Logo

MonoCalc

/

Capsule Volume Calculator

Geometry

Height Input Mode

Height of the straight cylindrical section only (excludes the two caps)

Radius (r)

Must be greater than 0

Cylinder Height (h)

Must be 0 or greater

Input Unit

Volume Output Unit

Decimal Places

rh

Total Volume

1466.0766 cm³

Hemisphere Volume

523.5988 cm³

(both caps = 1 sphere)

Cylinder Volume

942.4778 cm³

(body only)

Total Height

22.0000 cm

Cylinder Height

12.0000 cm

Step-by-step

Formula: V = π × r² × h + (4/3) × π × r³

Radius: 5.0000 cm

Cylinder height: 12.0000 cm

Cylinder volume = π × 5.0000² × 12.0000 = 942.4778 cm³

Hemisphere volume (sphere) = (4/3) × π × 5.0000³ = 523.5988 cm³

Total volume = 942.4778 + 523.5988 = 1466.0766 cm³

About This Tool

Capsule Volume Calculator – How to Find the Volume of a Capsule

A capsule is a three-dimensional solid made up of a cylinder with two hemispherical caps on each end — one cap at the top and one at the bottom. Because the two caps together form a complete sphere, the capsule volume formula combines a cylinder and a sphere into a single, elegant expression. Capsule shapes appear everywhere: from pharmaceutical tablets and gel-cap supplements to rocket propellant tanks, submarine pressure hulls, and industrial mixing vessels.

Capsule Volume Formula

The total volume of a capsule is the sum of the cylindrical body and the two hemispherical ends:

V = π × r² × h + (4/3) × π × r³

Where r is the radius of the cylinder (and the caps), and h is the height of the straight cylindrical section only — not the overall length. This can also be written as:

V = π × r² × (h + (4/3) × r)

For example, a capsule with r = 5 cm and h = 12 cm has:

  • Cylinder volume = π × 25 × 12 ≈ 942.48 cm³
  • Sphere volume = (4/3) × π × 125 ≈ 523.60 cm³
  • Total volume ≈ 1,466.08 cm³

Cylinder Height vs. Total Height

The calculator offers two height input modes to match how you have measured the capsule:

  • Cylinder Height mode — you provide h, the length of the straight cylindrical body only. The total end-to-end length is then derived as h + 2r. Use this mode when you know the body length from a design specification or cross-section measurement.
  • Total Height mode — you provide the full end-to-end length of the capsule. The cylinder body height is derived as total height − 2r. Use this when you have measured the capsule from tip to tip (for example, with calipers). The total height must be at least 2r; if it equals 2r the capsule degenerates into a sphere.

Volume Breakdown

The results panel shows three values separately:

  • Total Volume — the complete interior capacity of the capsule
  • Hemisphere Volume — the combined volume of both hemispherical caps, which always equals one full sphere: (4/3)πr³
  • Cylinder Volume — the volume of the straight cylindrical body alone:πr²h

When the cylinder height is zero the capsule reduces to a sphere, so the cylinder volume drops to zero and the total equals the sphere volume. As the cylinder height grows, the hemisphere volume stays constant while the cylinder volume increases linearly.

Unit Conversion

Both radius and height accept any of seven standard length units: mm, cm, m, km, in, ft, yd. Volume output is independently selectable in the corresponding cubic units. All inputs are converted to metres internally before the formula is applied, and the result is then expressed in the requested output unit. This means you can enter dimensions in centimetres and receive the volume directly in cubic inches or cubic metres without any manual conversion step.

How Radius and Height Affect Volume

The capsule volume has different sensitivity to radius and height:

  • Radius — appears in both the cylinder term (r²) and the sphere term (r³), so doubling the radius more than quadruples the total volume. For a purely spherical capsule (h = 0), doubling the radius multiplies the volume by 8.
  • Cylinder height — only affects the cylindrical body term linearly. Doubling h doubles the cylinder portion but leaves the hemisphere volume unchanged. For long capsules (h ≫ r), the cylinder volume dominates and the total is nearly proportional to h.

Practical Applications

Capsule volume calculations are needed across many fields:

  • Pharmaceuticals — sizing capsule tablets to deliver a precise drug dose; gel-cap volume must accommodate the exact powder fill weight.
  • Aerospace and defence — computing propellant capacity for cylindrical tanks with hemispherical end domes; the shape maximises volume-to-surface-area ratio under internal pressure.
  • Marine engineering — pressure hulls for submarines and underwater vehicles are capsule-shaped to resist hydrostatic forces uniformly.
  • Sporting goods — flotation devices, buoys, and water-polo goals use capsule geometry for predictable buoyancy.
  • Food and beverage — coffee capsules, protein shakers, and condiment dispensers are often capsule-shaped for ergonomics and efficient filling.

Step-by-Step Calculation Example

For a capsule with r = 3 cm and total height = 14 cm:

  1. Cylinder height h = 14 − 2 × 3 = 8 cm
  2. Cylinder volume = π × 3² × 8 = π × 9 × 8 ≈ 226.19 cm³
  3. Sphere volume = (4/3) × π × 3³ = (4/3) × π × 27 ≈ 113.10 cm³
  4. Total volume = 226.19 + 113.10 ≈ 339.29 cm³

Tips for Accurate Results

Use the same level of precision in your radius and height measurements. Because the sphere term scales with r³, a small error in radius has an outsized effect on the hemisphere portion. The calculator retains JavaScript's full 64-bit floating-point precision internally and rounds only the displayed result, so you can safely increase the decimal places for critical calculations.

Frequently Asked Questions

Is the Capsule Volume Calculator free?

Yes, Capsule Volume Calculator is totally free :)

Can I use the Capsule Volume Calculator offline?

Yes, you can install the webapp as PWA.

Is it safe to use Capsule Volume Calculator?

Yes, any data related to Capsule Volume Calculator only stored in your browser (if storage required). You can simply clear browser cache to clear all the stored data. We do not store any data on server.

What is the formula for the volume of a capsule?

The volume of a capsule is V = π × r² × h + (4/3) × π × r³, where r is the radius and h is the height of the cylindrical body (not the total length). This combines the cylinder volume (π r² h) with the volume of a full sphere (4/3 π r³) formed by the two hemispherical caps.

How does this capsule volume calculator work?

Enter the radius and either the cylinder body height or the total end-to-end length. The calculator converts your inputs to the chosen output unit, computes the cylinder volume and the combined hemisphere volume separately, then adds them for the total. Real-time results appear as you type, with a step-by-step breakdown of the calculation.

What is the difference between cylinder height and total height?

Cylinder height (h) is the length of the straight cylindrical section only, excluding the two hemispherical caps. Total height is the full end-to-end length of the capsule, equal to h + 2r. If you know the overall length of the capsule (for example, from a technical drawing), use Total Height mode; otherwise use Cylinder Height mode.

What units does the capsule calculator support?

Inputs accept millimetres (mm), centimetres (cm), metres (m), kilometres (km), inches (in), feet (ft), and yards (yd). Volume output is available in the corresponding cubic units: mm³, cm³, m³, km³, in³, ft³, and yd³. Input and output units are independent, so you can enter in cm and receive results in m³ or in³.

Where are capsule volume calculations used in practice?

Capsule shapes appear in pharmaceutical tablet design, pressurised fuel tanks, rocket propellant cells, submarine pressure hulls, industrial mixing vessels, and sporting goods such as capsule-shaped floats. Knowing the exact volume is critical for dosage control, structural safety, and material estimation.

How accurate is the capsule volume result?

The calculator uses JavaScript's 64-bit floating-point arithmetic with approximately 15 significant digits of precision. Results are displayed to four decimal places by default, which is more than sufficient for engineering, manufacturing, and academic work. For pharmaceutical applications, ensure your radius and height measurements are equally precise.