Answer first
What this calculator tells you
Calculate the volume and surface area of a capsule from its radius and straight length. Size a pill-shaped tank, a pressure vessel or a capsule-shaped container. Formula: Volume = π × r² × L + 4⁄3 × π × r³; surface area = 2 × π × r × L + 4 × π × r², with L the straight cylinder section. At the worked-example inputs, the volume is 339.3. Holding every other input steady, moving radius (r) from 2.4 to 3.6 moves the result from 202.7 to 521.2.
Transparent method
The formula
Size a pill-shaped tank, a pressure vessel or a capsule-shaped container.
Worked example
Example inputs
How to interpret the result
A capsule is a cylinder capped by two half-spheres, so its volume is a cylinder plus one full sphere. With a radius of 3 and a straight section 8 long, the cylinder holds about 226 and the two ends together about 113, for roughly 339 cubic units. The surface is the same story: the cylinder wall plus the surface of one sphere, about 264 square units.
At the worked-example inputs the volume is 339.3. It rises with radius (r) and cylinder length (l).
Formulas assume ideal geometric shapes. Real-world measurements carry their own error, and every input must use the same unit: mixing feet and inches silently produces a wrong answer.
Before you rely on it
What to check
Enter only the straight length. The rounded ends are already counted, so adding them to the length double counts about two radii at each end.
The common error
Where people go wrong with capsule volume calculator
Measuring the overall length and using it as the cylinder length. The overall length includes both caps, which makes the volume larger than the real one.
Sensitivity evidence
How radius (r) changes the volume
Holding every other input at the worked-example value, moving radius (r) from 2.4 to 3.6 moves the volume from 202.7 to 521.2: a spread of 318.5, or 94% of the worked-example result.
| Radius (r) | Volume | Surface area |
|---|---|---|
| 2.4 | 202.7 | 193 |
| 2.7 | 265.7 | 227.3 |
| 3worked example | 339.3 | 263.9 |
| 3.3 | 424.2 | 302.7 |
| 3.6 | 521.2 | 343.8 |
Every input, tested
Which input moves the volume most
Of the 2 inputs, radius (r) moves the volume most (158.6 across the range tested) and cylinder length (l) moves it least (56.5).
| Input | Tested from | To | Volume at each end | Swing |
|---|---|---|---|---|
| Radius (r) | 2.7 | 3.3 | 265.7 to 424.2 | 158.6 (47%) |
| Cylinder length (L) | 7 | 9 | 311 to 367.6 | 56.5 (17%) |
Two variables at once
Volume by radius (r) and cylinder length (l)
Across the grid the volume runs from 166.5 to 602.6. Moving radius (r) from 2.4 to 3.6 shifts it by 318.5 at the middle column, and moving cylinder length (l) from 6 to 10 shifts it by 113.1 at the middle row, so radius (r) is the bigger lever here.
| Radius (r) \ Cylinder length (L) | 6 | 8 | 10 |
|---|---|---|---|
| 2.4 | 166.5 | 202.7 | 238.9 |
| 2.7 | 219.9 | 265.7 | 311.5 |
| 3 | 282.7 | 339.3 | 395.8 |
| 3.3 | 355.8 | 424.2 | 492.7 |
| 3.6 | 439.7 | 521.2 | 602.6 |
The highlighted cell is the worked example: 339.3.
Step by step
The worked example, input by input
| Input | Value used | What it means |
|---|---|---|
| Radius (r) | 3 | Enter the radius (r) used in this calculation. |
| Cylinder length (L) | 8 | The straight part only, without the two rounded ends. |
| Volume | 339.3 | |
| Surface area | 263.9 | |
Inputs, definitions and assumptions
Radius (r)
Enter the radius (r) used in this calculation. The prefilled worked-example value is 3.
Cylinder length (L)
The straight part only, without the two rounded ends. The prefilled worked-example value is 8.
How to use this calculator
- 1Verify the inputs. Gather radius (r) and cylinder length (l) from your own documents; the prefilled values are examples.
- 2Save a baseline. The worked example puts the volume at 339.3. Store your own version of it as Scenario A.
- 3Test one change. Start with radius (r), the input with the biggest effect here: moving radius (r) from 2.7 to 3.3 takes the volume from 265.7 to 424.2, a swing of 47% of the worked-example figure.
- 4Check the extremes. At half the example radius (r) (1.5) the volume is 70.7; at double (6) it is 1,809.6.
People also ask
Frequently asked questions
How do you calculate capsule volume?
Volume = π × r² × L + 4⁄3 × π × r³; surface area = 2 × π × r × L + 4 × π × r², with L the straight cylinder section. At the worked-example inputs the volume is 339.3.
What does the capsule volume result mean?
Size a pill-shaped tank, a pressure vessel or a capsule-shaped container. At the worked-example inputs the volume is 339.3. It rises with radius (r) and cylinder length (l).
How much does radius (r) change the volume?
Holding every other input at the worked-example value, moving radius (r) from 2.4 to 3.6 moves the volume from 202.7 to 521.2, a spread of 318.5.
What are the limits of this capsule volume calculator?
Formulas assume ideal geometric shapes. Real-world measurements carry their own error, and every input must use the same unit: mixing feet and inches silently produces a wrong answer. The tables on this page test radius (r) only from 2.4 to 3.6; a value outside that range is not tabulated here.
Which input moves the volume most in the capsule volume calculator?
Ranked by how far each moves the volume across the range tested: radius (r) (158.6, 47%) and cylinder length (l) (56.5, 17%).
If I double radius (r) in the capsule volume calculator, does the volume double?
Doubling it from 3 to 6 takes the volume from 339.3 to 1,809.6, which is 5.33 times the worked-example figure. So the result grows faster than the input does. Halving it to 1.5 gives 70.7.
How much does cylinder length (l) matter in the capsule volume calculator?
The worked example uses 8. Holding every other input at its worked-example value, moving cylinder length (l) from 7 to 9 takes the volume from 311 to 367.6, a swing of 17% of the worked-example figure.
Which inputs change the surface area in the capsule volume calculator?
At the worked-example inputs it is 263.9. Radius (r) takes it from 227.3 to 302.7 and cylinder length (l) takes it from 245 to 282.7.
Do degrees and radians measure the same thing?
Yes, both measure angle. A full turn is 360 degrees or 2 pi radians. Trigonometric functions in most programs expect radians, while drawings and maps use degrees.
Sources and evidence
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