HesapHanem

Sphere from Volume Calculator

Find a sphere's radius from its volume.

Result

6.2035 units
12.4070 units
483.60 units²

How it is calculated

The sphere volume formula V = (4/3)·π·r³ is solved for the radius: r = (3V / 4π)^(1/3). From that radius the tool also gives the diameter d = 2r and the surface area A = 4πr². The radius and diameter are shown to four decimals, the surface area to two.

The volume must be greater than zero, otherwise there is no result. The tool has no unit selector and labels results as generic units: if the volume is in cubic centimetres, the lengths are in centimetres and the surface area in square centimetres, and the same holds for any other consistent unit.

Worked example

A spherical tank holds 1000 cubic units. First 3V / 4π = 3000 / 12.566 = 238.73. The cube root of 238.73 is the radius: 6.2035 units. The diameter is 2 × 6.2035 = 12.4070 units. The surface area is 4π × 6.2035² = 483.60 units².

Try this example →

Common mistakes

  • Mixing up litres and cubic metres: 1 m³ is 1000 litres, so convert to one consistent volume unit before entering it.
  • Reading the first result as the diameter; the main figure is the radius, the diameter is the separate line and is twice as large.
  • Expecting the radius to grow in proportion to the volume; it grows with the cube root, so doubling the volume increases the radius by only about 26%.
  • Using the formula for an internal capacity and forgetting wall thickness: the result is the inner radius if you entered the inner volume.
  • Entering a volume of 0 or a negative value, which gives no result.

Sources

About this calculator

This calculator inverts the sphere volume formula, V = (4/3)πr³, to solve for radius: r = (3V/4π)^(1/3). From that radius it also reports the diameter (2r) and surface area (4πr²), so a single known volume gives you every other size measurement of the sphere.

It comes up whenever volume is the number you actually have but size is what you need — sizing a spherical storage tank or pressure vessel to fit a given capacity, working out the radius of a water droplet or gas bubble from its measured volume in a lab, or checking a ball's diameter from a manufacturing spec. Engineers, chemistry and physics students, and packaging designers all use it the same way.

Was this helpful?

You can pick up to 3 reactions.

Comments (1)

  • Editorial team

    The tool has no unit selector, so the volume you enter decides every unit in the answer. A tank rated in litres has to be converted first: one litre is 1000 cubic centimetres, which gives the radius in centimetres. Treat the result as the inside size of a perfect sphere, since wall thickness is not included. Is your volume coming from a tank, a ball or something else?

Popular calculators

Loan Calculator

Monthly payment, total interest and full amortization schedule.

Percentage Calculator

Percent change, percent of, and ratio calculations.

Discount Calculator

Calculate final price, savings, and discount amount.

BMI Calculator

Body mass index from height and weight (metric or imperial).

Age Calculator

Compute your exact age in years, months and days from a birth date.

Compound Interest Calculator

Calculate the final amount and interest earned with compounding.

All Calculators