💊 Capsule Volume Calculator
Cylinder with hemispherical ends — tanks, pills, stadiums
Enter Radius & Cylinder Length
r = radius, L = cylinder length, T = total
📊 Results
Radius (r)
5 cm
Cylinder Length
15 cm
Total Length
25 cm
Total Volume
1,702 cm³
Cylinder Vol
1,178 cm³
Sphere Vol
524 cm³
Surface Area
785 cm²
📝 Step-by-Step Solution
Given: r = 5 cm, L = 15 cm
Cylinder volume: V_cyl = πr²L = π × 25 × 15 = 1,178.1 cm³
Sphere volume (2 hemispheres = 1 sphere): V_sph = (4/3)πr³ = 523.6
cm³
Total: V = πr²L + (4/3)πr³ = πr²(L + 4r/3)
Total volume = 1,701.7 cm³
📐 Capsule Volume Formulas
Total Volume: V = πr²L + (4/3)πr³ = πr²(L + 4r/3)
Cylinder Volume: Vcyl = πr²L
Sphere Volume (2 hemispheres): Vsph = (4/3)πr³
Total Length: T = L + 2r
Surface Area: A = 2πrL + 4πr² = 2πr(L + 2r)
Understanding Capsule Shapes
💊 Capsule Shape
Cylinder + two hemispheres. Also called stadium solid, discorectangle, or pill shape. Common in tanks and medicine.
📐 Two Lengths
L = cylinder only, T = total. T = L + 2r. The hemispheres add one full diameter to total length.
🔵 Complete Sphere
Two hemispheres = one sphere. Sphere volume = (4/3)πr³. Add to cylinder volume for total.
🏭 Applications
Pressure vessels, propane tanks, pharmaceutical capsules, fuel tanks. Rounded ends distribute pressure evenly.
Frequently Asked Questions
What is the volume formula for a capsule?
V = πr²L + (4/3)πr³. Cylinder volume plus sphere volume (two
hemispheres). Can be factored as πr²(L + 4r/3).
What is a cylinder with hemispherical ends called?
Capsule, stadium solid, spherocylinder, or discorectangle. Also
known as a pill shape or rounded cylinder.
What is L vs T in capsule dimensions?
L = cylinder length only (middle section). T = total
length (end to end). Relationship: T = L + 2r.
Why use hemispherical ends?
Pressure distribution. Rounded ends handle internal pressure
better than flat ends. Used in pressurized tanks.
How do I find cylinder length from volume?
L = (V - (4/3)πr³) / (πr²). Subtract sphere volume from total,
then divide by base area.
What if L = 0?
It becomes a sphere. Volume = (4/3)πr³. Two hemispheres with no
cylinder in between.
How do I calculate surface area?
A = 2πrL + 4πr². Cylinder curved surface plus complete sphere
surface. Simplified: A = 2πr(L + 2r).
Can I use diameter instead of radius?
Yes, r = d/2. Substitute in formulas. V = π(d/2)²L + (4/3)π(d/2)³
= (πd²L)/4 + (πd³)/6.
What is the volume of a propane tank?
Use capsule formula. Measure radius and cylinder length (or total
length minus diameter). Many are capsule-shaped.
How accurate for real tanks?
Very accurate for perfect hemispheres. Real tanks may have
slightly different end shapes (elliptical, torispherical).
What is a stadium solid?
Same as capsule. 2D stadium (rectangle + semicircles) extended
into 3D. Sometimes called discorectangle in 2D.
How do I convert to gallons or liters?
1 L = 1000 cm³, 1 gal = 3785 cm³. Our calculator outputs in your
preferred unit.
What is the ratio of cylinder to sphere volume?
Depends on L/r ratio. Higher L/r = more cylinder-dominated. Equal
when L/r = 4/3 ≈ 1.33.
Can one end be flat and one hemispherical?
Different shape. That's hemisphere-capped cylinder. Volume = πr²L
+ (2/3)πr³ (only one hemisphere).
How does this relate to pharmaceutical capsules?
Same shape principle. Medicine capsules are small-scale versions.
Volume determines capacity.
What if ends are elliptical not spherical?
Different formula needed. This calculator assumes perfect
hemispherical ends. Elliptical heads use different geometry.
How do I find radius from volume?
Requires numerical methods. Cubic equation in r. Our calculator
solves this iteratively when you select "Find Radius" mode.