What a freezer costs to run
Across 658 certified models ENERGY STAR currently lists in this category, the median uses 405 kWh/yr. The cheapest certified model to run costs about $26/year; the most expensive costs about $122/year, more than 5x the spread.
Efficient models versus the rest
Of the 658 certified freezers tracked here, 200 use meaningfully less energy than the category average and 300 use meaningfully more, the rest are within about 8% of it either way. The most efficient certified model found is the Avanti CF24Q0W at 137 kWh/yr; the least efficient is the Monogram ZIF361NBR**** at 649 kWh/yr.
Your state changes this more than you'd think
The figures above use the simple average of all 51 published state electricity rates (18.8¢/kWh). A median-efficiency freezer costs about $49/year to run in North Dakota (12.19¢/kWh, the cheapest state rate this site tracks) and about $186/year in Hawaii (45.95¢/kWh, the most expensive), the identical appliance. Every model page on this site lets you pick your own state to see the real number. See the guide to why location matters this much.
Shopping for a new one
If the freezer you own is old enough to be well past ENERGY STAR's current efficiency baseline, a current certified model like the ones above can cost meaningfully less to run.
Compare current ENERGY STAR certified freezers before buying.