capsule volume calculator
A capsule volume calculator adds a cylinder (πr² × length) to one sphere (4/3πr³). A 2 ft wide capsule with a 6 ft straight body holds 23.04 ft³, or 172 gal.
Capsule volume calculator: the formula
This capsule volume calculator treats the shape as a cylinder plus two half-sphere end caps. The two caps together make one full sphere, so V = π × r² × straight length + (4/3) × π × r³. Enter the diameter and the straight length in feet, and the calculator returns cubic feet, cubic yards (÷ 27), gallons (× 7.48052), and liters.
The shape turns up in horizontal propane tanks, pressure vessels, some septic and water tanks, and pills or rounded storage bins.
How the formula is built
Picture slicing the domes off each end. What remains is a plain cylinder whose volume is the circle area, π × r², times its length.
Now push the two domes together. Each is half a sphere of the same radius, so together they form one ball of volume (4/3) × π × r³.
Add the two pieces and you have the capsule. Nothing is double-counted because the domes meet the cylinder exactly at its flat ends.
Worked examples
- The default: 2 ft diameter, 6 ft straight length
- Radius: 2 ÷ 2 = 1 ft
- Cylinder: π × 1² × 6 = 18.85 ft³
- Sphere (both domes): 4/3 × π × 1³ = 4.19 ft³
- Total: 23.04 ft³
- Cubic yards: 23.04 ÷ 27 = 0.853 yd³
- Gallons: 23.04 × 7.48052 = 172.3 gal, or 652.4 L
- A propane-style tank, 37.5 in across and 120 in overall
- Diameter: 37.5 ÷ 12 = 3.125 ft, radius 1.5625 ft
- Straight length: (120 − 37.5) ÷ 12 = 6.875 ft
- Cylinder: π × 1.5625² × 6.875 = 52.73 ft³
- Domes: 4/3 × π × 1.5625³ = 15.98 ft³
- Total: 68.71 ft³, or 514.0 gal
Tanks are normally filled to only about 80% for vapor space, so the usable liquid in a tank like this is noticeably less than its full volume. Check the tank’s data plate for its rated water capacity.
Capsule volume reference
| Diameter | Straight length | Cubic feet | Gallons |
|---|---|---|---|
| 1 ft | 4 ft | 3.67 | 27.4 |
| 2 ft | 6 ft | 23.04 | 172.3 |
| 3 ft | 8 ft | 70.69 | 528.8 |
| 4 ft | 10 ft | 159.17 | 1,190.7 |
Capsule vs cylinder vs sphere
| Shape | Formula | 2 ft wide, 6 ft body |
|---|---|---|
| Flat-ended cylinder | π r² a | 18.85 ft³ |
| Capsule | π r² a + 4/3 π r³ | 23.04 ft³ |
| Sphere alone | 4/3 π r³ | 4.19 ft³ |
The domes add 22% to the flat cylinder here. On a long, skinny tank the domes matter less; on a short, wide one they matter more.
How to measure a capsule
- Diameter: measure across the widest part of the round body. If you can only reach around it, measure the circumference and divide by π (3.1416).
- Overall length: tip to tip, including both domes.
- Straight length: overall length minus the diameter, if the domes are true half-spheres.
- Units: the inputs are in feet. Convert inches by dividing by 12, so 37.5 in becomes 3.125 ft.
Common mistakes
- Entering overall length as straight length. That counts the domes twice and inflates the answer. In example 2 it would add another 15.98 ft³, about 120 gallons.
- Using radius in the diameter box. Halving the diameter by mistake cuts the cylinder volume to a quarter and the dome volume to an eighth.
- Assuming dished heads are hemispheres. Shallow heads hold less. For those, a cylinder volume calculator on the overall length gives a closer estimate than a capsule would.
- Reading a gauge as a straight fraction. A horizontal tank filled to half its height holds half its volume, but at other heights the share is not proportional, because the tank is narrow at the top and bottom. A gauge reading in percent of volume already accounts for that; a dipstick reading in inches does not. For upright cylinders, the tank volume calculator handles fill percentage.
To convert the result to other units, see the cubic feet to gallons calculator. For a ball-shaped tank, use the sphere volume calculator.
Frequently asked questions
What shape is a capsule in this calculator?
A straight cylinder with a half-sphere dome on each end, like a pill or a stadium shape spun around its long axis. Two half-spheres of the same diameter make one whole sphere, which is why the formula adds a single sphere to the cylinder.
What is the formula for capsule volume?
V = π × r² × a + (4/3) × π × r³, where r is the radius and a is the length of the straight middle section only. For a 2 ft diameter and 6 ft straight length, that is 18.85 + 4.19 = 23.04 cubic feet.
What is 'straight length' and how do I get it from the overall length?
Straight length is the cylindrical middle section, not counting the domes. For a true capsule, each dome sticks out by one radius, so the domes add one full diameter in total. Straight length = overall length − diameter. A tank 10 ft overall and 3 ft wide has a 7 ft straight section.
How many gallons are in a capsule-shaped tank?
Multiply cubic feet by 7.48052. A tank about 37.5 inches across and 120 inches overall, a size often quoted for a 500 gallon propane tank, works out to 68.7 cubic feet, or about 514 gallons if its ends were perfect half-spheres.
Are all round-ended tanks true capsules?
No. Many tanks use flatter ellipsoidal or dished heads that bulge out less than a full half-sphere. Treating those as capsules overstates volume a little. For a closer figure, measure how far each head actually protrudes, or use the maker's rated capacity.
Why does the diameter matter so much?
The cylinder part grows with radius squared and the domes grow with radius cubed. Doubling the diameter of a capsule while keeping the same straight length roughly quadruples the cylinder volume and multiplies the end volume by eight.
Estimates only. Verify quantities with your supplier before purchasing.