Daily Calorie Estimates
Lean dogs have longer lives
Median life span was significantly longer for dogs in which food was restricted. 
Lean dogs have healthier lives
delayed onset of chronic diseases
“diet restriction also was associated with a longer median time to first treatment of osteoarthritis (the most common chronic disease among dogs in this study) and a longer median time to first treatment of any chronic condition.” 
Overweight dogs and cats have an increased risk for urinary stone formations. 
“Weight gain could indicate medical conditions such as hypothyroidism and Cushing’s disease, or that you are overfeeding him.” 
Where to start?
How many calories a day does a dog need? A good starting point to establish your dog’s calories needs is to determine the total calories they are currently getting each day in the form of food and treats. Then determine their body condition score (BCS) and muscle condition score (MCS) to evaluate whether your dog needs the same (maintenance), or more or less calories each day. You should work with your veterinarian to determine your dog’s BCS and MCS and his/her ideal weight.
The Canine Daily Calorie Estimator will do all the math to help you determine daily calories needs. Calorie requirements can vary greatly depending on the dog’s breed, size, age, metabolism, activity level, environment, temperature, and humidity. Two dogs of the same breed and size living in the same environment can have completely differing energy (calorie) requirements. (See MER and DER below) “Individual pet needs can vary by as much as 50% from calculated values however, so these are only starting points for estimating the amount of food to be provided daily.” 
“Calculate the resting energy requirement (RER) using the pet’s estimated ideal weight, then feed a percentage of that amount. Although there is no established standard reduction, feeding 80% of ideal-weight RER is effective and well tolerated.”
"Calorie restriction—but not protein restriction should be pursued in overweight animals to achieve a slow rate of weight loss of 0.5% to 1% weekly." ... "Diets high in protein appear superior to those with moderate amounts of protein"
“foods producing low glycemic responses should be recommended for obese or diabetic patients” 
“Carbohydrate sources that result in a lower glycemic index are more desirable for metabolic weight control.“ 
“Limiting dietary carbohydrate is an important component of metabolic control for weight loss. There are three key advantages to limiting dietary carbohydrate to 20% (DM) or less: 1) lower glycemic index, 2) metabolic shift from energy storage to energy usage and 3) increased satiety.” 
One challenge when searching for dog food for a dog with a moderate activity level is finding one that has a percentage of fat that is no more than 50% of the protein listed. Higher fat diets are a great energy source for active dogs but most dogs will get more calories than they can burn on a high fat diet. For dogs that are overweight I would avoid foods marketed for the “less active” dogs. If you checked the label you may find that this food has the same calories or more than the food you are feeding now.
Many of these foods contain a high fiber content which can reduce the overall digestibility and insoluble fiber like cellulose can reduce mineral adsorption. High fiber can lead to increased need to defecate and a larger volume of feces. Instead I would limit treats and slightly reduce the amount of food feed, and increase their daily exercise. There’s an old saying, if your dog is fat you’re not getting enough exercise!
Using the gold standard pet food formulator Steve Brown recommends carbohydrates would be 6% of calories. (Dry kibble ranges from 20% to 60%+) The ideal remaining calorie breakdown would be 49% of the calories would come from protein, and 44% from fat. Remember that the percentage of calories is not the same as the "guaranteed analysis" %. We will show you how to determine the percentage of calories later with the Pet Food Math Cheat Sheet.
“Median life span was significantly longer for dogs in which food was restricted. The onset of clinical signs of chronic disease generally was delayed for food-restricted dogs.”
RER in kcal / day = 70 X (ideal BW kg [kg] 0.75