Sphere volume formula

The standard formula for the volume of a sphere is:

Here’s what each symbol means:

• V = the sphere’s volume (how much 3D space it occupies).
• π (pi) ≈ 3.14159… (a constant that shows up in circles and spheres).
• r = the radius (distance from the center to the surface).
• r³ means “radius cubed” (radius × radius × radius).

The most important “aha” detail is the cube. When something is cubed, small changes in the input create huge changes in the output. That’s why sphere volume scales so fast. If you’re used to 2D area formulas like A = πr², volume adds one more “dimension” so the exponent becomes 3.

If you are given the diameter instead of the radius, remember that the diameter is the full width across the sphere through the center. It’s exactly double the radius:

This calculator lets you choose either “Radius” or “Diameter” so you don’t have to do that conversion in your head. It will compute the radius internally and then apply the main volume formula.

What this calculator does step-by-step

Even though the result is instant, there are a few clean steps happening behind the scenes. Understanding the steps makes it easier to check your work, catch unit mistakes, and explain your solution on homework or exams.

You choose whether you’re entering a radius r or a diameter d, then type the value and the unit (mm, cm, m, inches, feet). The calculator validates that the number is positive and not empty.

If you chose Diameter, we compute r = d/2. If you chose Radius, we keep your input as-is. Either way, we now have a clean radius value to use.

We apply the sphere volume formula V = (4/3)πr³. The output is in “unit cubed,” meaning if your input unit is centimeters, the volume is in cubic centimeters (cm³). If your input unit is meters, the volume is in m³, and so on.

You can choose how many decimals you want. In many real problems, 3 decimals is a nice balance: accurate enough for science labs and engineering sketches, clean enough for screenshots. If you want the full raw number, select “No rounding.”

The result block is designed like a “share card.” You can copy the text, share to socials, or save results locally on your device to compare different radii later. Nothing leaves your browser.

Examples you can copy into homework

Let’s walk through a few common scenarios. These examples use the same steps the calculator uses, so you can match your calculation line-by-line. (Pro tip: when teachers say “show your work,” these are exactly the lines they want to see.)

If r = 3 cm, then:

So the sphere holds about 113.097 cm³ of volume. That’s a nice “pi” example because it simplifies cleanly to 36π.

If d = 10 in, then the radius is r = d/2 = 5 in. Now compute volume:

Notice the unit is in³ (cubic inches). If you later need liters or gallons, use a volume conversion tool after you calculate the cubic volume.

Suppose one sphere has radius r, and another has radius 2r. Compare their volumes:

Doubling the radius makes the volume 8× larger. Tripling the radius makes it 27× larger. This is why “small” increases in size can massively increase storage capacity in tanks, containers, and spherical designs.

Common mistakes (and how to avoid them)

Sphere volume problems are usually straightforward, but people regularly lose points due to small mistakes. Here are the biggest ones—plus quick fixes.

If you plug diameter into the radius formula directly, your answer will be off by a factor of 8. Always check: “Did I use r or d?” If you’re given diameter, convert using r = d/2 first.

A length unit becomes a cubic unit for volume. Centimeters become cm³, inches become in³, meters become m³. If you write “cm” instead of “cm³,” it’s a unit mismatch.

If you round π or intermediate steps early, your final answer can drift. Keep π as π (or 3.14159) until the end. The calculator keeps full precision internally and only rounds at the end based on your selection.

In real geometry, a radius can’t be negative. If your math produces a negative radius, it’s a sign you copied a value incorrectly or included a minus sign by mistake.

Sphere surface area is 4πr², while sphere volume is (4/3)πr³. They look similar, but the exponent and meaning are different. If the question asks “how much it holds,” you want volume.

Sphere Volume Calculator FAQs

• What is the volume of a sphere in simple terms?

  It’s the amount of space inside a perfectly round ball. Think “how much it could hold” if the sphere were hollow (like a spherical tank).

• Does the formula change if the sphere is hollow?

  For a hollow sphere (a shell), you usually compute the volume of the outer sphere minus the volume of the inner sphere: V = (4/3)π(R³ − r³), where R is outer radius and r is inner radius. This page calculates a single sphere volume; for shells, calculate twice and subtract.

• Why is there a 4/3 in the formula?

  It comes from calculus (integrating circular cross-sections). Intuitively, as you stack many thin circular slices, the “average” radius of slices across the sphere leads to that 4/3 factor.

• What unit will the answer be in?

  The output is always in cubic units of your input: cm → cm³, in → in³, ft → ft³, and so on.

• Can I convert the result to liters or gallons?

  Yes. First calculate in a cubic unit, then convert. For example, 1,000 cm³ equals 1 liter. For gallons, you’ll want a volume conversion tool (and confirm whether you mean US or Imperial).

• Is this accurate enough for engineering or 3D printing?

  For most practical use, yes—especially if you keep 4–6 decimals. But always validate units and tolerances for real builds. If you’re using inches/feet, confirm whether your CAD software expects metric or imperial units.

• What if I only know circumference?

  If you know the great-circle circumference C, then C = 2πr, so r = C/(2π). You can compute r and then plug it into this calculator.