On This Page
- How to use the Capsule Volume Calculator
- Capsule volume formula
- How to calculate capsule volume
- Total length vs. cylinder height
- Capsule tank volume
- Worked examples
- Capsule volume units, liters, and gallons
- Frequently asked questions
How to Use the Capsule Volume Calculator
Use this capsule volume calculator for a capsule-shaped solid or tank when you know the radius and the straight cylinder height. The page shows cylinder volume, rounded-end volume, total length, surface area, liters, gallons, cubic feet, and calculation steps.
Use it for capsule tanks, rounded pressure vessels, pill-shaped containers, geometry homework, and any shape made from a cylinder with one hemisphere on each end.
Capsule Volume Formula
A capsule is a cylinder plus two hemispheres. Since two hemispheres make one sphere, the total volume is cylinder volume plus sphere volume.
- V = capsule volume
- r = radius of the cylinder and rounded ends
- h = cylinder height, the straight section between the rounded ends
The first part, πr²h, calculates the middle cylinder. The second part, (4/3)πr³, calculates the two rounded ends together.
How to Calculate Capsule Volume
To calculate capsule volume by hand, split the shape into two familiar parts: a cylinder and a sphere. Both parts use the same radius.
Step 1: Find the Radius
The radius is half the diameter. If the problem gives diameter, divide it by 2 first.
Step 2: Find the Cylinder Height
Cylinder height is only the straight middle length. It excludes both rounded ends.
Step 3: Calculate the Cylinder Volume
Use πr²h for the straight middle section.
Step 4: Calculate the Rounded-End Volume
Use (4/3)πr³ for the two hemispheres together.
Step 5: Add Both Parts
Add the cylinder volume and rounded-end volume. Write the answer in cubic units.
- Find radius: r
- Find cylinder height: h
- Calculate cylinder volume: πr²h
- Calculate rounded ends: (4/3)πr³
- Add both volumes
Total Length vs. Cylinder Height
Capsule problems often give total length instead of cylinder height. Total length includes the straight cylinder section plus two radii at the rounded ends.
For example, if total length is 24 cm and radius is 4 cm, then cylinder height is 24 - 8 = 16 cm.
Capsule Tank Volume
A capsule tank volume calculator is useful for full-capacity estimates of rounded storage tanks. Horizontal capsule tank volume and vertical capsule tank volume use the same full-volume formula.
Orientation matters when the tank is partly filled. A horizontal capsule tank with liquid depth needs a partial-fill method, because the liquid surface cuts through the rounded ends. The tool above gives the full tank capacity.
Worked Capsule Volume Examples
In capsule problems, the key is separating the straight middle from the rounded ends. Watch whether the problem gives radius, diameter, cylinder height, or total length.
Example 1: Capsule Volume From Radius and Cylinder Height
Problem: A capsule-shaped solid has radius 3 cm and cylinder height 10 cm. Find the total volume. Use 3.14159 for π.
- Radius = 3 cm, cylinder height = 10 cm
- Cylinder volume = π × 3² × 10 = 282.74 cm³
- Rounded-end volume = (4/3)π × 3³ = 113.10 cm³
- Total volume = 282.74 + 113.10 = 395.84 cm³
Answer: The capsule volume is about 395.8 cm³.
Example 2: Capsule Volume From Total Length
Problem: A pill-shaped container is 24 cm long from end to end and has radius 4 cm. Find its volume.
- Cylinder height = 24 - (2 × 4) = 16 cm
- Cylinder volume = π × 4² × 16 = 804.25 cm³
- Rounded-end volume = (4/3)π × 4³ = 268.08 cm³
- Total volume = 1,072.33 cm³
Answer: The capsule volume is about 1,072.3 cm³.
Example 3: Horizontal Capsule Tank Capacity in Liters
Problem: A horizontal capsule tank has radius 0.6 m and straight cylinder length 2.8 m. Estimate its full capacity in liters.
- Cylinder volume = π × 0.6² × 2.8 = 3.167 m³
- Rounded-end volume = (4/3)π × 0.6³ = 0.905 m³
- Total volume = 3.167 + 0.905 = 4.072 m³
- Liters = 4.072 × 1,000 = 4,072 L
Answer: The tank holds about 4,072 liters when full.
Example 4: Diameter Given Instead of Radius
Problem: A capsule has diameter 8 inches and cylinder height 14 inches. Find the volume.
- Radius = 8 ÷ 2 = 4 in
- Cylinder volume = π × 4² × 14 = 703.72 in³
- Rounded-end volume = (4/3)π × 4³ = 268.08 in³
- Total volume = 971.80 in³
Answer: The capsule volume is about 971.8 cubic inches.
Example 5: Vertical Capsule Tank Full Capacity
Problem: A vertical capsule tank has radius 1.2 ft and cylinder height 5 ft. Estimate the full volume in cubic feet.
- Cylinder volume = π × 1.2² × 5 = 22.62 ft³
- Rounded-end volume = (4/3)π × 1.2³ = 7.24 ft³
- Total volume = 22.62 + 7.24 = 29.86 ft³
Answer: The vertical capsule tank holds about 29.9 ft³ when full.
Capsule Volume Units, Liters, and Gallons
Capsule volume is written in cubic units. For tanks and containers, cubic volume is often converted to liters or gallons.
| Input Unit | Volume Unit | Useful Conversion |
|---|---|---|
| Centimeters | cm³ | 1,000 cm³ = 1 liter |
| Meters | m³ | 1 m³ = 1,000 liters |
| Inches | in³ | 231 in³ = 1 US gallon |
| Feet | ft³ | 1 ft³ ≈ 7.48052 US gallons |
Capsule Volume Mistakes to Avoid
- Entering total length as cylinder height: Subtract 2r first if the problem gives full capsule length.
- Using diameter as radius: Divide diameter by 2 before calculating.
- Forgetting the rounded ends: A capsule is not just a cylinder.
- Using partial-fill assumptions: Full capsule tank volume is simpler than horizontal partial liquid volume.
Frequently Asked Questions
How do you calculate capsule volume?
Use V = πr²h + (4/3)πr³. Calculate the cylinder volume, calculate the two rounded ends as one sphere, then add them.
What is a capsule tank volume calculator?
It is a calculator for rounded-end tanks shaped like a cylinder with hemispheres on both ends. It estimates full tank capacity from radius and cylinder height.
Is horizontal capsule tank volume different from vertical capsule tank volume?
Full volume is the same. Orientation only matters for partial fill levels.
How do I calculate capsule volume from total length?
First find cylinder height with h = total length - 2r, then use the capsule volume formula.
What is the difference between capsule height and total length?
In this calculator, height means the straight cylinder section. Total length includes the cylinder plus both rounded ends.