What Is the Volume of a Sphere?
A sphere is a perfectly round three-dimensional object, like a ball, marble, or planet, where every point on its surface is the same distance from the center. That distance is the radius (r). The volume measures how much space the sphere occupies. This calculator computes the volume instantly from the radius using the classic formula \(V = \frac{4}{3}\pi r^3\), and also returns the diameter and surface area for convenience.
How to Use This Calculator
Enter the radius of your sphere in whatever unit you like — centimeters, inches, meters, etc. The result is expressed in the cube of that unit (for example, a radius in cm yields a volume in cm³). Press calculate and you'll get the volume, the diameter (\(2r\)), and the surface area (\(4\pi r^2\)).
The Formula Explained
The volume of a sphere is given by:
$$V = \frac{4}{3} \times \pi \times r^3$$
Here π (pi) is approximately 3.14159, and \(r^3\) means the radius multiplied by itself three times. Because the radius is cubed, the volume grows very quickly — doubling the radius makes the sphere eight times larger in volume.
Worked Example
Suppose a sphere has a radius of 5 units. Then $$r^3 = 5 \times 5 \times 5 = 125.$$ Multiply by π: \(125 \times 3.14159 \approx 392.699\). Multiply by 4/3: \(392.699 \times 1.3333 \approx 523.60\). So the volume is approximately 523.6 cubic units. The surface area is \(4 \times \pi \times 25 \approx 314.16\) square units.
FAQ
What if I only know the diameter? Divide the diameter by 2 to get the radius, then enter it here.
Why is the radius cubed? Volume is a three-dimensional measure, so it scales with the cube of any linear dimension.
What units does the answer use? The volume uses the cube of whatever unit you used for the radius — input in meters gives cubic meters.
