Enter the radius and the height of the cylinder part of the capsule. You get the volume (V = πr²h + 4/3πr³), its breakdown into the cylinder part and the sphere part, and the volume in cm³, L and m³.
Enter the radius and the height in the same unit, as numbers only (no units. For example, for 3 cm enter "3"). The "height" does not include the hemisphere ends. If you only know the total length of the capsule, enter the total length minus twice the radius as the height.
Result and figure
Enter the radius and the height of the cylinder part in the fields on the left and press "Calculate". The result will appear here.
Table of Contents
-
What you can do on this page
-
What is this calculation used for?
-
How to Use
-
Formulas and figures
-
The idea behind the volume of a capsule (split into a cylinder and a sphere, then add)
-
Volume of the cylinder part (basic formula 1)
-
Volume of the sphere made by the two ends (basic formula 2)
-
Volume of a capsule in one formula
-
Converting volume units (in³ → gallons)
-
Converting volume units (in³ → ft³)
-
-
Symbols and terms
-
Good to know before you start
-
How to calculate it in Excel
-
How to calculate it in Google Sheets
-
How to calculate it in Python
-
How to write it in LaTeX and other math languages (copy and paste)
-
How to have ChatGPT do the calculation
-
DataChef Features
-
Related Features
-
NumberChef Calculators List
What you can do on this page
- Enter the radius and the height of the cylinder part, and you get the volume of a capsule (a cylinder with a hemisphere on each end) on the spot (\(V = \pi r^2 h + \dfrac{4}{3}\pi r^3\))
- It also shows the volume of the cylinder part and of the sphere made by the two hemisphere ends separately, so you can see how the calculation works
- The result is also shown as a 3D shape that you can turn with your mouse or by swiping
- Volume unit conversions are shown too: gallons and ft³ when you enter inches, and gallons when you enter feet. Switch "Units" to Metric to get liters and m³ instead
- A plain-language explanation of the formulas and copy-and-paste formulas for Excel, Google Sheets and Python are all on this page
Enter the radius and the height in the same unit (both in inches, or both in feet). The "height" is the length of the cylinder part only, not including the hemisphere ends. Plain cylinders and spheres have their own pages.
What is this calculation used for?
Estimating how much a medicine capsule holds (pharmaceuticals and medicine)
A medicine capsule is the classic example of this shape. Treat a capsule with a radius of 0.16 in and a cylinder height of 0.55 in as this shape, and it holds \(\pi \times 0.16^2 \times 0.55 + \dfrac{4}{3}\pi \times 0.16^3 \approx 0.061\,\mathrm{in^3}\), or about 1 mL.
A real capsule is made of two overlapping parts (the cap and the body), so this is only an estimate. Still, this formula is the basis for estimating how much medicine a capsule of a given size can hold.
Capacity of a propane storage tank (energy and infrastructure)
Pressure tanks for propane and other gases are often capsules lying on their side, a cylinder with rounded ends. A shape with corners concentrates pressure at the corners and breaks more easily, while a rounded shape spreads the pressure evenly.
A typical 500-gallon home propane tank is about 37.5 in across and 120 in long. With a radius of 18.75 in, the cylinder part is \(120 - 37.5 = 82.5\) in, so the capacity is \(\pi \times 18.75^2 \times 82.5 + \dfrac{4}{3}\pi \times 18.75^3 \approx 118{,}730\,\mathrm{in^3}\), about 514 gallons. Finding how much a tank holds from its dimensions is a job for this formula in both design and inspection.
Estimating the load of a tank truck (logistics)
The tank of a truck that carries fuel is also close to a capsule: a cylinder with rounded end caps (called heads). Treat the heads as hemispheres, with a radius of 3.75 ft and a cylinder part of 22 ft, and you get \(\pi \times 3.75^2 \times 22 + \dfrac{4}{3}\pi \times 3.75^3 \approx 1{,}193\,\mathrm{ft^3}\), or about 8,900 gallons (× 7.48).
Real heads are usually shallower than a hemisphere, so the exact capacity depends on the drawings. Still, this is a good estimate in the same range as a large fuel tank truck (around 9,000 gallons).
Estimating the amount of stick-shaped foods such as hot dogs (food)
Stick-shaped foods with rounded ends, such as hot dogs, can be treated as capsules. For a hot dog 0.9 in across (radius 0.45 in) and 6 in long, the cylinder part is \(6 - 0.9 = 5.1\) in, and the volume is \(\pi \times 0.45^2 \times 5.1 + \dfrac{4}{3}\pi \times 0.45^3 \approx 3.6\,\mathrm{in^3}\) (about 59 mL).
Many foods have a density close to that of water (1 in³ of water weighs about 0.58 oz), so it weighs about 2.1 oz. That matches a real pack of 8 hot dogs per pound, which is 2 oz each. Estimating weight or calories from volume works both in food development and at home.
Formulas and figures
The idea behind the volume of a capsule (split into a cylinder and a sphere, then add)
Figure
Standard notation
(the usual math form)
\(V\)
\(=\)
\(V_1\)
\(+\)
\(V_2\)
In words
(symbols replaced with words)
③
\(V\): volume of the capsule
\(=\)
①
\(V_1\): volume of the cylinder part
\(+\)
②
\(V_2\): volume of the two hemispheres
The formula in words
①
Add the
\(V_1\): volume of the cylinder part
②
and the
\(V_2\): volume of the two hemispheres
(= one whole sphere made by the two ends)
③
and you get the
\(V\): volume of the capsule
Quick example
For a capsule with a radius of 3 in and a cylinder height of 4 in (worked out with basic formulas 1 and 2 below)
\(V\): volume of the capsule
\(=\)
cylinder part (36π in³)
\(+\)
sphere (36π in³)
\(36\pi + 36\pi = 72\pi \approx 226.19\,\mathrm{in^3}\)
Key idea
A capsule is a cylinder with a hemisphere (half of a sphere) on each end. The two hemispheres together make exactly one whole sphere, so the volume is just "one cylinder + one sphere".
Split a solid that looks complicated into shapes you already know (a cylinder and a sphere) and add them up. This is the most important idea on this page.
Volume of the cylinder part (basic formula 1)
Figure
Standard notation
(the usual math form)
\(V_1\)
\(=\)
\(\pi\)
\(\times\)
\(r\)
\(2\)
\(\times\)
\(h\)
In words
(symbols replaced with words)
⑤
\(V_1\): volume of the cylinder part
\(=\)
①
\(\pi\): pi
\(\times\)
②
\(r\): radius
③
squared (the number times itself)
\(\times\)
④
\(h\): height of the cylinder part
The formula in words
①
Take
\(\pi\): pi
②
multiply it by the
\(r\): radius
③
squared (the number times itself)
to get the area of the circular cross section
④
then multiply by the
\(h\): height of the cylinder part
⑤
and you get the
\(V_1\): volume of the cylinder part
Quick example
For a capsule with a radius of 3 in and a cylinder height of 4 in, the volume of the cylinder part is
\(V_1\): volume of the cylinder part
\(=\)
\(\pi\): pi
\(\times\)
radius (3 in)
squared
\(\times\)
cylinder height (4 in)
\(\pi \times 3^{2} \times 4 = 36\pi \approx 113.1\,\mathrm{in^3}\)
Key idea
The volume of a cylinder is "base area × height". The cross section of a capsule is a circle, so the base area is the area of a circle, \(\pi r^2\) (π × radius squared).
Note that the height \(h\) here is the length of the straight body only, not including the hemisphere ends. The Volume of a Cylinder Calculator page explains the cylinder formula in more detail.
Volume of the sphere made by the two ends (basic formula 2)
Figure
Standard notation
(the usual math form)
\(V_2\)
\(=\)
\(\dfrac{4}{3}\)
\(\times\)
\(\pi\)
\(\times\)
\(r\)
\(3\)
In words
(symbols replaced with words)
⑤
\(V_2\): volume of the sphere
\(=\)
①
\(\dfrac{4}{3}\): constant
\(\times\)
②
\(\pi\): pi
\(\times\)
③
\(r\): radius
④
cubed (the number used as a factor 3 times)
The formula in words
①
Take the
\(\dfrac{4}{3}\): constant
②
multiply it by
\(\pi\): pi
③
and by the
\(r\): radius
④
cubed (the number used as a factor 3 times)
⑤
and you get the
\(V_2\): volume of the sphere
Quick example
For a capsule with a radius of 3 in, the volume of the sphere made by the two hemisphere ends is
\(V_2\): volume of the sphere
\(=\)
\(\dfrac{4}{3}\): constant
\(\times\)
\(\pi\): pi
\(\times\)
radius (3 in)
cubed
\(\dfrac{4}{3} \times \pi \times 3^{3} = \dfrac{4}{3} \times \pi \times 27\)
\(= 36\pi \approx 113.1\,\mathrm{in^3}\)
Key idea
The radius of the hemisphere ends is the same as the radius \(r\) of the cylinder part. Two hemispheres make one sphere, so instead of working out "hemisphere volume × 2", you can use the sphere formula \(\dfrac{4}{3}\pi r^3\) just once.
\(\dfrac{4}{3}\) is the fixed coefficient (a constant) that always appears in the sphere formula. The Volume of a Sphere Calculator page explains the sphere formula in more detail.
Volume of a capsule in one formula
Figure
Standard notation
(the usual math form)
\(V\)
\(=\)
\(\pi\)
\(\times\)
\(r\)
\(2\)
\(\times\)
\(h\)
\(+\)
\(\dfrac{4}{3}\)
\(\times\)
\(\pi\)
\(\times\)
\(r\)
\(3\)
In words
(symbols replaced with words)
⑨
\(V\): volume of the capsule
\(=\)
①
\(\pi\): pi
\(\times\)
②
\(r\): radius
③
squared
\(\times\)
④
\(h\): height of the cylinder part
\(+\)
⑤
\(\dfrac{4}{3}\): constant
\(\times\)
⑥
\(\pi\): pi
\(\times\)
⑦
\(r\): radius
⑧
cubed
The formula in words
①
Take
\(\pi\): pi
②
multiply it by the
\(r\): radius
③
squared
④
and by the
\(h\): height of the cylinder part
to get the volume of the cylinder part.
⑤
Next, take the
\(\dfrac{4}{3}\): constant
⑥
multiply it by
\(\pi\): pi
⑦
and by the
\(r\): radius
⑧
cubed
to get the volume of the sphere made by the two hemisphere ends.
⑨
Add these two and you get the
\(V\): volume of the capsule
Quick example
Working out the volume of a capsule with a radius of 3 in and a cylinder height of 4 in all at once gives
\(V\): volume of the capsule
\(=\)
\(\pi\): pi
\(\times\)
radius (3 in)
squared
\(\times\)
cylinder height (4 in)
\(+\)
\(\dfrac{4}{3}\): constant
\(\times\)
\(\pi\): pi
\(\times\)
radius (3 in)
cubed
\(\pi \times 3^{2} \times 4 = 36\pi\)
\(\dfrac{4}{3} \times \pi \times 3^{3} = 36\pi\)
\(36\pi + 36\pi = 72\pi \approx 226.19\,\mathrm{in^3}\)
Key idea
This formula is the first one, "cylinder + sphere", with basic formula 1 (the cylinder part) and basic formula 2 (the sphere) put in. The first half (\(\pi r^2 h\)) is the cylinder part, and the second half (\(\dfrac{4}{3}\pi r^3\)) is the sphere made by the two hemisphere ends.
The exponents are easy to mix up. The radius is squared in the cylinder part and cubed in the sphere part, and the height \(h\) is multiplied only once. This calculator also shows the breakdown (cylinder part and sphere part), so you can check the values along the way.
Converting volume units (in³ → gallons)
Standard notation
(the usual math form)
\(V_{\mathrm{gal}}\)
\(=\)
\(V_{\mathrm{in^3}}\)
\(\div\)
\(231\)
In words
(symbols replaced with words)
③
\(V_{\mathrm{gal}}\): volume in gallons
\(=\)
①
\(V_{\mathrm{in^3}}\): volume in in³
\(\div\)
②
\(231\): cubic inches in 1 gallon
The formula in words
①
Take the
\(V_{\mathrm{in^3}}\): volume in in³
②
divide it by
\(231\): cubic inches in 1 gallon
③
and you get the
\(V_{\mathrm{gal}}\): volume in gallons
Quick example
The volume of the capsule with a radius of 3 in and a cylinder height of 4 in, about 226.19 in³, in gallons is
volume in gallons
\(=\)
volume in in³ (226.19)
\(\div\)
cubic inches in 1 gallon (231)
\(226.19 \div 231 \approx 0.979\,\mathrm{gal}\)
Key idea
One US gallon (a gallon jug of milk) is defined as exactly \(231\,\mathrm{in^3}\), so divide cubic inches by 231 to get gallons. The capsule above holds just under 1 gallon.
For smaller amounts, use fluid ounces: \(1\,\mathrm{gal} = 128\,\mathrm{fl\ oz}\), so \(1\,\mathrm{fl\ oz} \approx 1.80\,\mathrm{in^3}\). The capsule above is about \(0.979 \times 128 \approx 125\,\mathrm{fl\ oz}\).
Converting volume units (in³ → ft³)
Standard notation
(the usual math form)
\(V_{\mathrm{ft^3}}\)
\(=\)
\(V_{\mathrm{in^3}}\)
\(\div\)
\(1728\)
In words
(symbols replaced with words)
③
\(V_{\mathrm{ft^3}}\): volume in ft³
\(=\)
①
\(V_{\mathrm{in^3}}\): volume in in³
\(\div\)
②
\(1728\): cubic inches in 1 ft³
The formula in words
①
Take the
\(V_{\mathrm{in^3}}\): volume in in³
②
divide it by
\(1728\): cubic inches in 1 ft³
③
and you get the
\(V_{\mathrm{ft^3}}\): volume in ft³
Quick example
A capsule-shaped storage tank that holds 250 gallons has a volume of 57,750 in³. In cubic feet, that is
volume in ft³
\(=\)
volume in in³ (57,750)
\(\div\)
cubic inches in 1 ft³ (1728)
\(57750 \div 1728 \approx 33.4\,\mathrm{ft^3}\)
Key idea
The conversion factor for volume is the cube of the factor for length. Since \(1\,\mathrm{ft} = 12\,\mathrm{in}\), \(1\,\mathrm{ft^3}\) is \(12 \times 12 \times 12 = 1728\,\mathrm{in^3}\). It is not 12 times or 144 times but 1728 times, which is easy to get wrong.
To go back from ft³ to in³, multiply by 1728. The link with gallons is \(1\,\mathrm{ft^3} = 1728 \div 231 \approx 7.48\,\mathrm{gal}\).
The volume of a capsule is "cylinder part (πr²h) + the sphere made by the two hemisphere ends (4/3πr³)". Do not include the hemispheres in the height h, and do not mix up squared and cubed. The answer is in the cube of the unit you entered (in³ for inches).
Symbols and terms
Symbols
| \(V\) | vee | A common symbol for volume, from the first letter of "volume". On this page it is the volume of the whole capsule. |
| \(V_1\), \(V_2\) | V sub one, V sub two | When there are several quantities of the same kind (here, volumes), a small number at the lower right (a subscript) tells them apart. On this page, \(V_1\) is the volume of the cylinder part and \(V_2\) is the volume of the sphere made by the two hemisphere ends. |
| \(r\) | ar | The radius (the length from the center of a circle to its edge), from the first letter of "radius". In a capsule, the radius of the cylinder's cross section and the radius of the hemisphere ends are the same \(r\). It is half the diameter. |
| \(h\) | aitch | The height of the cylinder part (the length of the straight body, not including the hemisphere ends), from the first letter of "height". The total length of the capsule is \(h + 2r\). |
| \(\pi\) | pi | The Greek letter for the circumference ÷ diameter of a circle. It is \(3.14159\ldots\) and never ends. The 3.14 used in simple calculations is an approximation of it. |
| \(r^2\), \(r^3\) | r squared, r cubed | The small number at the upper right (the exponent) tells how many times the number is used as a factor: \(r^2 = r \times r\) and \(r^3 = r \times r \times r\). The cylinder part uses the square, and the sphere part uses the cube. |
| \(\dfrac{4}{3}\) | four thirds | The fixed coefficient (a constant) that always appears in the sphere formula. It is about 1.33, and it says that the volume of a sphere is \(\dfrac{4}{3}\) times "\(\pi\) times the radius cubed, \(r^3\)". |
| \(\mathrm{in^3}\) | cubic inch | A unit of volume. A cube 1 in on each side has a volume of 1 in³ (1 in³ ≈ 16.4 mL). |
| \(\mathrm{ft^3}\) | cubic foot | A unit of volume. A cube 1 ft on each side has a volume of 1 ft³. \(1\,\mathrm{ft^3} = 1728\,\mathrm{in^3} \approx 7.48\,\mathrm{gal}\). |
| \(\mathrm{gal}\) | gallon | A unit of volume (capacity), familiar from milk jugs and gas pumps. One US gallon is exactly \(231\,\mathrm{in^3}\), or \(128\,\mathrm{fl\ oz}\). |
Terms
| capsule | A solid made of a cylinder with a hemisphere on each end. You see this shape in medicine capsules and gas storage tanks. In video games and computer graphics, "capsule" shapes are also common, for example for collision detection. |
| hemisphere | A sphere cut exactly in half by a plane through its center. It is the rounded part on each end of a capsule. Two hemispheres together make one sphere. |
| cylinder | A straight solid with a circular base; slice it anywhere across and you get a circle of the same size. It is the body in the middle of a capsule. |
| sphere | A solid like a ball, made of all the points at the same distance from the center. Its volume is \(\dfrac{4}{3}\pi r^3\). |
| volume | The amount of space a solid takes up, given as a number. It is measured by how many unit cubes (such as 1 in³ cubes) would fill it. |
| pi | The number that tells how many times the circumference of a circle is its diameter. It is the same for a circle of any size and is written with the symbol \(\pi\) (about 3.14). |
| unit conversion | Writing the same amount in a different unit. For volume, the key is that the conversion factor is the cube of the length factor (1 ft = 12 in, so 1 ft³ = 1728 in³). |
Good to know before you start
Here is what helps you use the calculation on this page with real understanding, not just by pressing the button.
| Area of a circle (Grade 7) |
|
| What volume is and its units (Grade 5) |
|
| Volume of prisms and cylinders (Grade 8) |
|
| Volume of a sphere (Grade 8) |
|
| Pi and expressions with letters (Grades 6–7) |
|
| What exponents stand for (Grade 6) |
|
How to calculate it in Excel
Copy the whole table below and paste it into cell A1 in Excel. It works as is.
Table to add the cylinder and the sphere
| Cylinder part V1 (in³) | 113.1 |
| Sphere from the two ends V2 (in³) | 113.1 |
| Capsule volume (in³) | =B1+B2 |
Table to find the volume of the cylinder part
| Radius r (in) | 3 |
| Cylinder height h (in) | 4 |
| Cylinder part, πr²h (in³) | =PI()*B1^2*B2 |
Table to find the volume of the sphere from the two ends
| Radius r (in) | 3 |
| Sphere, 4/3πr³ (in³) | =4/3*PI()*B1^3 |
Table to find the capsule volume in one formula
| Radius r (in) | 3 |
| Cylinder height h (in) | 4 |
| Capsule volume (in³) | =PI()*B1^2*B2+4/3*PI()*B1^3 |
Table to convert in³ to gallons
| Volume in in³ | 226.19 |
| Volume in US gallons | =B1/231 |
Table to convert in³ to ft³
| Volume in in³ | 57750 |
| Volume in ft³ | =B1/1728 |
After pasting, column A holds the labels and column B holds the numbers. The upper rows are your inputs, and the formula in the last row calculates from them automatically.
In a formula, "PI()" is the Excel function that returns π (3.14159…), "B1" and "B2" tell the formula to use the number in that cell, "*" is multiplication, "/" is division and "^" raises to a power (how many times to multiply).
In the second table, for example, B3 shows about 113.097 (in in³, because the inputs are in inches). The third table shows about 113.097 in B2, and the fourth table shows about 226.195 in B3, which is almost the same as "cylinder part + sphere part" in B3 of the first table (226.2, because it adds values rounded to 113.1). The fifth table shows about 0.979 in B2, and the sixth table shows about 33.42 in B2. Just replace the input numbers with the size of your own capsule.
In a formula, "PI()" is the Excel function that returns π (3.14159…), "B1" and "B2" tell the formula to use the number in that cell, "*" is multiplication, "/" is division and "^" raises to a power (how many times to multiply).
In the second table, for example, B3 shows about 113.097 (in in³, because the inputs are in inches). The third table shows about 113.097 in B2, and the fourth table shows about 226.195 in B3, which is almost the same as "cylinder part + sphere part" in B3 of the first table (226.2, because it adds values rounded to 113.1). The fifth table shows about 0.979 in B2, and the sixth table shows about 33.42 in B2. Just replace the input numbers with the size of your own capsule.
How to calculate it in Google Sheets
Copy the whole table below and paste it into cell A1 in Google Sheets. It works as is.
Table to add the cylinder and the sphere
| Cylinder part V1 (in³) | 113.1 |
| Sphere from the two ends V2 (in³) | 113.1 |
| Capsule volume (in³) | =B1+B2 |
Table to find the volume of the cylinder part
| Radius r (in) | 3 |
| Cylinder height h (in) | 4 |
| Cylinder part, πr²h (in³) | =PI()*B1^2*B2 |
Table to find the volume of the sphere from the two ends
| Radius r (in) | 3 |
| Sphere, 4/3πr³ (in³) | =4/3*PI()*B1^3 |
Table to find the capsule volume in one formula
| Radius r (in) | 3 |
| Cylinder height h (in) | 4 |
| Capsule volume (in³) | =PI()*B1^2*B2+4/3*PI()*B1^3 |
Table to convert in³ to gallons
| Volume in in³ | 226.19 |
| Volume in US gallons | =B1/231 |
Table to convert in³ to ft³
| Volume in in³ | 57750 |
| Volume in ft³ | =B1/1728 |
The same formulas as in Excel (including the PI() function) work as is. Copy the whole table, paste it into cell A1, and replace the input numbers with the size of your own capsule.
How to calculate it in Python
import math
radius = 3 # radius (inches in this example)
height = 4 # height of the cylinder part (not including the hemisphere ends; same unit as the radius)
cylinder_volume = math.pi * radius ** 2 * height # volume of the cylinder part (pi r^2 h; in3 in this example)
sphere_volume = 4 / 3 * math.pi * radius ** 3 # volume of the sphere made by the two hemisphere ends (4/3 pi r^3)
volume = cylinder_volume + sphere_volume # capsule volume (cube of the input unit)
volume_gal = volume / 231 # volume in US gallons, if you entered inches (1 gal = 231 in3)
print(f"Cylinder part: {cylinder_volume} in3")
print(f"Sphere from the two ends: {sphere_volume} in3")
print(f"Capsule volume: {volume} in3")
print(f"In gallons: {volume_gal} gal")
Runs with the standard library only. "math.pi" is π, "**" raises to a power (squared or cubed) and "*" is multiplication. Change the radius and the cylinder height at the top and run it. (This example uses inches. If you enter feet, the volume is in ft³; multiply by 1728 and divide by 231 to get gallons.)
How to write it in LaTeX and other math languages (copy and paste)
The idea behind the volume of a capsule (split into a cylinder and a sphere, then add)
V = V₁ + V₂
V = V_{1} + V_{2}
<math xmlns="http://www.w3.org/1998/Math/MathML" display="block">
<mrow>
<mi>V</mi>
<mo>=</mo>
<msub><mi>V</mi><mn>1</mn></msub>
<mo>+</mo>
<msub><mi>V</mi><mn>2</mn></msub>
</mrow>
</math>
V = V_1 + V_2
v1 + v2
V := V1 + V2;
V = V1 + V2;
V = V_1 + V_2
Volume of the cylinder part (basic formula 1)
V₁ = π × r² × h
V_{1} = \pi r^{2} h
<math xmlns="http://www.w3.org/1998/Math/MathML" display="block">
<mrow>
<msub><mi>V</mi><mn>1</mn></msub>
<mo>=</mo>
<mi>π</mi>
<mo>⁢</mo>
<msup><mi>r</mi><mn>2</mn></msup>
<mo>⁢</mo>
<mi>h</mi>
</mrow>
</math>
V_1 = pi r^2 h
Pi*r^2*h
V1 := Pi*r^2*h;
V1 = pi*r^2*h;
V_1 = πr^2 h
Volume of the sphere made by the two ends (basic formula 2)
V₂ = 4/3 × π × r³
V_{2} = \dfrac{4}{3}\pi r^{3}
<math xmlns="http://www.w3.org/1998/Math/MathML" display="block">
<mrow>
<msub><mi>V</mi><mn>2</mn></msub>
<mo>=</mo>
<mfrac><mn>4</mn><mn>3</mn></mfrac>
<mo>⁢</mo>
<mi>π</mi>
<mo>⁢</mo>
<msup><mi>r</mi><mn>3</mn></msup>
</mrow>
</math>
V_2 = 4/3 pi r^3
4/3*Pi*r^3
V2 := (4/3)*Pi*r^3;
V2 = 4/3*pi*r^3;
V_2 = (4/3)πr^3
Volume of a capsule in one formula
V = π × r² × h + 4/3 × π × r³
V = \pi r^{2} h + \dfrac{4}{3}\pi r^{3}
<math xmlns="http://www.w3.org/1998/Math/MathML" display="block">
<mrow>
<mi>V</mi>
<mo>=</mo>
<mi>π</mi>
<mo>⁢</mo>
<msup><mi>r</mi><mn>2</mn></msup>
<mo>⁢</mo>
<mi>h</mi>
<mo>+</mo>
<mfrac><mn>4</mn><mn>3</mn></mfrac>
<mo>⁢</mo>
<mi>π</mi>
<mo>⁢</mo>
<msup><mi>r</mi><mn>3</mn></msup>
</mrow>
</math>
V = pi r^2 h + 4/3 pi r^3
Pi*r^2*h + 4/3*Pi*r^3
V := Pi*r^2*h + (4/3)*Pi*r^3;
V = pi*r^2*h + 4/3*pi*r^3;
V = πr^2 h + (4/3)πr^3
Converting volume units (in³ → gallons)
V[gal] = V[in³] ÷ 231
V_{\mathrm{gal}} = V_{\mathrm{in^3}} \div 231
<math xmlns="http://www.w3.org/1998/Math/MathML" display="block">
<mrow>
<msub><mi>V</mi><mi>gal</mi></msub>
<mo>=</mo>
<msub><mi>V</mi><mrow><msup><mi mathvariant="normal">in</mi><mn>3</mn></msup></mrow></msub>
<mo>÷</mo>
<mn>231</mn>
</mrow>
</math>
V_(gal) = V_(in^3) -: 231
vIn3/231
vGal := vIn3/231;
v_gal = v_in3/231;
V(gal) = V(in³)/231
Converting volume units (in³ → ft³)
V[ft³] = V[in³] ÷ 1728
V_{\mathrm{ft^3}} = V_{\mathrm{in^3}} \div 1728
<math xmlns="http://www.w3.org/1998/Math/MathML" display="block">
<mrow>
<msub><mi>V</mi><mrow><msup><mi mathvariant="normal">ft</mi><mn>3</mn></msup></mrow></msub>
<mo>=</mo>
<msub><mi>V</mi><mrow><msup><mi mathvariant="normal">in</mi><mn>3</mn></msup></mrow></msub>
<mo>÷</mo>
<mn>1728</mn>
</mrow>
</math>
V_(ft^3) = V_(in^3) -: 1728
vIn3/1728
vFt3 := vIn3/1728;
v_ft3 = v_in3/1728;
V(ft³) = V(in³)/1728
How to have ChatGPT do the calculation
You are a math calculation assistant. Do the following calculation by actually running Python code, and base your answer only on the numbers from the execution result (do not answer by mental math or guessing). A capsule (a cylinder with a hemisphere on each end) has a radius of 3 in and a cylinder part 4 in high. Find each of the following: 1. The volume of the cylinder part in in³ 2. The volume of the sphere made by the two hemisphere ends in in³ 3. The volume of the whole capsule in in³ 4. That volume in US gallons (1 gal = 231 in³) Show the formulas you used and the numbers from the execution result.
How to Use
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1Enter your numbersType the numbers you want to calculate with into the input fields
-
2CalculatePress the "Calculate" button
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3Check the resultThe result appears on the spot. The same page also explains the idea behind the calculation and the formula
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Related Features
Cylinder Volume Calculator (V = πr²h)
Explains in detail the volume of a cylinder (πr²h), the body of a capsule
Sphere Volume Calculator (V = 4/3 × π × r³)
Explains in detail the volume of a sphere (4/3πr³), which the two hemisphere ends of a capsule make together
Circle Calculator (Radius, Diameter, Circumference and Area)
Calculates the radius, diameter, circumference and area of a circle, the cross section of a capsule. Also handy for getting the radius from the diameter
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