Capsule Volume Calculator
Calculate the volume of a capsule (cylinder with hemispherical caps)
By Drew Budwin · Last updated July 2026 · Methodology
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Capsule Volume Calculator Formula
Volume of a capsule:
V = π × r² × h + (4/3) × π × r³
r = radius, h = cylinder height (straight section only)
How to Use This Calculator
- Enter the radius of the capsule (same for the cylinder and both hemispherical caps).
- Enter the cylinder height: the length of the straight middle section only, not the total capsule length.
- Click Calculate Volume to see the result.
Frequently Asked Questions
What is a capsule shape?
A capsule is a cylinder with a hemisphere attached to each end. The total length is h + 2r, where h is the cylinder height and r is the radius. The formula combines the cylinder volume (πr²h) and a full sphere volume (4/3 πr³) from the two caps.
What is the cylinder height vs. total capsule length?
The cylinder height (h) is only the straight middle section. The total capsule length is h + 2r, since each hemispherical cap adds one radius of length. Enter only the straight portion here.
What units does this calculator use?
This calculator is unit-agnostic. If r and h are in centimeters, the result is in cubic centimeters (cm³). Use the same unit for both inputs.
Where are capsule shapes found in real life?
Capsule shapes show up in pharmaceutical pills, propane tanks, submarine hulls, pressure vessels, and stadium roofs. The rounded ends spread pressure evenly, which is why pressure vessels use them.
What happens when the cylinder height is zero?
When h = 0, the two hemispherical caps meet directly and the capsule becomes a full sphere. The volume simplifies to (4/3)πr³, which is the standard sphere formula. You can verify this with the sphere calculator.
How does increasing radius vs. cylinder height affect capsule volume more?
Radius has a larger effect. It appears as r³ in the spherical cap term and r² in the cylinder term. Doubling the radius roughly triples or more the total volume, depending on the h/r ratio. Doubling the cylinder height adds only πr²h to the total.
What is the surface area of a capsule?
The total surface area is 2πr(2r + h) — the lateral surface of the cylinder plus the full sphere formed by the two hemispherical caps. This calculator computes volume only; surface area uses the same r and h inputs.
How do I estimate the volume of a pharmaceutical capsule?
Standard pharmaceutical capsule sizes are specified by industry codes. A size 0 capsule holds about 0.68 mL. Measure the outer radius and the cylindrical body length, then use this calculator for the exact volume.