Sphere Volume Calculator — Volume, Surface Area & Circumference
Enter the radius or diameter of a sphere to instantly calculate volume (V = 4⁄3 π r³), surface area (4 π r²), diameter, great-circle circumference, and cross-sectional area — with full step-by-step working.
Input type
units
V = 4⁄3 × π × r³
V ≈ 523.6
Radius
Volume formula
Volume result
Surface area formula
Surface area result
- 1
Radius cubed
5 × 5 × 5 = 125 - 2
Volume
4⁄3 × π × 125 = 523.5988V = 4⁄3 π r³
How does this calculator work?
The volume of a sphere is V = 4⁄3 π r³ and the surface area is 4 π r². Diameter = 2r. Doubling the radius multiplies volume by 8 and surface area by 4. Enter radius or diameter to get all five measurements plus step-by-step working.
Formula
How this is calculated
A sphere is the set of all points in three-dimensional space equidistant from a central point. Its geometry is completely determined by a single measurement: the radius r. The volume formula V = 4⁄3 π r³ is derived by integration of infinitesimally thin circular cross-sections stacked along one axis; the surface area formula SA = 4 π r² equals exactly four times the area of the sphere's great circle (π r²).
Because volume scales as r³ and surface area scales as r², doubling the radius multiplies the volume by 8 (2³) but the surface area by only 4 (2²). This means that as spheres grow larger, they enclose proportionally more volume relative to their skin — the reason that large cells cannot exchange nutrients efficiently through their membranes without special adaptations.
The calculator accepts either radius or diameter as input (diameter = 2r). The great-circle circumference (2 π r) is the perimeter of the largest possible circle that fits inside the sphere, and the cross-sectional area (π r²) is the area of that circle. All results are in the units you choose for the radius input — if you enter centimetres, volume is in cm³ and area in cm².
Frequently asked questions
Volume = 4⁄3 × π × r³, where r is the radius. For example, a sphere of radius 5 cm has volume ≈ 523.60 cm³. If you only know the diameter d, use r = d/2 first.
The surface area (4 π r²) is exactly four times the area of the great circle (π r²). Archimedes discovered that the surface area of a sphere equals the lateral surface area of the circumscribed cylinder with the same diameter — a result he considered his greatest achievement.
Rearrange V = 4⁄3 π r³ to r = ∛(3V / 4π). Take the cube root of (3 × Volume) ÷ (4π). For example, a sphere of volume 100 cm³ has r = ∛(300 / 4π) ≈ 2.879 cm.
TG we-Calculate Editorial Team. (2026). Sphere Volume Calculator — Volume, Surface Area & Circumference [Online calculator]. TG we-Calculate. https://we-calculate.com/calculator/sphere-volume-calculator
TG we-Calculate Editorial Team. "Sphere Volume Calculator — Volume, Surface Area & Circumference." TG we-Calculate. 2026. https://we-calculate.com/calculator/sphere-volume-calculator.
TG we-Calculate Editorial Team, "Sphere Volume Calculator — Volume, Surface Area & Circumference," TG we-Calculate, 2026. [Online]. Available: https://we-calculate.com/calculator/sphere-volume-calculator
@misc{wecalculate_sphere_volume_calculator, title = {Sphere Volume Calculator — Volume, Surface Area & Circumference}, author = {{TG we-Calculate Editorial Team}}, howpublished = {\url{https://we-calculate.com/calculator/sphere-volume-calculator}}, year = {2026}, note = {TG we-Calculate} }
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