Volume Calculator: Sphere, Cube, Cylinder, Cone & Prism

Q: What units is volume measured in?

Volume uses **cubic units** such as $cm^3$, $m^3$, $in^3$, and $ft^3$. For liquid capacity, common conversions are **1 L = 1,000 cm³** and **1 US gallon ≈ 231 in³ ≈ 3.785 L**. The calculator does not guess the unit; it returns cubic units matching the dimensions you entered.

Q: Should I enter radius or diameter?

For spheres, cylinders, and cones, this calculator uses **radius**. If you measured diameter, divide by 2 first: $$ r = \frac{d}{2} $$ A cylinder with a **10 cm diameter** has radius **5 cm**, so the cylinder formula uses $r = 5$, not $r = 10$.

Q: Why is a cone one-third of a cylinder with the same base and height?

A cone with the same radius and height as a cylinder has one-third of the cylinder volume: $$ V_{cone} = \frac{1}{3}\pi r^2h $$ For $r = 5$ and $h = 10$, the cylinder is **785.40 cm³** and the matching cone is **261.80 cm³**.

Q: Why can real container capacity differ from the calculated volume?

The formula assumes a perfect shape and full usable space. Real capacity can be lower because of wall thickness, rounded corners, handles, lids, fill lines, sloping sides, trapped air, or a safety gap at the top. For buying materials or sizing a tank, measure the internal dimensions and add a practical margin.

Result

Volume

523.5988 cubic units

Shape

Sphere

Formula

(4/3)πr³

Volume (cm³→L)

0.5236 L (if cm)

Radius5 units

Volume523.5988 cubic units

Volume of sphere = 523.5988 cubic units

How this calculator works

Use the explanation to understand the formula, assumptions, and practical limits behind the calculator result.

What Volume Measures

Volume is the amount of three-dimensional space inside a solid shape. If the dimensions are in centimeters, the result is in cubic centimeters; if they are in meters, the result is in cubic meters. Every length input must use the same unit before calculation.

Formulas Used by This Calculator

Shape	Inputs	Volume formula
Sphere	radius $r$	$V = \frac{4}{3}\pi r^3$
Cube	side $s$	$V = s^3$
Cylinder	radius $r$ , height $h$	$V = \pi r^2h$
Cone	radius $r$ , height $h$	$V = \frac{1}{3}\pi r^2h$
Rectangular prism	length $l$ , width $w$ , height $h$	$V = lwh$

Radius is half the diameter. If a container label gives a diameter of 10 cm, enter a radius of 5 cm.

Worked Example — Cylinder

For a cylinder with radius 5 cm and height 10 cm:

V = \pi \times 5^2 \times 10 = 785.40\text{ cm}^3

Because 1 liter = 1,000 cm³, the same volume is:

785.40 \div 1,000 = 0.7854\text{ L}

How to Use the Result

Use the volume result for storage estimates, container sizing, concrete or fill calculations, aquarium planning, packaging checks, geometry problems, and comparing shape efficiency. For materials, add a margin for spillage, compaction, wall thickness, uneven surfaces, or unusable internal space.

Limits to Check

This calculator assumes ideal geometric shapes. Real containers often have rounded corners, tapered sides, lids, wall thickness, fill lines, and safety headroom. Measure internal dimensions when you need usable capacity rather than outer package size.

Frequently asked questions

What units is volume measured in?

Should I enter radius or diameter?

Why is a cone one-third of a cylinder with the same base and height?

Why can real container capacity differ from the calculated volume?