When to use
- Estimating brain region volumes from serial histological sections
- Quantifying tumor volume from pathology slides
- Calculating area fractions of tissue compartments (e.g., fibrosis, necrosis)
- Teaching stereology point-counting methods
ToolsConductScience tool
StereologyFree in-browser calculator
Cavalieri Point Mask Generator.
Cavalieri stereology point counting for area fraction and volume estimation from tissue sections. Enter grid parameters, count points per section, and get real-time volume estimates with coefficient of error.
PrivateData stays in your browser
LiveNo sign-up required
Validated2026-04-08
CitableMethods and citation included
Calculator
Results update in placeGrid Configuration
Grid points for these dimensions: 88
Section Parameters
Section Counts
Section 1
Leave "Total" at 0 to use the grid point count (88) for that section.
Enter hit counts for at least one section to see results
Do not use for
- As a substitute for automated image segmentation when pixel-level accuracy is needed
- For counting discrete objects (use the optical fractionator instead)
- When sections are not systematically sampled
Grid spacing matters
Too coarse a grid gives too few hits (high CE). Too fine wastes time. Aim for 100–200 total hits across all sections.
Random grid offset is essential
The grid must have a random starting position on each section (or a single random start for all sections in SRS). Without randomization, the estimate is biased.
Section thickness assumptions
Cavalieri assumes uniform section thickness. Tissue shrinkage or uneven cutting introduces systematic error. Measure actual thickness when possible.
CE vs. biological variance
A low CE means precise counting, but between-animal variance usually dominates total variance. Invest effort in more animals rather than over-counting per animal.
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Method
Area per point = (grid spacing scale)². Area fraction = P_hit / P_total. Cavalieri volume = Σ(A_i) t k. CE = 1/√(ΣP_hit) per Gundersen 1999.
2
Validated
Last validated 2026-04-08. Calculations are designed for planning and documentation support; verify procurement decisions against manufacturer specifications or institutional SOPs.
3
How to cite
How to Cite
ConductScience Cavalieri Point Mask Generator (v1.0). ConductScience, Inc. 2026. https://conductscience.com/tools/cavalieri-point-mask-generator
Gundersen HJG et al. J Microsc. 1999;196(1):20–30.
Howard CV, Reed MG. Unbiased Stereology. 2nd ed. Garland Science/BIOS; 2005.
Stereology Fundamentals
Stereology uses systematic random sampling to obtain unbiased quantitative estimates of 3D structures from 2D sections.
Key principles:
- Systematic random sampling — a random start with fixed intervals ensures every part of the structure has equal probability of being sampled
- Unbiased estimation — Cavalieri and other estimators are design-based, not model-based
- Precision control — the Coefficient of Error (CE) quantifies reliability and guides sampling effort
The Cavalieri Method Step by Step
1. Section the tissue systematically (e.g., every 6th section at 30 µm) 2. Overlay a point grid at random position on each section image 3. Count hit points (P_hit) falling within the region of interest 4. Calculate area per section: A = P_hit a(p), where a(p) is the area per point 5. Sum across sections and multiply by thickness interval to get volume 6. Assess CE — if CE > 0.05, increase sampling
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