How to Calculate the Volume of a Sphere

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Updated: September 19, 2019

A sphere is a perfectly round geometrical object that is three dimensional, with every point on its surface equidistant from its center.[1] Many commonly-used objects such as balls or globes are spheres. If you want to calculate the volume of a sphere, you just have to find its radius and plug it into a simple formula, V = ⁴⁄₃πr³.[2]

Steps

1. 1
Write down the equation for calculating the volume of a sphere. This is the equation: V = ⁴⁄₃πr³. In this equation, "V" represents volume and "r" represents the radius of the sphere.
2. 2
Find the radius. If you're given the radius, then you can move on to the next step. If you're given the diameter, then you can just divide it by two to get the radius.[3] Once you know what it is, write it down. Let's say the radius we're working with is 1 inch (2.5 cm).
• If you're only given the surface area of the sphere, then you can find the radius by finding the square root of the surface area divided by 4π. In that case, r = root (surface area/4π)[4]
3. 3
Cube the radius. To cube the radius, simply multiply it by itself thrice, or raise it to the third power. For example, 1 inch3 is really just 1 inch (2.5 cm) x 1 inch (2.5 cm) x 1 inch (2.5 cm). The result of 1 inch3 is really just 1, since 1 multiplied by itself any number of times will be 1. You'll reintroduce the unit of measurement, inches, when you state your final answer. After you've done this, you can plug the cubed radius into the original equation for calculating the volume of a sphere, V = ⁴⁄₃πr³. Therefore, V = ⁴⁄₃π x 1
• If the radius was 2 inches (5.1 cm), for example, then to cube it, you would find 23, which is 2 x 2 x 2, or 8.
4. 4
Multiply the cubed radius by 4/3. Now that you've plugged r3, or 1, into the equation, you can multiply this result by 4/3 to continue plugging in to the equation, V = ⁴⁄₃πr³. 4/3 x 1 = 4/3. Now, the equation will read V = ⁴⁄₃ x π x 1, or V = ⁴⁄₃π.
5. 5
Multiply the equation by π. This is the last step to finding the volume of a sphere. You can leave π as it is, stating the final answer as V = ⁴⁄₃π. Or, you can plug π into your calculator and multiply its value by 4/3. The value of π[5] (approximately 3.14159) x 4/3 = 4.1887, which can be rounded to 4.19. Don't forget to state your units of measurement and to state the result in cubic units. The volume of a sphere with the radius of 1 is 4.19 in.3

Community Q&A

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• Question
How do I calculate the volume of a sphere if neither the radius nor the diameter is given?
Donagan
If you know the surface area, solve the area formula for the radius, and use that to find the volume. Without the radius, you can't determine the volume.
• Question
Why is the formula not V = pi x R squared x H?
Diante Watts
Height is not included when measuring spheres, since usually they are congruent in all directions; it wouldn't be a necessity, because the radius is included.
• Question
How can I tell the volume with only the diameter given?
Divide the diameter by 2, giving you the radius and continue from there.
• Question
How can I calculate volume from a diameter?
Donagan
Divide by 2, then take that radius and plug it into the volume formula.
• Question
How do I find the volume with only the circumference given?
Use the circumference formula (C=2πr) and rearrange it to solve for the radius (r=C/2π). Once you have the radius (r), you can use that value in the volume of a sphere formula (V = 4/3πr³).
• Question
What is the volume of a sphere if the radius is 6?
Smile Happy
Use the formula V= 4/3(3.14)(6^3). 6*6*6 = 216, V= 4/3*3.14*216, V=4*3.14*216= 2,712.96, 2,712.96/3 = 904.32. So the volume would be 904.32.
• Question
How can I find the surface area of a cylinder?
A cylinder's "curved" part is really just a rectangle with the one side as the circumference of the circular base of the cylinder. The other side is the height of the cylinder. Using the area of a rectangle formula, the surface area can then be written as: A = (2 * pi * r) * (h) = 2* pi * r * h. If you are including the circle ends of the cylinder, then add 2 * the area of the circle : 2 * pi * r * h + 2 * pi * r^2.
• Question
How do I find the diameter with only the volume given?
Donagan
Use the volume formula to solve for the radius, then double the radius.
• Question
I need to know the volume of a cylindrical water tank with ellipsoidal bases.
V=pi *a*b*h where "a" and "b" are the semi-major and semi-minor axes of the ellipse, and "h" is the height of the cylinder.
• Question
Between a sphere 32 mm diameter and a sphere 18 mm diameter, what is percentage difference?
Donagan
If you're asking only about the diameters, divide 18 by 32. That gives you a decimal number. Multiply it by 100 to get what percentage 18 is of 32. If you want to compare the two volumes, you'll have to cube each diameter and then perform the same division operation.
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Tips

• Make sure your measurements are all in the same unit. If they aren't, you will need to convert them.
Thanks!
• Note that the "*" symbol is used as a multiplication sign to avoid confusion with the variable "x".
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• If you only need part of a sphere, like half or a quarter, find the full volume first, then multiply by the fraction you want to find. For instance, to find the volume of half a sphere with a volume 8, you would multiply 8 by one half or divide 8 by 2 to get 4.
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• Don't forget to use cubed units (e.g. 31 ft³ ).
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Things You'll Need

• Calculator (reason: to calculate problems that would be annoying to do without it)
• Pencil and paper (not needed if you have an advanced calculator)

wikiHow is a “wiki,” similar to Wikipedia, which means that many of our articles are co-written by multiple authors. To create this article, 107 people, some anonymous, worked to edit and improve it over time. Together, they cited 5 references.
Co-authors: 107
Updated: September 19, 2019
Views: 1,915,080
Categories: Volume
Article SummaryX

To calculate the volume of a sphere, use the formula v = ⁴⁄₃πr³, where r is the radius of the sphere. If you don't have the radius, you can find it by dividing the diameter by 2. Once you have the radius, plug it into the formula and solve to find the volume. For more tips, including examples you can use for practice, read on!

Thanks to all authors for creating a page that has been read 1,915,080 times.

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Sep 16, 2016

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