How to Estimate Reserves with Cross-Sections
Before block models, every reserve on Earth was estimated with cross-sections and the average end-area method — and for tabular deposits, quarries, and PE exam problems, it's still the fastest defensible answer. Here's the full method with the math shown.
01Cut sections perpendicular to the trend
Draw parallel sections across the deposit at regular spacing — 100 ft is common for quarry work, tighter where geology is jumpy. Perpendicular to strike, or the areas distort. Each section shows topography, overburden, the mineable unit between your floor and crest, and any setbacks.
02Compute the mineable area on each section
Planimeter in the old days; CAD or even careful grid-counting now. Apply the real constraints on the section itself — property setbacks, slope angles, floor elevation, high-wall offsets — so the area is mineable rock, not geologic rock. Example: Section 1 = 45,000 ft², Section 2 = 52,000 ft².
03Average end area for each panel
V = L × (A₁ + A₂) ÷ 2. With 100 ft spacing: V = 100 × (45,000 + 52,000)/2 = 4,850,000 ft³. Divide by 27: 179,630 CY. Repeat panel by panel down the deposit and sum.
04Handle the ends honestly
The deposit doesn't stop at your last section. Common closures: a half-spacing extension, a cone/wedge (V = L×A/3) tapering to zero, or trimming to a mapped property or geologic limit. State which you used — end treatment can swing small deposits by double digits.
05Convert to tons with in-place density
Tons = CY × in-place density. At 2.2 tons/CY (typical Southeast granite): 179,630 × 2.2 = 395,000 tons for that panel. In-place, not loose — the swelled truck-bed density belongs to hauling, not reserves. Then apply mining recovery and any quality discount to get from resource toward reserve.
06Know when the method lies
Average end area assumes areas vary linearly between sections — it overestimates when the deposit pinches (a prism has more volume than the cone reality). The prismoidal formula V = L(A₁ + 4Aₕ + A₂)/6 fixes it with a middle section. In practice: tighten section spacing where geometry changes fast, and the error stays inside the density uncertainty anyway.
The Study Vault drills exactly this problem type — including the end-area-vs-prismoidal trap the exam loves.
Studying for the PE Mining exam?
The free Study Vault has exam-style problems with worked solutions, trap warnings, and rules of thumb.
Figures are approximate, compiled from public sources as of mid-2026, and rounded for readability. Rankings shift with markets, mergers, and new discoveries. Nothing here is investment, legal, or engineering advice for a specific site — for that, hire an engineer. We know one.