Sphere Calculator

Calculate volume, surface area, radius, and diameter of a sphere from any known measurement. Perfect for geometry and engineering.

Distance from center to surface

Distance across sphere through center

Space inside the sphere

Area covering the sphere

Surface Area = 4PIr^2\nVolume = (4/3)PIr^3\nDiameter = 2r\nCircumference = 2PIr\n\nReverse Formulas:\nr = sqrt(A/4PI) from surface area\nr = cbrt(3V/4PI) from volume\nr = d/2 from diameter
Example 1 (From Radius):\nRadius = 5 cm\n\nDiameter = 2 * 5 = 10 cm\nSurface Area = 4PI * 5^2 = 314.16 cm^2\nVolume = (4/3)PI * 5^3 = 523.60 cm^3\nCircumference = 2PI * 5 = 31.42 cm\n\nExample 2 (From Volume):\nVolume = 100 cm^3\n\nRadius = cbrt(3*100/4PI) = 2.88 cm\nDiameter = 5.76 cm\nSurface Area = 104.19 cm^2

What are the formulas for a sphere?

Surface Area = 4PIr^2 (four times the area of a circle). Volume = (4/3)PIr^3. Diameter = 2r. Circumference (great circle) = 2PIr. Where r is the radius and PI ≈ 3.14159. All formulas depend only on the radius.

How do I find the radius if I know the volume?

Rearrange volume formula: r = cbrt(3V/4PI). Example: Volume = 100 cm^3. r = cbrt(3*100/4PI) = cbrt(23.87) = 2.88 cm. Similarly, from surface area: r = sqrt(A/4PI).

What is the difference between surface area and volume?

Surface area is the 2D area covering the sphere's exterior (in square units like cm^2). Volume is the 3D space inside the sphere (in cubic units like cm^3). Example: A ball with r=5cm has surface area 314.16 cm^2 and volume 523.6 cm^3.

What are real-world examples of spheres?

Sports balls (basketball, soccer, golf), planets and moons, ball bearings, bubbles, water droplets, oranges, marbles, ball-shaped tanks, dome structures, molecular models, and spherical lenses. Many natural objects approximate spheres due to surface tension or gravity.

How do you measure a sphere in real life?

Measure diameter with calipers or measure circumference with flexible tape and divide by PI to get diameter, then radius = diameter/2. For irregular spheres, use water displacement to find volume, then calculate radius from volume formula.