Kidney Stone Calculator — Size & Passage Probability
Enter the three dimensions of a kidney stone from an imaging report to estimate its volume and the likelihood it will pass on its own without surgical intervention.
mm
mm
mm
Population-level estimate based on maximum stone diameter
- 1
Maximum dimension
max(5, 4, 4) = 5 mmThe largest axis drives spontaneous passage probability. - 2
Ellipsoid volume
(π ÷ 6) × 5 × 4 × 4 = 41.9 mm³
How does this calculator work?
Stone volume is estimated as an ellipsoid: (π/6) × L × W × D mm³. Passage probability depends on maximum diameter: ≤4 mm ≈ 80%, 4–6 mm ≈ 59%, 6–10 mm ≈ 21%, >10 mm <5%. These are population averages from AUA/EAU guidelines — consult a urologist for your specific case.
Formula
How this is calculated
Kidney stones (renal calculi) are described on ultrasound and CT reports by their maximum diameter or two/three dimensions in millimetres. Stone volume is approximated as an ellipsoid: V = (π/6) × L × W × D, where L, W and D are the three diameters (the same formula gives the volume of a sphere when L = W = D). If you only know two dimensions, the calculator assumes the unknown depth equals the measured width — a common working assumption for roughly ellipsoidal stones.
The most clinically important dimension is the maximum diameter, because it drives the likelihood of spontaneous passage. AUA and EAU guidelines, backed by multiple studies including Coll et al. (2002) and Preminger et al. (2007), report approximate passage rates of around 80% for stones ≤4 mm, 59% for 4–6 mm, 21% for 6–10 mm, and under 5% for stones larger than 10 mm. These are population-level averages: stone location (ureteral vs. renal pelvis), composition, hydration and patient anatomy all affect the actual probability.
This calculator is a reference tool, not a clinical decision aid. Always follow the treatment plan recommended by your urologist or emergency physician.
Frequently asked questions
Stones smaller than 4 mm pass spontaneously in roughly 80% of cases. From 4–6 mm the rate drops to about 59%, and above 6 mm most stones require medical or surgical intervention such as shock-wave lithotripsy or ureteroscopy.
Stone volume is estimated using the ellipsoid formula: V = (π/6) × length × width × depth. When the depth is unknown it is assumed to equal the width. This gives a good approximation for most calculi, though unusually shaped stones may deviate.
Mean passage times from studies are roughly 8 days for stones under 4 mm and 12–22 days for those up to 6 mm. Larger stones that do not pass within 4–6 weeks are usually treated. Your urologist can advise on watchful waiting vs. active intervention for your specific stone.
Also known as
TG we-Calculate Editorial Team. (2026). Kidney Stone Calculator — Size & Passage Probability [Online calculator]. TG we-Calculate. https://we-calculate.com/calculator/kidney-stone-calculator
TG we-Calculate Editorial Team. "Kidney Stone Calculator — Size & Passage Probability." TG we-Calculate. 2026. https://we-calculate.com/calculator/kidney-stone-calculator.
TG we-Calculate Editorial Team, "Kidney Stone Calculator — Size & Passage Probability," TG we-Calculate, 2026. [Online]. Available: https://we-calculate.com/calculator/kidney-stone-calculator
@misc{wecalculate_kidney_stone_calculator, title = {Kidney Stone Calculator — Size & Passage Probability}, author = {{TG we-Calculate Editorial Team}}, howpublished = {\url{https://we-calculate.com/calculator/kidney-stone-calculator}}, year = {2026}, note = {TG we-Calculate} }
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