Sphere Calculator

Find radius, diameter, volume, surface area, and circumference from any one sphere measurement

By Drew Budwin · Last updated July 2026 · Methodology

Enter the radius (must be greater than 0)

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Sphere Calculator Formula

Volume of a sphere:

V = (4/3) × π × r³

r = radius.

Surface area of a sphere:

A = 4 × π × r²

r = radius.

Great-circle circumference:

C = 2π × r

r = radius.

Radius from volume:

r = ∛(3V / 4π)

V = volume.

Radius from surface area:

r = √(A / 4π)

A = surface area.

How to Use This Calculator

  1. Choose what you already know: Radius, Diameter, Volume, Surface Area, or Circumference.
  2. Enter your known value in the field.
  3. Click Calculate to see all five sphere measurements instantly.

Frequently Asked Questions

Can I find the radius of a sphere from its volume?

Yes. Rearranging V = (4/3)πr³ gives r = ∛(3V / 4π). Enter the volume in the Volume tab and this calculator solves for the radius, diameter, surface area, and circumference at once.

What is the surface area of a sphere?

The surface area is A = 4πr², where r is the radius. It is exactly four times the area of the sphere's great circle. Enter any measurement and this calculator reports the surface area alongside the volume, diameter, and circumference.

What units does this calculator use?

This calculator is unit-agnostic. If you enter the radius in inches, the volume is in cubic inches (in³) and the surface area in square inches (in²). Use whatever unit matches your measurement.

How much water does a spherical tank hold?

Calculate the volume with V = (4/3)πr³, then convert to your liquid unit. For example, 1 cubic meter = 1,000 liters, so a sphere with r = 0.5 m holds about 524 liters. Enter the radius (or diameter) and read the volume directly.

Why does the sphere volume formula use 4/3?

The 4/3 factor comes from integrating the areas of infinitely thin circular slices stacked along the diameter. It can also be derived by showing that a sphere's volume equals exactly 2/3 of the cylinder that encloses it, giving (4/3)πr³. If you only need half a sphere, use the hemisphere calculator.

How does sphere volume scale with radius?

Volume scales with the cube of the radius: doubling the radius increases volume eightfold (2³ = 8). A sphere with radius 2 m has eight times the volume of one with radius 1 m. This is why small increases in tank radius have a large effect on capacity.

What is the volume of a balloon?

Model the balloon as a sphere with the inflated radius. A balloon inflated to a 15 cm radius has a volume of (4/3)π × 15³ ≈ 14,137 cm³, or about 14.1 liters. This works well for round balloons; elongated ones are closer to a capsule shape.

How do I find the volume of a partially filled spherical tank?

For a sphere filled to height h from the bottom, the volume is πh²(r − h/3). When the sphere is exactly half full, the volume is simply (2/3)πr³, the hemisphere formula. Use the hemisphere calculator for that case.

Further Reading

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