Contents · 9 sections
The problem "a 7-month-old child, birth weight 3,200 g, calculate the expected weight and daily feeding volume" appears on virtually every pediatrics exam. The formulas are simple, but there are many of them, and each has its own range of application. Below is everything in one place, complete with examples and WHO standards for verification.
Body weight
| Age | Formula | Example |
|---|---|---|
| 1–6 mo | M = M_birth + 800 × n | 4 mo, M_birth 3,300 → 3,300 + 3,200 = 6,500 g |
| 7–12 months | M = M_birth + 800 × 6 + 400 × (n − 6) | 9 mo, M_birth 3,300 → 3,300 + 4,800 + 1,200 = 9,300 g |
| 1–10 years | M = 10 + 2 × n (kg) | 6 years → 22 kg |
| Over 10 years | M = 30 + 4 × (n − 10) (kg) | 13 years → 42 kg |
Verification benchmarks: weight doubles by 4.5–5 months, triples by one year (10–10.5 kg), and reaches about 20 kg by 5 years. Physiological weight loss in newborns is up to 6–8% by day 3–4, with recovery by day 7–10; a loss of more than 10% is pathological. Monthly weight gain: 600 g in the first month, 800 g in the second and third, decreasing by 50 g each subsequent month (according to Mazurin). Formula-based assessment is approximate; precise evaluation uses WHO centile charts, see child physical development.
Body length and height
| Age | Formula or benchmark |
|---|---|
| At birth | 50–52 cm |
| 1st year | Gain by quarters: 3 cm/mo (I), 2.5 (II), 1.5 (III), 1 (IV) → +25 cm; 75 cm at one year |
| 2nd year | +12–13 cm; 3rd year — +7–8 cm; then +5–6 cm per year |
| Up to 4 years | L = 100 − 8 × (4 − n) |
| 4 years | 100 cm (height doubles relative to birth) |
| After 4 years | L = 100 + 6 × (n − 4) |
| 8 years | About 130 cm; 12 years — about 150 cm (tripled) |
Example: 7 years → 100 + 18 = 118 cm. There are two growth spurts — at 5–7 years and during puberty (girls 11–13, boys 13–15 years), when formulas tend to underestimate.
Head circumference
34–36 cm at birth. First half of life — +1.5 cm per month (about 43 cm at 6 months), second half — +0.5 cm per month (46–47 cm at one year). Formulas: up to 5 years HC = 50 − 1 × (5 − n); after 5 years HC = 50 + 0.6 × (n − 5). At 5 years — 50 cm, at 10 — 53 cm, in adults — 55–58 cm. Rapid growth (more than 2 cm per month) with suture separation indicates hydrocephalus; lag indicates microcephaly or premature suture closure.
Chest circumference
32–34 cm at birth, 1–2 cm less than head circumference. First half of life — +2 cm per month, second half — +0.5 cm; 48 cm at one year. Head and chest circumferences equalize at 3–4 months, after which the chest circumference overtakes the head. Formulas: up to 10 years CC = 63 − 1.5 × (10 − n); after 10 years CC = 63 + 3 × (n − 10). Example: 6 years → 63 − 6 = 57 cm.
Feeding volume in the first year of life
First 10 days of life
- Finkelstein's (Zaitseva's) formula: daily volume = 70 × n (for birth weight under 3,200 g) or 80 × n (3,200 g and over), where n is the day of life. Day 5, 3,400 g → 400 ml per day.
- Zaitseva's formula: volume = 2% of birth weight × n. Day 5, 3,400 g → 68 × 5 = 340 ml.
- Single feeding volume: 10 × n (ml) per feeding, or 3 × day of life × weight (kg).
From 10 days to one year: volume-based method
| Age | Fraction of body weight | Example (weight 5,000 g) |
|---|---|---|
| 10 days – 2 mo | 1/5 | 1,000 ml |
| 2–4 mo | 1/6 | 833 ml |
| 4–6 mo | 1/7 | 714 ml |
| 6–9 mo | 1/8 | — |
| 9–12 mo | 1/9, but not more than 1,000–1,200 ml | — |
Daily volume should not exceed 1 liter up to 6 months and 1.2 liters up to one year, regardless of body weight. Single feeding volume = daily volume / number of feedings (7 up to 3 months, 6 at 3–5 months, 5 from 6 months).
Caloric method
Energy requirement: 1st quarter — 115 kcal/kg daily, 2nd — 115, 3rd — 110, 4th — 100. Knowing the caloric value of formula or breast milk (about 70 kcal per 100 ml), the volume is calculated: 4 months, 6,500 g → 6.5 × 115 = 748 kcal → 748 / 70 × 100 ≈ 1,070 ml, i.e., we limit it to 1,000 ml. This method is needed in prematurity and hypotrophy, when weight does not reflect the requirements.
Requirement for protein, fats, carbohydrates, and fluids
| Age | Proteins, g/kg | Fats, g/kg | Carbohydrates, g/kg | Fluid, ml/kg |
|---|---|---|---|---|
| 0–3 months | 2.2 (breast milk), 2.6 (formula) | 6,5 | 13 | 130–150 |
| 4–6 mo | 2,6–2,9 | 6,0 | 13 | 130–150 |
| 7–12 months | 2,9 | 5,5 | 13 | 120–130 |
| 1–3 years | 3.5–4 (total) | 4 | 16 | 100–120 |
| 4–6 years | 3,0–3,5 | 3,5 | 15 | 90–100 |
| 7–10 years | 2,5–3 | 3 | 13 | 70–80 |
To calculate infusion or fluid intake, the Holliday–Segar formula is used: 100 ml/kg for the first 10 kg + 50 ml/kg for the next 10 kg + 20 ml/kg for the rest. A 24 kg child → 1,000 + 500 + 80 = 1,580 ml per day.
Other formulas that are frequently asked
- Number of milk teeth: n − 4 (n — months), permanent teeth: 4n − 20 (n — years). Detailed — teeth eruption schedule.
- Body surface area (for dosing): up to 9 kg — weight × 0.05 + 0.05; 10–20 kg — weight × 0.04 + 0.1; over 20 kg — weight × 0.02 + 0.4 (m²).
- Diuresis after one year: 600 + 100 × (n − 1) ml per day; frequency of urination — 20–25 in infants, 7–10 in school age.
- Blood pressure: SBP = 90 + 2n, DBP = 60 + n (after one year) — see normal heart rate, blood pressure, and respiratory rate in children.
- Hemoglobin: lower limit of normal is 110 g/L up to 5 years, 115 at 5–11 years, 120 in adolescents.
Example of a complete calculation
A 5-month-old child, birth weight 3,400 g, length 51 cm, formula-fed. Expected weight: 3,400 + 800 × 5 = 7,400 g. Expected length: 51 + 3 × 3 + 2.5 × 2 = 65 cm. Daily formula volume (volume method, 4–6 months — 1/7): 7,400 / 7 ≈ 1,057 → limited to 1,000 ml. Feedings 6 times (from 5 months, 5 times are possible) → 165–200 ml each. Protein: 2.6–2.9 × 7.4 ≈ 20 g per day. Caloric check: 7.4 × 115 = 851 kcal; in 1,000 ml of formula (about 67 kcal/100 ml) — 670 kcal, the remainder is made up by complementary feeding (porridge or vegetable puree is introduced from 4–6 months). You can practice such calculations with real products in the child meal planner on the platform.
Frequently asked questions
What is the difference between the Mazurin and WHO formulas? Formulas are a reference point for oral answers and problem-solving; WHO provides centile charts and Z-scores used to establish a diagnosis. Formulas are asked on the exam, while charts are used in the clinic.
Which method of calculating nutrition is the main one? Up to 10 days — Finkelstein's method, then the volume method; the caloric method is used for weight deviations.
Why do different textbooks give different figures? A 5–10% variation between authors is normal; use the ones provided by your department and cite the source.
See also: Breastfeeding and complementary feeding · Physical development: centiles and Z-scores · Apgar score · Pediatrics course