Last night I had a 133 mile drive home. The was battery was showing around 170 miles of range on the home screen so I thought I had enough to get home. The navigation however directed us to stop at a Supercharger for 10 minutes and would arrive at the charger with 6% battery. Why does the battery display on the main screen not show the actual mileage as there is a huge difference between that and the battery level on the trip display?
Although Tesla's choice to use "miles" as the units is understandably confusing, the battery display is
not a display of distance, or range. It's a quite precise estimate of available
energy, in units of "rated miles." It's really very, very good at displaying how much energy you have left. What you do with the energy is up to you.
Here are the conversions factors to help you out:
2020, 2019, 2018 Model 3 Battery Capacities & Charging Constants
You should use the column headed "Trip Meter 'Constant'" (second to last column) for your vehicle that will allow you to multiply with your rated miles remaining and tell you your available kWh remaining. Once you know that, you can just look at the trip meter (left pane of screen, leftmost card (swipe left to right, then scroll up/down)) and see your kWh consumed, reset it to zero, and from there it will all line up perfectly. When that kWh displayed on the trip meter matches the initial calculation (Trip meter constant * remaining rated miles), your battery % will be at 0%/0rmi!
Or (greatly preferred!), you can just do what you did, and use the Trip Planner. It's quite good, as long as you aren't running aftermarket tires/wheels (if you are, and they're higher rolling resistance, you may be able to select a different wheel configuration on the Service Menu (19 or 20") and get it to be a bit more accurate), and accounts for terrain and recent driving behavior & consumption.
The trip meter method suggested is just for improving understanding. The battery gauge is all extremely deterministic and predictable. But the Trip Planner knows what is coming and will account for it, so it's generally a better way to go.