1 gram of fat contains 9 Calories of energy. Therefore to lose 1 kg of fat mass you would need to create a deficit of approximately 9000 Calories.
On average an adult burns between 2000 to 2500 Calories a day due to their normal metabolism (depending on activity level this can be significantly lower if sedentary or higher if very active). If your Calorie intake exceeds your Calorie burn you will gain weight. If your Calorie burn exceeds your intake you will lose weight. As such to lose weight you must either reduce the number of Calories consumed (diet), increase the number of Calories burned (exercise) or ideally combine the two!
Therefore to lose 1 kg of fat mass, you would need to burn an extra 9000 Calories. To put that into context, a moderate running speed of 6MPH will depending on your weight burn between 600 and 1000 Calories per hour (assuming a mass within the range 60 - 100 kg).
Therefore to lose a kilogram of fat you would have to run for between 9 and 15 hour over the course of the week. Or you would have to reduce your Calorie intake by 1285 Calories per day. These are both fairly unfeasable.
A much better solution would be a reduction of Calorie intake by 500 Calories a day (which will add up to 3500 Calories over the week) when combined with the exercise (5 1/2 to 9 hours of running - 45 mins to 1 1/4 hours per day) would potentially achieve your target weight loss of 1 kg.
