Sphere Calculator — Radius, Surface Area, Volume
Diagram & Inputs
Tip: Enter any one value (r, d, S, or V). The calculator checks consistency if you provide multiple values.
Results
How the Sphere Calculator Works
A sphere is fully determined by its radius r (or diameter d = 2r). From r you can compute the surface area S = 4πr² and the volume V = (4/3)πr³. This tool infers r from whatever you provide and derives the rest, checking consistency if multiple values are entered.
- From S:
r = √(S/(4π)) - From V:
r = ³√(3V/(4π)) - Then:
d = 2r,S = 4πr²,V = (4/3)πr³
Units: r and d use length units (e.g., cm); S uses squared units (e.g., cm²); V uses cubed units (e.g., cm³). You can set decimal places and choose a π approximation for classroom alignment.
Formulas & Relationships
- Diameter:
d = 2r - Surface area:
S = 4πr² - Volume:
V = (4/3)πr³ - Solve for r:
r = √(S/(4π)) = ³√(3V/(4π))
Common pitfalls: mixing units between inputs, entering negative values, or rounding too early. If you see an inconsistency warning, double-check your unit labels and π choice.
Sphere Calculator: FAQs
Which inputs are valid to solve a sphere?
Any one of radius (r), diameter (d), surface area (S), or volume (V). Two or more values are also fine.
What formulas are used?
d = 2r, S = 4πr², V = (4/3)πr³.
Does the calculator keep my data private?
Yes. Computation is entirely client-side; nothing is uploaded.
Can I change units, decimal places, or π?
Yes. Choose a length unit for r and d. Surface area is labeled with the squared unit; volume with the cubed unit. You can also choose decimal places and π precision.