Volume Calculator for 3D Shapes
This volume calculator works out how much space a three-dimensional shape occupies. Choose one of the five most common solids — cube, rectangular box, sphere, cylinder or cone — enter its dimensions, and the volume is computed instantly as you type. It is handy for schoolwork and geometry homework, but also for everyday tasks: estimating how much water a tank holds, how much soil fills a planter, the capacity of a box for shipping, or the concrete needed for a cylindrical column. Just make sure every measurement uses the same unit, and the answer comes back in the matching cubic unit.
Enter every measurement in the same unit of length. The result is expressed in cubic units of that unit (for example, if you use centimeters the volume will be in cm³).
Volume
Publicidad
How it works
Each solid has its own formula. A cube of side s has volume s³ (three equal edges multiplied together). A rectangular box multiplies its length, width and height: l · w · h. A sphere of radius r uses 4/3 · π · r³. A cylinder is the area of its circular base times its height: π · r² · h. A cone holds exactly one third of the cylinder that would enclose it, so its volume is 1/3 · π · r² · h. The calculator applies the formula for the shape you select and formats the result to three decimals. Because π is irrational, sphere, cylinder and cone results are approximations, while the cube and box are exact.
Volume formulas for the most common shapes
Each geometric solid has its own volume formula. This table gathers the six most used, with the letter r for the radius, h for the height and s for the edge of the cube. Notice that the cone and the pyramid carry the 1/3 factor: they hold exactly one third of the cylinder or prism that would share their base and height.
| Shape | Volume formula |
|---|---|
| Cube | s³ (edge cubed) |
| Rectangular box | l · w · h |
| Cylinder | π · r² · h |
| Sphere | 4/3 · π · r³ |
| Cone | 1/3 · π · r² · h |
| Pyramid | 1/3 · base area · h |
Worked example and units
Take a cylinder with a radius of 5 cm and a height of 10 cm. Applying π · r² · h gives π · 25 · 10 = 785.40 cm³ (for comparison, a sphere of radius 3 cm gives 113.10 cm³ and a cone of radius 5 cm and height 10 cm gives 261.80 cm³). To convert that volume to liters, remember that 1 liter equals 1000 cm³: those 785.40 cm³ are 0.785 liters. The one essential rule is to use the same unit of length for every measurement so the result comes out in the correct cubic unit.
Publicidad
Preguntas frecuentes
- What units does the result use?
- The calculator is unit-agnostic: it uses whatever unit you enter. If your dimensions are in centimeters the volume is in cubic centimeters (cm³); if they are in meters it is in cubic meters (m³). The key rule is to enter every measurement in the same unit so the result is consistent.
- How do I convert the volume to liters?
- One liter equals 1000 cubic centimeters (1 dm³). So if you measured in centimeters, divide the cm³ result by 1000 to get liters. If you measured in meters, one cubic meter equals 1000 liters, so multiply the m³ result by 1000.
- What is the difference between the diameter and the radius?
- The radius is the distance from the center of a circle or sphere to its edge, while the diameter goes all the way across through the center. The diameter is twice the radius. This calculator asks for the radius, so if you only know the diameter, divide it by two first.
- Why is a cone exactly one third of a cylinder?
- A cone and a cylinder with the same base radius and the same height are related by a factor of three: three identical cones would fill one cylinder. That is why the cone formula 1/3 · π · r² · h is simply the cylinder formula divided by three.
- Are the results exact?
- The cube and rectangular box are exact because they involve only multiplication of your inputs. The sphere, cylinder and cone use π, which is an irrational number, so those results are rounded approximations — here to three decimal places, which is precise enough for almost any practical purpose.