Updated · Built and checked by the PlinzoTools team, formulas tested against published sources
Calculate a sphere's volume and surface area from its radius.
This tool calculates both the volume and surface area of a sphere from its radius.
Enter the radius. Volume and surface area appear instantly.
Volume = (4/3) × π × r³
Surface Area = 4 × π × r²
The calculator takes a single input, the radius, which is the distance from the center of the sphere to its surface. Many real objects are described by their diameter instead, such as a ball, a tank, or a bearing. Divide the diameter by 2 before entering it. Entering the diameter by mistake is the most common error with this tool, and because volume depends on the cube of the radius, the result will be eight times too large.
Keep the unit consistent. If your radius is in centimeters, the surface area is in square centimeters and the volume is in cubic centimeters. The tool does not convert units for you, so measure everything in the same unit and read the answers in that unit squared or cubed.
Suppose a spherical water tank has a diameter of 10 meters, so the radius is 5 meters. These numbers are hypothetical, chosen only to show the steps.
Volume = (4/3) × π × 5³ = (4/3) × π × 125 ≈ 523.60 cubic meters
Surface Area = 4 × π × 5² = 4 × π × 25 ≈ 314.16 square meters
Since one cubic meter holds 1,000 liters, that tank would hold roughly 523,600 liters when completely full. The surface area figure is useful for estimating how much paint, insulation, or sheet material would be needed to cover the outside, before allowing for waste and overlap.
Surface area grows with the square of the radius, while volume grows with the cube. That has practical consequences:
You can test this yourself by running radius 3 and then radius 6 and comparing the outputs. The second volume should be exactly eight times the first.
Students use it to check homework in geometry and physics. Hobbyists use it to estimate how much material a globe, a sphere-shaped lantern, or a model needs. People planning storage or shipping use it to compare capacity between spherical containers of different sizes. Whenever a problem gives you a radius and asks for capacity or covering area, this is the quickest check.
For anything safety-critical, such as pressure vessels or structural components, use the result only as a rough figure and rely on qualified engineering calculations.
Pure coincidence of the numbers at that specific radius -- they use different formulas and generally give different values.
Divide the diameter by 2 to get the radius, then enter that value. For example, a 12 cm ball has a radius of 6 cm.
Volume depends on the radius cubed, and 2 cubed is 8. Surface area depends on the radius squared, so it only grows by a factor of 4.
The tool is unit-agnostic. If the radius is in inches, the surface area is in square inches and the volume is in cubic inches. Convert the units yourself if you need something else.
For volume, halve the result. For a solid hemisphere's total surface area, use 3 × π × r² instead, since the flat base adds area that a full sphere does not have.
Reference: NIST Weights and Measures