Sphere Calculator: Instantly Find Volume, Surface Area, and Diameter

How to use the tool

• 1. Type the radius of your sphere into the Radius box—for example 2.5 or 15.
• 2. Press Calculate; the tool displays volume, surface area, diameter and the radius you entered.
• 3. Review the results on-screen or copy them for reports, orders or homework.

Underlying formulas

• Volume: $$V = rac{4}{3}\pi r^{3}$$
• Surface area: $$A = 4\pi r^{2}$$
• Diameter: $$d = 2r$$

Example calculations

• Radius = 2.5 units
  $$V = rac{4}{3}\pi(2.5)^{3} = 65.45\ \text{units}^{3}$$
  $$A = 4\pi(2.5)^{2} = 78.54\ \text{units}^{2}$$
  $$d = 5\ \text{units}$$
• Radius = 15 units
  $$V = rac{4}{3}\pi(15)^{3} = 14\,137.17\ \text{units}^{3}$$
  $$A = 4\pi(15)^{2} = 2\,827.43\ \text{units}^{2}$$
  $$d = 30\ \text{units}$$

Quick-Facts

• Volume grows with the cube of radius; doubling r multiplies V by eight (MathWorld Sphere, https://mathworld.wolfram.com/Sphere.html).
• π is defined to at least 100 billion digits; most engineering uses 3.14159 (NIST Handbook of Mathematical Functions, 2010).
• ISO 31-1 recommends reporting geometric lengths to the same unit family used for inputs (ISO 31-1, 1992).
• Commercial ball bearings span 0.4–200 mm diameters (SKF Rolling Bearings Catalogue, 2023).

FAQ

What is a sphere?

A sphere is a set of points in 3-D space equidistant from a central point (MathWorld Sphere, https://mathworld.wolfram.com/Sphere.html).

Why does the calculator need only the radius?

Volume, surface area and diameter all depend solely on r, so one measurement delivers every other property (NIST 2010).

How accurate are the results?

The tool computes with double-precision JavaScript (≈15 decimal digits) and rounds to two decimals for readability (ECMA-262 Spec, 2023).

Can I use any unit?

Yes—enter metres, inches or miles; outputs appear in the corresponding cubic or square units (ISO 31-1, 1992).

How do I convert to hemisphere values?

Halve the volume and add a base area $$\pi r^{2}$$ to the curved area to get $$3\pi r^{2}$$ total (MathWorld Hemisphere, https://mathworld.wolfram.com/Hemisphere.html).

Where are spherical calculations used?

Applications include tank sizing, astronomy, ballistics and medical imaging (NASA Systems Engineering Handbook, 2022).

What happens if I input a negative radius?

The form blocks it; negative length lacks physical meaning and violates ISO 80000-1 definitions (ISO 80000-1, 2009).

Can I reuse the formulas offline?

Yes—copy the equations above; they are standard geometry valid in any spreadsheet or programming language (NIST 2010).