According to a report in New Scientist, the research was done by Robert and Brenda Vale, two architects who specialise in sustainable living at Victoria University of Wellington in New Zealand.
As well as guzzling resources, cats and dogs devastate wildlife populations, spread disease and add to pollution.
To measure the ecological paw, claw and fin-prints of the family pet, the Vales analysed the ingredients of common brands of pet food.
They calculated, for example, that a medium-sized dog would consume 90 grams of meat and 156 grams of cereals daily in its recommended 300-gram portion of dried dog food.
At its pre-dried weight, that equates to 450 grams of fresh meat and 260 grams of cereal.
That means that over the course of a year, Fido wolfs down about 164 kilograms of meat and 95 kilograms of cereals.
It takes 43.3 square metres of land to generate 1 kilogram of chicken per year - far more for beef and lamb - and 13.4 square metres to generate a kilogram of cereals. So that gives him a footprint of 0.84 hectares.
For a big dog such as a German shepherd, the figure is 1.1 hectares.
Meanwhile, an SUV, driven a modest 10,000 kilometres a year, uses 55.1 gigajoules, which includes the energy required both to fuel and to build it.
The Vales used a 4.6-litre Toyota Land Cruiser in their comparison.
One hectare of land can produce approximately 135 gigajoules of energy per year, so the Land Cruiser's eco-footprint is about 0.41 hectares - less than half that of a medium-sized dog.
Doing similar calculations for a variety of pets and their foods, the Vales found that cats have an eco-footprint of about 0.15 hectares (slightly less than a Volkswagen Golf), hamsters come in at 0.014 hectares apiece and canaries half that.
Even a goldfish requires 0.00034 hectares (3.4 square metres) of land to sustain it, giving it an ecological fin-print equal to two cellphones.
The Vales suggest that eco-friendly animal lovers should change the diet of their pet. Meat is the key, since its production is so energy-intensive.
They can almost halve the eco-pawprint of their dogs, simply by feeding it many of the same sort of savory foods that they eat, which are likely to be far less protein-rich than most dog foods, they added.