Radius Of Sphere Calculator

Background.

Volume is often the easiest thing to know about a ball and the radius the hardest to measure. Drop a marble into a measuring cylinder and the water level gives its volume at once, while a ruler held across a curved surface never quite finds the widest point. Tanks, droplets, ball bearings and bubbles are routinely described by what they hold rather than how wide they are. Getting from volume back to radius means undoing V = 4⁄3 πr³, and that takes a cube root: r = ∛(3V ÷ 4π).

The cube root makes the radius slow to respond. Doubling the volume lengthens the radius by only about 26%, and it takes eight times the volume to double it. The same damping helps when the volume is uncertain: a 3% error in the measured volume becomes an error of roughly 1% in the radius.

Alongside the radius the page gives the diameter, twice the radius, and the surface area, 4πr². Of all solid shapes, a sphere wraps a given volume in the least surface. A one-liter sphere has a radius of 6.20 cm and a surface of about 484 cm², where a one-liter cube, 10 cm on a side, needs 600 cm². That economy is why soap bubbles and small droplets pull themselves round, and why a spherical tank needs the least wall area for what it holds.

No unit is imposed. Whatever length your volume is cubed in comes back for the radius and diameter, and squared for the area, so cubic centimeters give centimeters and square centimeters. A liter is 1,000 cm³, so convert first if your figure is in liters. The calculation assumes a solid, perfectly round sphere; a hollow shell or a squashed ellipsoid needs a different approach.

What is radius of sphere calculator?

The radius of a sphere is the distance from its center to any point on its surface. Every such distance is the same, which is what makes the shape a sphere, and the diameter, twice the radius, is the widest straight line through it. Because V = 4⁄3 πr³ ties the two together exactly, a single measurement of capacity or displaced water is enough to fix the radius, the diameter and the surface area of a ball.

How to use this calculator.

1. 01Enter the volume in any cubic unit: cm³, m³ or cubic inches. Milliliters are already cubic centimeters; liters need multiplying by 1,000 first.
2. 02To measure a solid ball, submerge it completely in a graduated container of water and read the rise in level; the displaced water equals the ball's volume. If you know its mass and density instead, the volume is mass divided by density.
3. 03Read the radius and diameter in the matching length unit and the surface area in that unit squared.
4. 04For a hollow ball or tank, the capacity it holds gives the inner radius and the water it displaces gives the outer radius; one volume alone cannot give the wall thickness.

The formula.

r = (3V ÷ 4π)^(1/3). It comes from rearranging the volume formula V = 4⁄3 πr³: multiply both sides by 3, divide by 4π, then take the cube root. V is the volume, π is about 3.14159265, and the cube root is the step that turns a volume back into a length. The diameter follows as d = 2r and the surface area as A = 4πr², which can also be written straight from the volume as A = ∛(36πV²). Because the radius depends on the cube root of the volume, it moves slowly: multiplying V by 8 doubles r, and multiplying V by 1,000 multiplies r by 10. The area grows faster, with V to the power two-thirds, so eight times the volume means four times the surface. Volume must be positive, and the shape is assumed to be a perfect solid sphere.

A worked example.

Frequently asked questions.

References& sources.

1. [1]OpenStax, Rice University. Precalculus 2e, 2021. Trigonometry and analytic geometry chapters. Retrieved 2026-08-06.
2. [2]OpenStax, Rice University. College Algebra 2e, 2021. Algebra and function chapters. Retrieved 2026-08-06.
3. [3]NIST/SEMATECH. e-Handbook of Statistical Methods, 2012. Chapter 1.3 and Chapter 4. Retrieved 2026-08-06.