Sphere Surface Area Calculator
Find the surface area and volume of a sphere.
Results update as you type.
How it works
A sphere is a perfectly round three-dimensional shape, and this calculator finds both its surface area and volume from the radius. You enter the radius, the distance from the center to the surface, and it returns the surface area and the volume. The surface area is four pi times the radius squared, a remarkably clean formula meaning a sphere's surface is exactly four times the area of a circle with the same radius. The volume is four-thirds pi times the radius cubed. Both quantities depend only on the radius, but they scale differently: surface area grows with the square of the radius, while volume grows with the cube, so a sphere twice as large has four times the surface area but eight times the volume. This difference explains many real-world phenomena, such as why small animals lose heat faster than large ones, since they have more surface area relative to volume. Spheres appear everywhere: planets, balls, bubbles, droplets, and tanks. Engineers, scientists, and students use these formulas to find material needed to cover a sphere, the capacity of spherical containers, and physical properties. Remember to use the radius, not the diameter; if you have the diameter, halve it first. The results are in square and cubic units of your radius unit. Enter the radius to compute the sphere's surface area and volume.
Surface area = 4·π·r²; Volume = (4/3)·π·r³
The surface area of a sphere is four pi times the radius squared, and its volume is four-thirds pi times the radius cubed. Both depend only on the radius. Surface area grows with the square of the radius, while volume grows with the cube, so doubling the radius quadruples the area but multiplies the volume eightfold.
Source:Solid geometry
We review all our tools from time to time to ensure accuracy.
Worked example
How to use this calculator
- 1
Enter your values
Enter radius.
- 2
Adjust the options
Fine-tune any options to match your situation.
- 3
Read your result
Surface area updates instantly as you type — no button to press.
Frequently asked questions
How do you find the surface area of a sphere?
Multiply four pi by the radius squared. For a radius of 3, the surface area is 36 pi, about 113.1 square units. The calculator applies this exact formula and also gives the volume. Be sure to use the radius, not the diameter, which is twice the radius.
What is the volume of a sphere?
The volume of a sphere is four-thirds pi times the radius cubed. For a radius of 3, that is 36 pi, about 113.1 cubic units. Interestingly, a sphere of radius 3 has the same numerical value for surface area and volume, a coincidence that happens only at that specific radius.
Why does surface area grow slower than volume?
Surface area depends on the radius squared, while volume depends on the radius cubed. So as a sphere grows, its volume increases faster than its surface area. Doubling the radius quadruples the area but multiplies the volume by eight. This square-cube relationship has major consequences in biology, engineering, and physics.
Do I use the radius or the diameter?
Use the radius, the distance from the center to the surface. If you only know the diameter, which spans the full width through the center, divide it by two to get the radius before entering it. Using the diameter by mistake would make the surface area four times too large.
Where are these formulas used?
Sphere surface area and volume formulas are used to calculate the material needed to coat or paint a spherical object, the capacity of spherical tanks and containers, the properties of planets, bubbles, and droplets, and in physics for fields and forces around spherical bodies. They are essential in engineering, science, and geometry.