Bedside Schwartz equation: how to calculate pediatric eGFR
The 2009 bedside Schwartz equation estimates a child's glomerular filtration rate (GFR) as 0.413 × height in centimeters ÷ serum creatinine in mg/dL. For a child who is 140 cm tall with a creatinine of 1.0 mg/dL, eGFR = 0.413 × 140 ÷ 1.0 = 57.8 mL/min/1.73 m².
Not a medical device. Not a diagnosis or dosing recommendation.
What is the bedside Schwartz equation?
It's a one-line estimate of kidney filtration for children, built from two numbers that are almost always on hand: height and serum creatinine. The result is an estimated GFR (eGFR) in mL/min per 1.73 m² of body surface area, the same unit adult equations use.
It comes from the 2009 Chronic Kidney Disease in Children (CKiD) work by Schwartz and colleagues, so it's also called the 2009 Schwartz equation, the revised or updated Schwartz formula, CKiD eGFR, or simply bedside Schwartz.
It isn't the original 1976 Schwartz formula, which used a different constant and an older way of measuring creatinine.
This page explains the arithmetic. It doesn't give a cutoff, it doesn't assign a kidney disease stage, and it doesn't say what a value means for a particular child.
The bedside Schwartz formula
eGFR (mL/min/1.73 m2) = 0.413 * height_cm / creatinine_mg_dLExact expression the calculator uses:
egfr_ml_min_1_73m2 = 0.413 * height_cm / creatinine_mg_dlIn words: multiply height in centimeters by 0.413, then divide by serum creatinine in mg/dL. Magent's calculator reports the result to 1 decimal place.
What each part means
| Term | Plain-English meaning | Unit | Accepted range |
|---|---|---|---|
height_cm | The child's height | cm | 50–250 |
height_in | Height, if measured in inches | in | 20–98 (cm = in × 2.54) |
creatinine_mg_dl | Serum creatinine | mg/dL | 0.1–20 |
creatinine_umol_l | Serum creatinine in SI units | µmol/L | 9–1768 (mg/dL = µmol/L ÷ 88.42) |
egfr_ml_min_1_73m2 | Estimated GFR | mL/min/1.73 m² | 1 decimal place |
How the formula works
- Put height in centimeters. If you have inches, multiply by 2.54.
- Put creatinine in mg/dL. If you have µmol/L, divide by 88.42.
- Multiply height by 0.413.
- Divide by creatinine.
- Round to 1 decimal place.
Height sits on top, so a taller child with the same creatinine gets a higher estimate. Creatinine sits underneath, so doubling creatinine halves the estimate.
Units
- Creatinine in µmol/L. Labs in many countries report creatinine this way. The calculator converts it with mg/dL = µmol/L ÷ 88.42 before applying 0.413. Plugging µmol/L straight into the formula gives a number about 88 times too small.
- Height in inches. The calculator converts inches with cm = in × 2.54. Plugging inches straight in gives a number that is too small.
- The 0.413 constant assumes height in centimeters. Some sources write the same equation with height in meters and a constant of 41.3; the arithmetic is identical.
There's no age, sex or weight input. The equation uses height and creatinine alone.
Worked examples
These use Magent's own expected values for the calculator.
Example 1: 140 cm, creatinine 1.0 mg/dL
- 0.413 × 140 = 57.82
- 57.82 ÷ 1.0 = 57.82 → 57.8 mL/min/1.73 m²
Example 2: 60 inches, creatinine 1.0 mg/dL
- Height: 60 × 2.54 = 152.4 cm
- 0.413 × 152.4 = 62.9412
- ÷ 1.0 → 62.9 mL/min/1.73 m²
Example 3: 140 cm, creatinine 88.42 µmol/L
- Creatinine: 88.42 ÷ 88.42 = 1.0 mg/dL
- 0.413 × 140 ÷ 1.0 = 57.82 → 57.8 mL/min/1.73 m²
Examples 1 and 3 are the same child with creatinine reported in two unit systems. The answer is identical once the units are converted.
Example 4: 120 cm, creatinine 1.1 mg/dL
- 0.413 × 120 = 49.56
- 49.56 ÷ 1.1 = 45.0545… → 45.1 mL/min/1.73 m²
Bedside Schwartz reference table
These values are computed from the formula and rounded to 1 decimal, as the calculator reports them. Rows are height in centimeters; columns are serum creatinine in mg/dL. The table shows how the estimate moves with height and creatinine; the values aren't targets, reference ranges or kidney disease stages.
| Height (cm) \ creatinine (mg/dL) | 0.3 | 0.5 | 0.6 | 0.7 | 1.0 | 1.5 |
|---|---|---|---|---|---|---|
| 60 | 82.6 | 49.6 | 41.3 | 35.4 | 24.8 | 16.5 |
| 80 | 110.1 | 66.1 | 55.1 | 47.2 | 33.0 | 22.0 |
| 100 | 137.7 | 82.6 | 68.8 | 59.0 | 41.3 | 27.5 |
| 120 | 165.2 | 99.1 | 82.6 | 70.8 | 49.6 | 33.0 |
| 140 | 192.7 | 115.6 | 96.4 | 82.6 | 57.8 | 38.5 |
| 160 | 220.3 | 132.2 | 110.1 | 94.4 | 66.1 | 44.1 |
Example 1 is the cell for 140 cm and 1.0 mg/dL. Reading across any row shows that the estimate falls as creatinine rises; reading down any column shows it rising with height.
History of the bedside Schwartz equation
The equation comes from George J. Schwartz, Alvaro Muñoz, Michael F. Schneider and colleagues, New equations to estimate GFR in children with CKD, published in the Journal of the American Society of Nephrology in 2009 (volume 20, issue 3, pages 629–637).
The paper's abstract explains the starting problem: the Schwartz formula from the mid-1970s was now overestimating GFR measured by iohexol disappearance, likely because the methods used to measure creatinine had changed. The authors used data from 349 children aged 1 to 16 years in the CKiD cohort to build new equations, the fullest of which used height, creatinine, cystatin C, blood urea nitrogen and sex. The abstract adds that, with height in centimeters, a bedside calculation of 0.413 × (height ÷ serum creatinine) provides a good approximation to that fuller equation. That bedside version is the one on this page.
When it's used
A 2012 study in PLoS One describes how improvements in laboratory technique, including enzymatic creatinine methods and standardization to isotope dilution mass spectrometry (IDMS), gave lower creatinine results than the classic Jaffé reaction, so formulas built on the older methods needed revising.[1] The same paper notes that the original Schwartz formula had been adapted to current creatinine assays and that its use is recommended for estimating GFR in children.[1]
Where it's used
The 2012 study re-estimated the equation's constant in a French cohort of children and adolescents and checked it in a Swedish cohort.[1] It points out that the 2009 equation was built in North American children with mild to severe chronic kidney disease and notable growth retardation.[1]
Who uses it
The 2012 paper says plasma-creatinine-based equations for estimating GFR are recommended by several clinical guidelines, and describes the 2009 equation as Schwartz and colleagues' adaptation of the traditional formula to children and adolescents.[1]
Limits of the calculation
- It's an estimate from height and creatinine. It isn't a measured GFR.
- It's the 2009 bedside equation with 0.413. It isn't the 1976 Schwartz formula with 0.55.
- It doesn't use cystatin C, blood urea nitrogen, age or sex, unlike the fuller 2009 CKiD equation.
- It isn't an adult equation. It isn't CKD-EPI and it isn't Cockcroft–Gault.
- It doesn't assign a chronic kidney disease stage.
- It was derived in children with chronic kidney disease. Magent doesn't re-derive the constant for other groups.
- Inputs outside the accepted ranges are rejected, not estimated.
Clinical decisions belong to a qualified clinician who knows the patient.
How it differs from related calculators
- eGFR (CKD-EPI) uses creatinine, age and sex, not height, and the record says it doesn't apply pediatric equations.
- Creatinine clearance (Cockcroft–Gault) estimates clearance in mL/min from age, weight, sex and creatinine. It isn't indexed to 1.73 m².
Glossary
- GFR: glomerular filtration rate, the volume of blood plasma the kidneys filter per minute.
- eGFR: an estimated GFR calculated from blood tests and body measurements instead of measured directly.
- Serum creatinine: a waste product of muscle, measured in a blood sample.
- 1.73 m²: a standard body surface area that GFR is scaled to so children and adults can be compared.
- CKiD: Chronic Kidney Disease in Children, the North American cohort the 2009 equations came from.
- IDMS: isotope dilution mass spectrometry, a reference method that creatinine assays are calibrated to.
Common mistakes
- Using 0.55 instead of 0.413. That's the 1976 constant. With 0.55, the 140 cm example would come out too high.
- Entering creatinine in µmol/L as if it were mg/dL. Convert first, or use the calculator's µmol/L field.
- Entering height in inches as if it were centimeters. Multiply by 2.54 first, or use the inches field.
- Using it for an adult. Adult estimates come from different equations.
Source
Schwartz GJ, Muñoz A, Schneider MF, et al. New equations to estimate GFR in children with CKD. J Am Soc Nephrol. 2009;20(3):629-637. DOI: 10.1681/ASN.2008030287
Further reading
- De Souza VC, Rabilloud M, Cochat P, et al. Schwartz formula: is one k-coefficient adequate for all children? PLoS One. 2012;7(12):e53439.
Frequently asked questions
How do you calculate eGFR with the bedside Schwartz equation?
Multiply height in centimeters by 0.413 and divide by serum creatinine in mg/dL. For 140 cm and 1.0 mg/dL, that's 57.8 mL/min/1.73 m².
What is a normal eGFR for a child?
This page doesn't give a cutoff or a reference interval. It calculates the estimate; what a value means depends on the child and the clinical context.
What's the difference between the 1976 and 2009 Schwartz formulas?
The 2009 bedside equation uses 0.413 and was built with modern creatinine methods. The 1976 formula used 0.55 with older creatinine measurement.
Can I use creatinine in µmol/L?
Yes. Divide by 88.42 to get mg/dL first. The calculator does this for you if you enter µmol/L.
Does the bedside Schwartz equation use age or sex?
No. It uses height and serum creatinine alone.
Who developed the bedside Schwartz equation?
George J. Schwartz and colleagues from the CKiD study, in a 2009 paper in the Journal of the American Society of Nephrology.