Enter a sphere's radius, diameter or circumference to get its volume and surface area, with liters and gallons and the formula worked out. Already know the volume or surface area? Switch the input and the calculator works backwards to the radius.
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For volume or surface area, enter it in cubic or square units of this unit
Enter your values to see the result.
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How to use the Sphere Volume Calculator
Choose what you know: radius, diameter, circumference, volume or surface area.
Enter the value and pick the unit it is measured in.
Read the volume and surface area, plus liters and gallons.
Check the steps to see the formula with your numbers.
Use the tables for other volume units or to see how size changes with the radius.
Sphere formulas
Find
Formula
Example: r = 5 cm
Volume
V = (4/3)πr³
523.60 cm³ (0.524 L)
Volume from diameter
V = πd³ ÷ 6
π × 10³ ÷ 6 = 523.60 cm³
Surface area
A = 4πr²
314.16 cm²
Radius from volume
r = ∛(3V ÷ 4π)
V = 523.60 → r = 5
Radius from surface area
r = √(A ÷ 4π)
A = 314.16 → r = 5
Radius from circumference
r = C ÷ 2π
C = 31.42 → r = 5
Volume and surface area for common radii
Because volume depends on r³ and area on r², the two numbers are equal only at r = 3 (in any unit). Smaller spheres have more surface per unit of volume, which is why crushed ice melts faster than one big ice ball.
Radius
Volume (4/3)πr³
Surface area 4πr²
1
4.189
12.566
2
33.510
50.265
3
113.097
113.097
5
523.599
314.159
10
4,188.790
1,256.637
Measuring a real ball
Measure the circumference with a flexible tape around the widest part. That is easier and more accurate than finding the center for a radius.
Use the outside size for how much space a ball takes up and the inside size for how much it holds. For a hollow ball, subtract the inner volume from the outer to get the volume of the shell material.
Watch your units. If you measure in inches, the volume comes out in cubic inches; the calculator converts it to liters and gallons for you.
Frequently asked questions
What is the formula for the volume of a sphere?
V = (4/3)πr³, where r is the radius. A sphere with radius 5 cm has a volume of (4/3) × π × 125 ≈ 523.6 cm³. Using the diameter d, the same formula is V = πd³ ÷ 6.
What is the surface area of a sphere?
A = 4πr², exactly four times the area of a circle with the same radius. For r = 5 cm, A = 4 × π × 25 ≈ 314.16 cm².
How do I find the volume of a sphere from its circumference?
First get the radius: r = C ÷ 2π. Then use V = (4/3)πr³. A basketball measuring 29.5 inches around has r ≈ 4.695 in and a volume of about 433.5 in³ (7.1 liters).
How do I find the radius from the volume?
Rearrange the formula: r = ∛(3V ÷ 4π). For a volume of 1,000 cm³ (1 liter), r = ∛(3000 ÷ 12.566) ≈ 6.2 cm, so a 1-liter ball is about 12.4 cm across.
What happens to the volume if I double the radius?
The volume grows with the cube of the radius, so doubling r multiplies the volume by 8, while the surface area (which grows with the square) only multiplies by 4.
How do I convert sphere volume to liters or gallons?
1 liter = 1,000 cm³ and 1 US gallon = 231 in³ = 3.785 liters. The calculator converts automatically and lists the volume in mL, liters, cubic feet, cups and gallons.
What is the volume of a hemisphere?
Half of a sphere: V = (2/3)πr³. Its curved surface area is 2πr², or 3πr² including the flat circular base.
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