Capsule Surface Area Calculator (Pill Shape)

A capsule (spherocylinder) is a cylinder with hemispherical caps on each end. Surface area combines the cylinder side with one full sphere (the two hemispheres make one sphere).

SA = 2 × π × r × h + 4 × π × r² = 2 × π × r × (h + 2r)

Where r is the radius (also the cap hemisphere radius) and h is the cylinder length (NOT counting the rounded ends).

Worked example — 100 lb propane tank painting: A typical 100 lb propane tank: r = 6 in, total length 48 in (so cylinder length h = 48 − 2 × 6 = 36 in). SA = 2π × 6 × (36 + 12) = 12π × 48 = 576π ≈ 1,810 sq in = 12.6 sq ft.

Industrial-grade tank paint covers about 50-100 sq ft per gallon depending on viscosity. A gallon of marine-grade epoxy paint covers ~70 sq ft per coat. Two coats on this tank uses about 1/3 gallon — plus prep work, mineral spirits for cleanup.

Worked example — pharmaceutical pill coating: A size 0 vitamin capsule: r = 3.4 mm, total length 21.7 mm (so cylinder length h = 21.7 − 6.8 = 14.9 mm). SA = 2π × 3.4 × (14.9 + 6.8) = 6.8π × 21.7 ≈ 463.4 mm² per capsule.

For a batch of 10,000 capsules: 4.63 m² of total capsule surface. Pan-coating in a vitamin manufacturing tumbler applies ~50-100 mg of coating material per cm² — about 23-46 grams of total coating material for the batch.

Where capsule surface area matters in practice:

• Pill coating chemistry. Time-release coatings, flavor masking, enteric coatings — all priced per surface area.
• Propane and LPG tank painting. White or silver “all-weather” tank paint.
• Pressure vessel external coating. Industrial chemical storage, fuel tanks, air receivers.
• Submarine and torpedo hulls. Anti-fouling and anti-corrosion paint.
• Vitamin and supplement capsule shells. Gelatin or vegetable-based shell material.
• Buoys and floats. Marine navigation buoys with pill-shape designs.

The “tank end caps” architecture insight:

Hemispherical end caps reduce wall stress for the same internal pressure. A cylindrical tank with FLAT end caps has roughly 2× the stress at the corners compared to one with hemispherical end caps. That’s why almost all pressure vessels (propane, oxygen, nitrogen) use the capsule shape — better mechanical efficiency for the same volume capacity.

The surface area trade-off: a capsule has slightly more surface area than a same-volume short cylinder (because hemispheres bulge), but the structural benefit outweighs the small extra material cost.

Comparing capsule SA to a cylinder of the same total length:

A cylinder of length (h + 2r) and radius r: SA_cyl = 2πr × (h + 2r) + 2πr² (lateral + 2 flat ends) SA_capsule = 2πr × h + 4πr² (lateral + sphere) Difference: 2πr² (the capsule has more surface, by 2πr²).

So a capsule has 2πr² more surface than a flat-ended cylinder of the same total length. That’s the “rounding cost” — you trade structural strength for a bit more material.

Sanity check:

• h = 0: capsule = sphere. SA = 4πr². ✓
• r → 0: capsule → line. SA → 0. ✓
• h = r case: SA = 2πr × 3r = 6πr².