You plan a deficit of 500 kilocalories a day. The calculator promises 0.45 kg (1 lb) per week, so 1.8 kg (4 lb) after four weeks. Your trend weight shows 1.4 kg (3.1 lb) lost, and you wonder whether you counted wrong.
Usually you did not. A calorie deficit calculator uses a fixed conversion, and that works as a starting value: the rule of thumb is about 7,700 kcal per kilogram of body weight (3,500 per pound), and the figure depends on body composition. You read your actual deficit more reliably from the slope of your trend weight.
The arithmetic behind a deficit calculator
Every calculator divides the saved kilocalories by 7,700. A deficit of 500 kcal a day adds up to 3,500 kcal a week, and divided by 7,700 that is 0.45 kg.
| Deficit per day | Deficit per week | Predicted loss per week |
|---|---|---|
| 250 kcal | 1,750 kcal | 0.23 kg (0.5 lb) |
| 500 kcal | 3,500 kcal | 0.45 kg (1.0 lb) |
| 750 kcal | 5,250 kcal | 0.68 kg (1.5 lb) |
| 1,000 kcal | 7,000 kcal | 0.91 kg (2.0 lb) |
The table assumes a body that does not change while you lose weight. A calculator that names a target date divides the same way and stretches the result over many weeks: for 6 kg (13 lb) at 0.45 kg per week it says just under 13 weeks. The longer the period, the further off the result usually lands, because your energy expenditure does not stay constant over that many weeks.
Why the prediction drifts after a few weeks
If you eat less, you eventually weigh less, and a lighter body burns less energy. Hall and Chow name exactly this as the reason the fixed rule fails as a predictor: expenditure falls as weight falls, so the original deficit shrinks week by week.
Thomas and colleagues work through an example. Someone who cuts 140 kcal a day loses about 6.8 kg (15 lb) in a year by the fixed rule. Dynamic models arrive at 2.6 to 3.8 kg (5.7 to 8.4 lb). The fixed rule lands at roughly double to two and a half times the modelled loss.
Weight also reacts slowly. In model calculations by Hall and colleagues the half-times for a change in intake are around one year. A deficit therefore acts more strongly at the start than later, and the curve does not stay a straight line.
During the first one or two weeks, water also distorts the picture. If you eat fewer carbohydrates and less salt, you lose glycogen and the water bound to it, and the trend falls faster than fat alone explains. Extrapolate a deficit from that phase and you overestimate it. Leave the opening drop out of your projection; the reliable weekly rates begin after it.
How to read your real deficit from the trend
Turning the calculation around works better than the prediction. You measure how fast your trend weight falls and calculate backwards: weekly rate times 7,700, divided by 7, gives your average daily balance.
You cannot use the daily scale value for this. It swings through water and digestion by more than your fat changes in a week, which Why your weight fluctuates daily explains. You need a rate that filters that swing out.
Trendcurve calculates the weekly rate by regression over the last 14 trend values. The calorie budget (Pro) turns it into your current daily balance and your estimated intake. It takes your resting energy from the Mifflin and St Jeor equation, optionally adds active energy from Apple Health, and works with the same 7,700 kcal per kilogram. For a desired pace it derives a target budget, with a lower limit and a warning below it.
A worked example with a trend
You weigh 80 kg (176 lb), estimate your maintenance at 2,500 kcal and plan a 500 kcal deficit, so an intake of 2,000 kcal.
- The calculator expects 0.45 kg (1.0 lb) per week.
- Your trend falls by an average of 0.35 kg (0.8 lb) per week over the first four weeks.
- That equals 0.35 times 7,700, divided by 7: about 385 kcal of deficit per day.
- The gap of 115 kcal has two possible causes. Either you eat about 115 kcal more than you counted, or your maintenance sits that much lower than estimated.
- If you want to stay at 0.45 kg per week, you are missing 115 kcal of deficit. You lower your intake by that amount or raise your expenditure, and you change only one of the two.
Both errors are everyday ones: portions get underestimated, and formulas for resting energy return averages, not individual values. The trend cannot tell you which error you have, but it tells you how large the sum of both is. You correct your budget on that basis, not on the basis of the formula. Then you keep measuring for two weeks and calculate again. One change per measuring phase keeps the cause readable: if intake and activity change together, you cannot tell later which step worked.
When the rate shifts over the weeks, your measurement is not at fault. It falls with body weight, as described above. How to judge the rate is covered in Realistic rate of weight loss.
Limits of the method
- The 7,700 kcal are a rule of thumb. How much fat, muscle and water leaves with one kilogram differs from person to person, and most of all in the first weeks of a diet.
- A regression over 14 trend values lags behind reality. After a change in your eating, the rate shows a dependable picture only after about two weeks.
- An estimated intake is only as good as the estimate of your maintenance. Treat it as an order of magnitude, not as a measured value.
- If you take medication, are ill, pregnant or have an eating disorder, a deficit belongs in a doctor's hands. The app is not a medical device.
The calorie budget is part of Pro. Trend weight, the 7-day change and the desired pace with its pace warning are in the free version, and with them you can follow the calculation above by hand.
After four weeks of steady eating, take the 7-day change of your trend weight, multiply it by 1,100 and read the result as your actual daily deficit in kilocalories. 7,700 divided by 7 is 1,100 kcal per kilogram per week.