Capsule Volume Calculator
Instantly find the volume and surface area of any capsule — a cylinder capped with two hemispheres. Get step-by-step formula explanations, real-world worked examples, and a complete guide — all free, all in one place.
📋 Table of Contents
- Interactive Capsule Volume Calculator
- What Is a Capsule? — Complete Definition & Properties
- Capsule Formulas — Volume, Surface Area & Derivations
- How to Use the Capsule Volume Calculator (Step-by-Step)
- Worked Examples — Step-by-Step Solutions
- Reverse Calculations — Finding Radius or Height from Volume
- Unit Conversions for Capsule Volume
- Real-World Applications of Capsule Volume
- Capsule vs. Cylinder vs. Sphere — Comparison
- Common Mistakes to Avoid
- Quick Reference Formula Table
- Frequently Asked Questions (FAQ)
🧮 Capsule Volume Calculator
Enter the radius of the circular cross-section and the height of the cylindrical middle section, choose a unit, and press Calculate. The tool instantly computes Volume, Surface Area, Total Capsule Length, and Diameter.
Figure: A capsule with radius r (dark green), cylinder height h (blue dashed), total length L = h + 2r (amber), and diameter d = 2r (purple). The two hemispherical caps together form a complete sphere.
📘 What Is a Capsule? — Complete Definition & Properties
A capsule — also called a spherocylinder or stadium solid — is a three-dimensional geometric shape formed by a cylinder with a hemispherical cap attached seamlessly to each end. Imagine taking a standard cylinder and instead of leaving the two flat circular bases exposed, you smoothly rounded each end into a half-sphere of the same radius. The result is a perfectly smooth, edge-free solid that looks exactly like a pharmaceutical pill capsule — which is precisely where the common name comes from.
Formally, a capsule is the Minkowski sum of a line segment and a sphere. If you take a line segment of length \( h \) and "inflate" it by a sphere of radius \( r \) — meaning you place a sphere of radius \( r \) centered at every point on the segment — you trace out a capsule. This beautiful geometric construction explains why the capsule has a perfectly smooth, constant-curvature surface with no sharp edges or corners anywhere on it.
Key Properties of a Capsule
- Radius (r): The radius of the circular cross-section. Critically, the cylindrical body and both hemispherical caps share the exact same radius — this is what makes the shape seamlessly smooth.
- Cylinder Height (h): The length of the straight cylindrical middle section. When \( h = 0 \), the capsule degenerates into a complete sphere of radius \( r \).
- Total Length (L): The end-to-end length of the capsule: \( L = h + 2r \). Each hemispherical cap contributes a length of exactly \( r \) (its radius) to either end.
- Diameter (d): The maximum width of the capsule: \( d = 2r \). The capsule is widest at any cross-section through the cylindrical portion.
- No Flat Faces, No Edges, No Vertices: Unlike a cylinder (which has two flat circular faces and two circular edges), a capsule has a completely smooth, continuous curved surface. There are no sharp transitions between the hemispherical caps and the cylindrical body.
- Axis of Symmetry: A capsule has one primary axis of rotational symmetry — its long central axis. Any rotation about this axis maps the capsule to itself. It also has infinitely many planes of reflective symmetry containing its long axis, plus one mirror plane perpendicular to the axis through the midpoint (if \( h > 0 \)).
- Special Case — Sphere: When \( h = 0 \), the capsule becomes a perfect sphere. All capsule formulas reduce exactly to the sphere formulas in this limiting case: \( V = \frac{4}{3}\pi r^3 \) and \( SA = 4\pi r^2 \).
Capsule Terminology at a Glance
| Term | Definition | Formula | Example (r = 3 cm, h = 8 cm) |
|---|---|---|---|
| Radius (r) | Radius of cross-section & both hemispherical caps | \( r \) | 3 cm |
| Diameter (d) | Maximum width | \( d = 2r \) | 6 cm |
| Cylinder Height (h) | Length of straight cylindrical middle section | \( h \) | 8 cm |
| Total Length (L) | End-to-end length of the complete capsule | \( L = h + 2r \) | 14 cm |
| Volume (V) | Total enclosed 3D space | \( \pi r^2 h + \tfrac{4}{3}\pi r^3 \) | \( 72\pi + 36\pi = 108\pi \approx 339.29 \) cm³ |
| Surface Area (SA) | Total outer surface area | \( 2\pi r(2r + h) \) | \( 84\pi \approx 263.89 \) cm² |
The Capsule as a Limiting Shape
The capsule occupies a special position in the spectrum of 3D shapes:
- When h = 0: the capsule becomes a sphere of radius \( r \). Both formulas reduce perfectly: \( V = \frac{4}{3}\pi r^3 \) and \( SA = 4\pi r^2 \).
- When h → ∞: the capsule approaches an infinitely long cylinder. The hemispherical end-caps become negligible compared to the cylinder body, so volume ≈ \( \pi r^2 h \) and surface area ≈ \( 2\pi rh \).
- When r → 0: the capsule degenerates to a line segment of length \( h \) with zero volume. This is the "1D" limit.
This spectrum — sphere at one end, cylinder at the other, with the capsule interpolating smoothly between — makes the capsule one of geometry's most elegant and versatile shapes.
📐 Capsule Formulas — Volume, Surface Area & Full Derivations
A capsule's measurements follow from decomposing it into two familiar sub-shapes: a cylinder (the middle section) and a complete sphere (assembled from the two hemispherical end-caps). This decomposition strategy makes the derivations elegantly straightforward.
Formula 1: Volume of a Capsule
The capsule is decomposed into: (1) a cylinder of radius \( r \) and height \( h \), and (2) two hemispheres of radius \( r \), which together form one complete sphere.
This can also be written in factored form as:
\[ V = \pi r^2 \!\left( h + \frac{4r}{3} \right) \]
Where:
• V = Volume (in cubic units, e.g., cm³, m³, in³)
• r = Radius of the circular cross-section (shared by body and caps)
• h = Height of the straight cylindrical middle section
• π ≈ 3.14159265358979
Derivation:
Volume of cylinder part: \( V_{cyl} = \pi r^2 h \)
Volume of two hemispheres (= one full sphere): \( V_{sphere} = \dfrac{4}{3}\pi r^3 \)
Total capsule volume: \( V = V_{cyl} + V_{sphere} = \pi r^2 h + \dfrac{4}{3}\pi r^3 \)
Formula 2: Surface Area of a Capsule
Similarly, the surface area is the sum of the cylinder's lateral surface area (the side wall — both circular flat ends are replaced by the hemispherical caps) plus the total surface area of a complete sphere (the two caps together).
Where:
• 2πrh = Lateral surface area of the cylindrical middle section
• 4πr² = Surface area of the complete sphere formed by both hemispherical caps
• 2πr(h + 2r) = Compact factored form
Important note: The capsule has no flat faces. The circular ends of the cylinder are entirely replaced by the hemispherical caps, so there is no \( 2\pi r^2 \) "two circular base" term that appears in the cylinder's TSA formula. The entire surface is curved.
Derivation:
LSA of cylinder (side wall only): \( 2\pi r h \)
SA of two hemispheres (= one sphere): \( 4\pi r^2 \)
Total: \( SA = 2\pi r h + 4\pi r^2 = 2\pi r(h + 2r) \)
Formula 3: Total Length of a Capsule
Each hemispherical cap adds a length equal to the radius \( r \) to each end of the cylindrical section, giving total length \( L = h + 2r \). If you know only the total length and the radius, then the cylinder height is \( h = L - 2r \).
Formula 4: Volume Using Total Length
If you are given total length \( L \) instead of cylinder height \( h \), substitute \( h = L - 2r \):
Or compactly:
\[ V = \pi r^2 \!\left( L - \frac{2r}{3} \right) \]This is useful when pharmaceutical, engineering, or packaging specifications give the overall capsule length rather than the cylinder-only height.
Formula 5: Capsule Volume as a Function of Sphere Volume
A capsule always contains more volume than a sphere of the same radius. The "extra" volume is exactly the cylinder contribution \( \pi r^2 h \). When \( h = 0 \), the two shapes are identical.
🛠️ How to Use the Capsule Volume Calculator (Step-by-Step)
Our free online capsule calculator is designed for simplicity and precision. Follow these five steps to get your results instantly.
- Enter the Radius (r): Type the radius of the capsule's circular cross-section. This single radius applies to both the cylindrical body and both hemispherical end-caps — they all share the same radius. If you know only the diameter, divide it by 2 to get the radius. Enter any positive number, including decimals.
- Enter the Cylinder Height (h): Type the length of the straight cylindrical middle section only — not the total end-to-end length of the capsule. If you're given the total length \( L \), subtract \( 2r \) to get \( h = L - 2r \). Enter 0 if the capsule has no cylindrical section (making it a sphere).
- Select Your Unit: Choose mm, cm, m, km, in, ft, or yd from the dropdown. All results will use the same unit consistently — Volume in cubic units, Surface Area in square units, and Lengths in linear units.
- Click "Calculate": Press the green Calculate button. The calculator applies \( V = \pi r^2 h + \frac{4}{3}\pi r^3 \) and \( SA = 2\pi r(2r + h) \) instantly and displays four result cards.
- Read and Use Your Results: Four result cards appear: Volume, Surface Area, Total Capsule Length, and Diameter — all rounded to two decimal places. Press Reset to clear and start a new calculation.
✏️ Worked Examples — Step-by-Step Solutions
These five carefully chosen examples cover the full range of capsule calculation scenarios — from simple classroom problems to real engineering applications.
Example 1 — Standard Capsule (Classroom Problem)
A capsule has a radius of 5 cm and a cylinder height of 12 cm. Find its volume and surface area.
- Step 1 — Identify values: r = 5 cm, h = 12 cm, π ≈ 3.14159
- Step 2 — Cylinder volume: \( V_{cyl} = \pi r^2 h = \pi \times 25 \times 12 = 300\pi \) cm³
- Step 3 — Sphere volume (two caps): \( V_{sph} = \dfrac{4}{3}\pi r^3 = \dfrac{4}{3}\pi \times 125 = \dfrac{500\pi}{3} \) cm³
- Step 4 — Total volume: \( V = 300\pi + \dfrac{500\pi}{3} = \dfrac{900\pi + 500\pi}{3} = \dfrac{1{,}400\pi}{3} \approx 1{,}466.08 \) cm³
- Step 5 — Surface area: \( SA = 2\pi r(2r + h) = 2\pi \times 5 \times (10 + 12) = 10\pi \times 22 = 220\pi \approx 691.15 \) cm²
- Step 6 — Total length: \( L = h + 2r = 12 + 10 = 22 \) cm
Example 2 — Pharmaceutical Capsule (Pill Sizing)
A size 00 pharmaceutical capsule has a total length of 23.3 mm and a diameter of 8.53 mm. Find its internal volume (assuming walls are negligible).
- Step 1 — Find radius: d = 8.53 mm, so r = 8.53 / 2 = 4.265 mm
- Step 2 — Find cylinder height: h = L − 2r = 23.3 − 2 × 4.265 = 23.3 − 8.53 = 14.77 mm
- Step 3 — Cylinder volume: \( \pi \times 4.265^2 \times 14.77 = \pi \times 18.19 \times 14.77 \approx 845.31 \) mm³
- Step 4 — Sphere volume (caps): \( \dfrac{4}{3}\pi \times 4.265^3 = \dfrac{4}{3}\pi \times 77.46 \approx 324.75 \) mm³
- Step 5 — Total volume: \( V \approx 845.31 + 324.75 = 1{,}170.06 \) mm³ ≈ 1.17 mL
Example 3 — Pressure Vessel (Engineering)
A cylindrical pressure vessel with hemispherical end-caps has a radius of 0.8 m and a cylinder section length of 4 m. What is its total internal volume?
- Step 1 — Identify values: r = 0.8 m, h = 4 m
- Step 2 — Cylinder volume: \( \pi \times 0.64 \times 4 = 2.56\pi \approx 8.042 \) m³
- Step 3 — Sphere volume (caps): \( \dfrac{4}{3}\pi \times 0.512 = \dfrac{2.048\pi}{3} \approx 2.145 \) m³
- Step 4 — Total volume: \( V \approx 8.042 + 2.145 = 10.187 \) m³ ≈ 10,187 liters
- Step 5 — Surface area: \( SA = 2\pi \times 0.8 \times (1.6 + 4) = 2\pi \times 0.8 \times 5.6 = 8.96\pi \approx 28.15 \) m²
Example 4 — Capsule vs. Sphere (Comparison)
Compare the volume of a capsule with r = 4 cm and h = 6 cm against a sphere of the same radius.
- Step 1 — Capsule volume: \( V_{cap} = \pi \times 16 \times 6 + \dfrac{4}{3}\pi \times 64 = 96\pi + \dfrac{256\pi}{3} = \dfrac{288\pi + 256\pi}{3} = \dfrac{544\pi}{3} \approx 569.39 \) cm³
- Step 2 — Sphere volume (same radius): \( V_{sph} = \dfrac{4}{3}\pi \times 64 = \dfrac{256\pi}{3} \approx 268.08 \) cm³
- Step 3 — Extra volume from cylinder: \( 569.39 - 268.08 = 301.31 \) cm³ (the cylinder section adds 112.4% more volume!)
Example 5 — Capsule When h = 0 (Sphere Verification)
Verify that the capsule formula gives the sphere formula when h = 0, using r = 6 cm.
- Step 1 — Capsule volume with h = 0: \( V = \pi \times 36 \times 0 + \dfrac{4}{3}\pi \times 216 = 0 + \dfrac{4}{3}\pi \times 216 = \dfrac{864\pi}{3} = 288\pi \approx 904.78 \) cm³
- Step 2 — Sphere volume formula: \( V_{sph} = \dfrac{4}{3}\pi r^3 = \dfrac{4}{3}\pi \times 216 = 288\pi \approx 904.78 \) cm³ ✓
- Step 3 — Surface area with h = 0: \( SA = 2\pi \times 6 \times (12 + 0) = 2\pi \times 6 \times 12 = 144\pi \approx 452.39 \) cm²
- Step 4 — Sphere SA formula: \( 4\pi r^2 = 4\pi \times 36 = 144\pi \approx 452.39 \) cm² ✓
🔄 Reverse Calculations — Finding Radius or Height from Volume
Sometimes you know the desired volume and need to find the dimensions. Rearranging the capsule volume formula is less straightforward than for a cylinder, because the volume formula contains both \( r^2 \) and \( r^3 \) terms. Here are the practical reverse approaches.
Finding the Cylinder Height from Volume and Radius
Derivation: Start with \( V = \pi r^2 h + \dfrac{4}{3}\pi r^3 \). Subtract the spherical caps contribution: \( \pi r^2 h = V - \dfrac{4}{3}\pi r^3 \). Divide by \( \pi r^2 \): \( h = \dfrac{V - \dfrac{4}{3}\pi r^3}{\pi r^2} \).
Example: A capsule has V = 1,000 cm³ and r = 5 cm. Then: sphere contribution = \( \dfrac{4}{3}\pi \times 125 \approx 523.60 \) cm³. \( h = \dfrac{1{,}000 - 523.60}{\pi \times 25} = \dfrac{476.40}{78.54} \approx 6.07 \) cm.
Important constraint: This formula only gives valid (non-negative) results when \( V \geq \dfrac{4}{3}\pi r^3 \) — i.e., the target volume must be at least as large as the sphere formed by the two caps alone.
Finding the Radius (Numerical Approach)
Finding the radius from a known volume and height is more complex, because the equation \( \pi r^2 h + \dfrac{4}{3}\pi r^3 = V \) is a cubic in \( r \) and has no simple closed-form solution for general \( h \). The practical approach is:
This is a depressed cubic in \( r \) which can be solved using Cardano's formula or numerically. In practice, engineers use iterative methods (Newton–Raphson) or look-up tables. For the special case \( h = 0 \) (sphere), it simplifies to \( r = \left(\dfrac{3V}{4\pi}\right)^{1/3} \). Our online calculator starts from radius and height as inputs — enter known values to find volume and surface area, then adjust the radius until you reach your target volume.
📏 Unit Conversions for Capsule Volume
Capsule volumes span an enormous range — from sub-millimeter pharmaceutical capsules measured in microliters to multi-meter industrial vessels measured in kiloliters. The table below provides the key unit conversions.
| Volume Unit | Equivalent in cm³ | Equivalent in mL | Common Capsule Use |
|---|---|---|---|
| 1 mm³ | 0.001 cm³ | 0.001 mL | Micro-capsules, drug delivery beads |
| 1 cm³ | 1 cm³ | 1 mL | Pharmaceutical capsules (size 0–5) |
| 1 mL | 1 cm³ | 1 mL | Equivalent: 1 cm³ = 1 mL exactly |
| 1 in³ | 16.387 cm³ | 16.39 mL | Small industrial capsule vessels |
| 1 L (liter) | 1,000 cm³ | 1,000 mL | Medium pressure vessels, containers |
| 1 ft³ | 28,316.8 cm³ | 28,317 mL | Large pressure tanks, submarine sections |
| 1 m³ | 1,000,000 cm³ | 1,000,000 mL | Industrial pressure vessels, tanks |
🌍 Real-World Applications of Capsule Volume
The capsule shape appears in more engineering and scientific contexts than most people realize. Its combination of structural efficiency, smooth aerodynamics, and ease of manufacture makes it a default choice across multiple industries.
Pharmaceutical Manufacturing
The most immediately recognizable application is the pharmaceutical capsule — the hard-gel or soft-gel pill taken with medicine. Pharmacists and drug manufacturers must calculate capsule volume precisely to: (a) determine how much active drug powder or liquid fits inside; (b) ensure consistent dosing across millions of units; and (c) select the correct capsule size based on the dose required. The capsule geometry formula \( V = \pi r^2 h + \frac{4}{3}\pi r^3 \) is baked into pharmaceutical formulation software that every drug company uses daily.
Hard-gel capsules are manufactured in standardized sizes (000 through 5), each with a precise radius and total length. Knowing the geometry is essential for regulatory submissions to bodies like the FDA, where dosing accuracy is a legal requirement, not merely a preference.
Aerospace and Pressure Vessel Engineering
Rocket fuel tanks, spacecraft re-entry capsules, and submarine pressure hulls all use the capsule geometry. The hemispherical ends are structurally superior to flat ends because they distribute internal pressure uniformly across the surface, avoiding stress concentrations. A flat-ended cylinder under internal pressure will fail at the flat caps first; a hemispherical-ended capsule can withstand significantly higher pressure for the same wall thickness and material.
The NASA Orion crew module, the SpaceX Dragon capsule, and virtually all pressure vessels in chemical plants and submarines use this exact geometry. Engineers calculate both volume (for capacity planning) and surface area (for structural analysis and coating material estimation) using the capsule formulas.
Architecture and Futuristic Design
Nakagin Capsule Tower in Tokyo (1972, architect Kisho Kurokawa) famously used modular living capsules — rectangular but inspired by the capsule concept. Contemporary architects designing pods, tiny homes, and modular habitats frequently use capsule geometry because it minimizes surface area (and therefore construction material and heat loss) for a given interior volume. The capsule maximizes spatial efficiency and structural integrity simultaneously.
Biology and Medicine
Many biological structures are approximately capsule-shaped. Bacterial cells of the genus Bacillus and Lactobacillus are roughly capsule-shaped (spherocylindrical). Microbiologists use the capsule volume formula to estimate cell biomass and nutrient uptake rates. In medicine, MRI capsule endoscopes — swallowable camera pills that image the digestive tract — are precisely manufactured capsule-shaped devices whose internal volume determines battery life, camera resolution, and wireless antenna size.
Engineering: Hydraulic Cylinders and Actuators
Industrial hydraulic cylinders often have hemispherical end-caps to withstand hydraulic pressures of hundreds of bar. The volume of hydraulic fluid the cylinder can contain directly determines the force and stroke of the actuator. Mechanical engineers calculate both the swept volume (only the cylinder section, as the hemispherical portions don't contribute to the working stroke) and the total fluid volume (the full capsule) for hydraulic system design.
Sports Science: Rugby and American Football
A rugby ball and an American football are both close approximations to a prolate spheroid, but the capsule is a simpler model that many sports scientists use for first-order volume and aerodynamic calculations. The airflow around a capsule-shaped projectile is well-studied, making capsule geometry a useful idealization for spiral trajectory analysis.
⚖️ Capsule vs. Cylinder vs. Sphere — Volume & Surface Area Comparison
How does a capsule compare to the shapes it is built from? This comparison clarifies precisely what the hemispherical caps "add" and why the capsule is the shape of choice for so many pressure and containment applications.
For all shapes, we use r = 5 cm and h = 10 cm (the cylinder section height):
| Shape | Volume Formula | Volume (r=5, h=10) | Surface Area Formula | Surface Area (r=5, h=10) |
|---|---|---|---|---|
| Cylinder only | \( \pi r^2 h \) | \( 250\pi \approx 785.40 \) cm³ | \( 2\pi r(r+h) \) | \( 150\pi \approx 471.24 \) cm² |
| Sphere (r=5) | \( \frac{4}{3}\pi r^3 \) | \( \frac{500\pi}{3} \approx 523.60 \) cm³ | \( 4\pi r^2 \) | \( 100\pi \approx 314.16 \) cm² |
| Capsule (r=5, h=10) | \( \pi r^2 h + \frac{4}{3}\pi r^3 \) | \( \frac{1{,}250\pi}{3} \approx 1{,}309.00 \) cm³ | \( 2\pi r(2r+h) \) | \( 200\pi \approx 628.32 \) cm² |
Notice an elegant relationship: the capsule's volume equals the cylinder's volume plus the sphere's volume when all three share the same radius and the cylinder and capsule share the same cylindrical section height:
The capsule is literally a cylinder with a sphere attached — its volume is the exact sum of the two component volumes. Similarly, the capsule's surface area equals the cylinder's lateral surface area (not total — there are no flat end caps on a capsule) plus the sphere's full surface area: \( SA_{capsule} = 2\pi rh + 4\pi r^2 \).
⚠️ Common Mistakes to Avoid When Calculating Capsule Volume
Capsule calculations are straightforward once you understand the geometry, but the same mistakes appear repeatedly. Knowing these pitfalls will help you avoid incorrect answers on exams and in professional settings.
- Confusing Total Length with Cylinder Height: The most common error by far. The formula uses \( h \) = height of the cylindrical middle section, NOT the complete end-to-end length of the capsule. If you're given total length \( L \), calculate \( h = L - 2r \) before substituting. Entering \( L \) as \( h \) overstates volume by \( \frac{2}{3}\pi r^3 \).
- Using "r" When You Know the Diameter: Like all circular-cross-section formulas, the capsule formula uses the radius, not the diameter. Divide the given diameter by 2 first: \( r = d / 2 \). Entering the diameter instead of radius overstates volume by a factor of 4 (from \( r^2 \)) to 8 (from \( r^3 \)).
- Adding Two Hemisphere Volumes Instead of One Sphere: Two hemispheres of radius \( r \) together form exactly one sphere of radius \( r \). Their combined volume is \( \frac{4}{3}\pi r^3 \) — not \( 2 \times \frac{2}{3}\pi r^3 \), which equals the same thing. Either approach works, but some students add \( \frac{2}{3}\pi r^3 + \frac{2}{3}\pi r^3 \) correctly while others write \( \frac{2}{3}\pi r^3 \) once, forgetting the second hemisphere.
- Including Flat Circular Faces in Surface Area: A capsule has no flat faces. Do not add \( 2\pi r^2 \) (two circular bases) the way you would for a cylinder's total surface area. The hemispherical caps entirely replace and cover the circular ends. The surface area formula \( SA = 2\pi r(2r + h) = 4\pi r^2 + 2\pi rh \) correctly includes the spherical caps' area as \( 4\pi r^2 \), not as flat circles.
- Forgetting to Square/Cube the Radius Correctly: The volume formula has both \( r^2 \) (in the cylinder part) and \( r^3 \) (in the sphere part). Applying the wrong exponent to either term is a frequent arithmetic error. Always compute \( r^2 \) and \( r^3 \) separately before multiplying.
- Applying the Capsule Formula to an Oblique or Non-Circular Shape: The formula \( V = \pi r^2 h + \frac{4}{3}\pi r^3 \) applies to a right circular capsule — one where the cylinder axis is perpendicular to the circular cross-sections and both caps are true hemispheres of the same radius. For elliptic capsules (with elliptical cross-sections), different formulas apply.
📋 Quick Reference Formula Table
All capsule formulas in one place — bookmark or screenshot for quick access.
| Quantity | Formula | r = 3 cm, h = 6 cm | r = 5 cm, h = 12 cm |
|---|---|---|---|
| Radius | \( r \) | 3 cm | 5 cm |
| Cylinder Height | \( h \) | 6 cm | 12 cm |
| Diameter | \( d = 2r \) | 6 cm | 10 cm |
| Total Length | \( L = h + 2r \) | 12 cm | 22 cm |
| Volume | \( \pi r^2 h + \tfrac{4}{3}\pi r^3 \) | \( 54\pi + 36\pi = 90\pi \approx 282.74 \) cm³ | \( 300\pi + \tfrac{500\pi}{3} \approx 1{,}466.08 \) cm³ |
| Surface Area | \( 2\pi r(2r+h) \) | \( 2\pi \times 3 \times 12 = 72\pi \approx 226.19 \) cm² | \( 2\pi \times 5 \times 22 = 220\pi \approx 691.15 \) cm² |
| Height from Volume | \( h = \dfrac{V - \tfrac{4}{3}\pi r^3}{\pi r^2} \) | Use when V and r are known; h must be ≥ 0 | |
❓ Frequently Asked Questions (FAQ)
Complete answers to the most searched questions about capsule volume, surface area, and geometry.
