Day 2 Progress: Side 1 started, but the foundations had to go deeper than expected using more materials so the side was not quite completed and the spend was $220

Day 3 Progress: Side 1 was finished, only half of the back wall was built, but the team left early and only spent $140 that day

So are we ahead or behind?
How much over/under budget are we?

This is the type of thing that happens on real projects, some things go fine; other things go slower than anticipated and before long you need to determine, on balance, how much ahead or behind from the original plan you are.

Just from common sense we can tell we are behind, by the end of day 3 we should have finished 3 sides not 2.5.

Spend wise, we can make some estimates too; we have achieved 2.5 out of 4 sides which is 62.5% (2.5 / 4 *100 = 62.5) of the overall project. We have spent $200 + $220 + $140 = $560 of the $800 which is 70% (560/800 *100 = 70) of the budget. Having spent 70% of your budget and only achieved 62.5% of your budgetted progress indicates you are spending faster than anticipated.

Congratulations you now understand the basics of Earned Value!

Earned Value has some unique terminology that throws off lots of people, but none of it is too complicated, here are the terms:
   
In our example, at the end of Day 3 we have the following values:
 

To fill in the remaining fields we need some formulae, again don’t be put off by the terminology, it is really quite easy:
 

The first two values (Cost Variance and Schedule Variance) are measures of how much ahead or behind cost and schedule we are. Just remember negative values here are negative signs for the project, it means we are over budget or behind schedule.

The next two values (Cost Performance Index and Schedule Performance Index) are factors where the value 1 means on budget or schedule, anything below 1 means behind, anything above 1 means ahead.
So plugging in our numbers we get:

So we can estimate that at this rate it is more likely to cost $900 rather than the $800 budget and given we are only progressing at 83% of the rate we first estimated, this will now take 4.8 days to finish (original 4 days / 0.83 rate of progress = 4.82).

That is it, no quantum mechanics necessary. Negative Variance figures are generally bad as are performance indexes below 1. There are other formulae, and alternative formulae that can be used in certain circumstances, but these are the basics.

All of these numbers were available to us in our initial common sense assessment of progress. Having completed only 2.5 sides instead of 3 by the end of day 3 gives us the 2.5/3 = 0.83 Schedule Performance Index (SPI) we calculated. Likewise spending $560 and only building $500 worth of original plan work is our 500/600 = 0.89 Cost Performance Index (CPI).

You can download a handy one-page summary of all the terms and formulae here.

Download Earned Value - One Page Summary

Agile Issues With Earned Value
Now the value of measuring conformance to a plan that could well be wrong is another discussion. As too is the idea that a linear extrapolation of past performance to predict future performance works for anything except defined, repeatable, low-risk tasks. For discussions on those topics see some of my earlier EV posts.