If you ever wondered what's the volume of the Earth, a soccer ball, or a helium balloon, our sphere volume calculator is here for you. It can help to calculate the volume of the sphere, given the radius or the circumference. Also, thanks to this calculator, you can determine the spherical cap volume or hemisphere volume.
Volume of a sphere formula
A sphere is a perfectly round geometrical 3D object. The formula for its volume equals:
volume = (4/3) × π × r³
Usually, you don't know the radius - but you can measure the circumference of the sphere instead, e.g., using the string or rope. The sphere circumference is the one-dimensional distance around the sphere at its widest point.
circumference = 2 × π × r, so
r = circumference / (2 × π)
How to find the volume of a sphere?
Do you know what the volume of an official FIFA World Cup soccer ball called size 5 is? Or basketball, size 7? Let's check!
- Enter the radius of the sphere. For size 5 soccer ball radius should be equal to 4.3-4.5 in. Let's take 4.4 in.
- The sphere volume appeared as the circumference. It is equal to 357 cu in and 27.6 in.
- Assume that we don't know the radius for the basketball. Type in the circumference instead. For basketball size 7, the typical one is 29.5 in.
- The volume of a sphere and radius is displayed, 433.5 cu in and 4.7 in, respectively.
Now try to calculate something else, take something bigger... Maybe you want to know the volume of the Earth? The mean radius is approximately 6.37 × 106 m. The volume is then:
volume = (4/3) × π × (6370000 m)³ = 1,082,696,932,430,002,306,149 m³
Spherical cap volume calculation
The spherical cap, also called the spherical dome, is a portion of a sphere cut off by a plane. The formula behind its volume is:
volume = ((π × h²) / 3) × (3r - h) or
volume = (1/6) × π × h × (3a² + h²), where the radius of the sphere is
r, the height of the cap (the blue one) is
a is the radius of the base of the cap.
We can also use these formulas to find the volume of the opposite dome (the orange one), as shown in the illustration. However, be sure to use the correct measurement for
h, which should always be the height of the spherical cap or dome we're interested in finding.
One example of the spherical dome is the fish tank. Let's calculate how much water we need to fill it:
- Find the height of the cap. For example, 7 in.
- Determine the radius of the base of the cap. That is also the same as the radius of the fish tank's opening. Let's say it's equal to 3.1305 in.
- Enter these values into our calculator. Upon doing so, our calculator will display the spherical cap volume to be equal to 287.35 cu in and its corresponding sphere radius to be equal to 4.2 in.
- To calculate the volume of the full sphere, use the basic calculator. Enter the radius 4.2 in.
- Now you know that our example fish tank has the volume 287.35 cu in, compared to 310.3 cu in for full sphere volume with the same radius.
Hemisphere volume calculation
How to calculate it? Just use the spherical cap volume formula with the parameters equal to each other:
sphere radius = height of the cap = cap base radius. Also, you can divide the full sphere result by 2 .
How do I calculate the volume of a sphere with diameter?
volume = (1/6) × π × d³
To derive this from the standard sphere volume formula
volume = (4/3) × π × r³, substitute
d/2. In this way, we use the fact that the radius is half the diameter.
What is the volume of a sphere with radius 2?
volume = (4/3) × π × 8 ≈ 33.5
To derive this result, recall the volume formula
volume = (4/3) × π × r³ and plug in
r = 2.
What is the volume of a sphere with circumference 10?
To derive the volume of a sphere from its circumference
c = 10:
- Compute the radius from the circumference:
r = c / (2 × π) ≈ 1.59.
- Apply the formula
volume = (4/3) × π × r³with
r = 2.
- We obtain
volume = (4/3) × π × 1.59³ ≈ 16.89.
How to find radius of sphere given volume?
We need to solve the formula
volume = (4/3) × π × radius³ for radius:
- Divide both sides by
(4/3) × π. We get
3/(4π) × volume = radius³.
- Take the cube root
∛of both sides:
∛(3/(4π) × volume) = radius.
- That's it! Now you merely need to plug in the value of volume to compute the radius.