Everyday Math
Intermediate

Weight Loss Estimate

Approximate body-mass loss from a calorie deficit (kg).

Formula

Δw=deficit×days7700\Delta w = \frac{\text{deficit} \times days}{7700}

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Variables

deficitDaily kcal deficit
daysDuration

Example

500 kcal/day for 30 days ≈ 1.95 kg

How it works

This formula estimates how much body mass might change when someone maintains a calorie deficit for a number of days. It uses the rough conversion that about 7,700 kilocalories corresponds to 1 kilogram of body fat, so dividing the total deficit by 7,700 gives an approximate mass loss in kilograms. It is only a shortcut: real weight change is affected by water, glycogen, digestion, and changes in activity or metabolism, so the result is best treated as an estimate rather than a guarantee.

When to use it

Use this when you want a quick planning estimate for diet tracking, fitness goals, or classroom problems involving energy balance. It is especially useful for comparing different deficit sizes or time periods without needing a detailed nutrition model.

Worked example, step by step

Suppose a person eats 300 kcal less than maintenance each day for 45 days. Total deficit = 300 × 45 = 13,500 kcal Estimated weight loss = 13,500 ÷ 7,700 Estimated weight loss ≈ 1.75 kg So the estimated body-mass loss is about 1.75 kg.

Common mistakes to avoid

  • Using the formula for short-term scale changes, which can be dominated by water weight
  • Forgetting that the deficit must be per day, then multiplying by days to get total calories
  • Assuming the result is exact instead of an approximate estimate based on body fat energy content

Did You Know?

Roughly 7700 kcal equals one kilogram of body fat.

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Reviewed & maintained by the FormulaWon editorial teamLast reviewed September 2026