Get element height with Vuejs

The way you are doing it is fine. But there is another vue specific way via a ref attribute.

 mounted () {
   this.matchHeight()
 },
 matchHeight () {
   let height = this.$refs.infoBox.clientHeight;
 }

    <div class="columns">
        <div class="left-column" id="context">
            <p>Some text</p>
        </div>
        <div class="right-column" id="info-box" ref="infoBox"></>
            <img />
            <ul>
                some list
            </ul>
        </div>
    </div>

In this case, since you are just getting the value it really doesn't matter whether you use your original getElementById approach or the vue specific ref approach. However if you were setting the value on the element then it's much better to use the ref approach so that vue understands that the value has changed and won't possibly overwrite the value with the original value if it needs to update that node in the DOM.

You can learn more here: https://v2.vuejs.org/v2/api/#vm-refs

Update

A few people had left comments that the above solution didn't work for them. That solution provided the concepts but not full working code as example, so I have augmented my answer with the code below which demonstrates the concepts.

var app = new Vue({
    el: '#app',
    data: function () {
        return {
            leftColStyles: { },
            lines: ['one', 'two','three']
        }
    },
    methods: {
        matchHeight() {
            var heightString = this.$refs.infoBox.clientHeight + 'px';
            Vue.set(this.leftColStyles, 'height', heightString); 
        }
    },
    mounted() {
        this.matchHeight();
    }

});

.columns{width:300px}
.left-column {float:left; width:200px; border:solid 1px black}
.right-column {float:right; border:solid 1px blue; }

<div id="app">
    <div class="columns">
        <div class="left-column" id="context" v-bind:style="leftColStyles">
            <p>Some text</p>
        </div>
        <div class="right-column" id="info-box" ref="infoBox"> 
            <img />
            <ul>
                <li v-for="line in lines" v-text="line"></li>
            </ul>
        </div>
    </div>

</div>

 <script src="https://unpkg.com/[email protected]/dist/vue.min.js"></script>
 

Here is a screenshot of the results in the browser:

Note:
My answer assumes that you are loading vue.js from a cdn or locally into the browser and executing it there. If instead you are running your code via the cli and my answer is not working for you, please see @mayank1513's answer instead.

Took a lot of time ⌚ resolving the issue. Initially I tried to follow answer by Ron C. Trying to get this.$refs.infoBox.clientHeight; just didn't work - it gave undefined.

Then I explored the this.$refs.infoBox object.

Wow!!! I don't know how the code he wrote works for him and all others, but there wasn't any property called clientHeight. Finally got it inside $el.

so we need to replace this.$refs.infoBox.clientHeight; with this.$refs.infoBox.$el.clientHeight;

This just worked well for me.

Update

While using nuxt this.$refs.infoBox.$el.clientHeight; didn't work. but Ron C's answer works for this case. this.$refs.infoBox.$el.clientHeight; seems to work while using @vue/cli