitation the rights to use, copy, modify, merge, publish, distribute, sublicense, and/or sell copies of the Software, and to permit persons to whom the Software is furnished to do so, subject to the following conditions:
 * The above copyright notice and this permission notice shall be included in all copies or substantial portions of the Software.
 * THE SOFTWARE IS PROVIDED "AS IS", WITHOUT WARRANTY OF ANY KIND, EXPRESS OR IMPLIED, INCLUDING BUT NOT LIMITED TO THE WARRANTIES OF MERCHANTABILITY, FITNESS FOR A PARTICULAR PURPOSE AND NONINFRINGEMENT. IN NO EVENT SHALL THE AUTHORS OR COPYRIGHT HOLDERS BE LIABLE FOR ANY CLAIM, DAMAGES OR OTHER LIABILITY, WHETHER IN AN ACTION OF CONTRACT, TORT OR OTHERWISE, ARISING FROM, OUT OF OR IN CONNECTION WITH THE SOFTWARE OR THE USE OR OTHER DEALINGS IN THE SOFTWARE.
 *
 */


var EPPZScrollTo =
{
    /**
     * Helpers.
     */
    documentVerticalScrollPosition: function()
    {
        if (self.pageYOffset) return self.pageYOffset; // Firefox, Chrome, Opera, Safari.
        if (document.documentElement && document.documentElement.scrollTop) return document.documentElement.scrollTop; // Internet Explorer 6 (standards mode).
        if (document.body.scrollTop) return document.body.scrollTop; // Internet Explorer 6, 7 and 8.
        return 0; // None of the above.
    },

    viewportHeight: function()
    { return (document.compatMode === "CSS1Compat") ? document.documentElement.clientHeight : document.body.clientHeight; },

    documentHeight: function()
    { return (document.height !== undefined) ? document.height : document.body.offsetHeight; },

    documentMaximumScrollPosition: function()
    { return this.documentHeight() - this.viewportHeight(); },

    elementVerticalClientPositionById: function(id)
    {
        var element = document.getElementById(id);
        var rectangle = element.getBoundingClientRect();
        return rectangle.top;
    },

    /**
     * Animation tick.
     */
    scrollVerticalTickToPosition: function(currentPosition, targetPosition)
    {
        var filter = 0.2;
        var fps = 60;
        var difference = parseFloat(targetPosition) - parseFloat(currentPosition);

        // Snap, then stop if arrived.
        var arrived = (Math.abs(difference) <= 0.5);
        if (arrived)
        {
            // Apply target.
            scrollTo(0.0, targetPosition);
            return;
        }

        // Filtered position.
        currentPosition = (parseFloat(currentPosition) * (1.0 - filter)) + (parseFloat(targetPosition) * filter);

        // Apply target.
        scrollTo(0.0, Math.round(currentPosition));

        // Schedule next tick.
        setTimeout("EPPZScrollTo.scrollVerticalTickToPosition("+currentPosition+", "+targetPosition+")", (1000 / fps));
    },

    /**
     * For public use.
     *
     * @param id The id of the element to scroll to.
     * @param padding Top padding to apply above element.
     */
    scrollVerticalToElementById: function(id, padding)
    {
        var element = document.getElementById(id);
        if (element == null)
        {
            console.warn('Cannot find element with id \''+id+'\'.');
            return;
        }

        var targetPosition = this.documentVerticalScrollPosition() + this.elementVerticalClientPositionById(id) - padding;
        var currentPosition = this.documentVerticalScrollPosition();

        // Clamp.
        var maximumScrollPosition = this.documentMaximumScrollPosition();
        if (targetPosition > maximumScrollPosition) targetPosition = maximumScrollPosition;

        // Start animation.
        this.scrollVerticalTickToPosition(currentPosition, targetPosition);
    }
};