Rectangular Prism Volume Calculator
Fast, accurate and free online rectangular prism volume calculator tool running directly in your browser.
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Other tools you may find usefulVolume of a cuboid - precise online geometric calculator
A cuboid is one of the most common three-dimensional solids in our environment. Cardboard boxes, furniture, rooms, garden pools, aquariums, and even entire buildings - most of these objects have a cuboidal shape. Understanding how to calculate the volume (capacity) of such a figure is useful in many life and professional situations. It helps to plan the amount of soil needed to fill a trench, calculate the capacity of a fish aquarium, check the capacity of a car trunk or determine the costs of shipping a courier parcel. Our quick cuboid volume calculator allows you to quickly determine the volume of a solid based on the given dimensions.
How to calculate the volume of a cuboid? Mathematical formula
Calculating the volume of a cuboid is very simple, provided that we know the lengths of its three edges converging at one vertex. These are usually: width (a), length (b) and height (h) or depth (c).
The formula for the volume of a cuboid is:
V = a * b * c
Where:
- V– volume,
- a– length of the first edge of the base,
- b– length of the second edge of the base,
- c(or h) – height (length of the side edge).
Important rule:Before multiplying, make sure that all three dimensions (a, b, c) are inthe same unit of measurement(e.g. all in centimeters or all in meters). If the dimensions are mixed (e.g. width in centimeters and height in meters), you must first convert the units.
Volume units – how to convert cubic centimeters, liters and cubic meters?
Volume is expressed in cubic units (resulting from multiplying three linear units) or fluid capacity units. Here are the most popular of them and the relationships between them:
- Milliliter (ml) and cubic centimeter (cm³):These are the same units. 1 cm³ is exactly 1 ml. Used for small items, cosmetics or medicine doses.
- Liter (l) and cubic decimeter (dm³):1 letter is exactly 1 dm³. A cubic decimeter is a cube with sides of 10 cm. The relation here is:1 letter = 1000 cm³ (ml).
- Cubic meter (m³, so-called cubic):Standard unit in construction, forestry and water supply. This is the space equivalent to a cube with sides of 1 meter.1 m³ = 1000 liters (dm³) = 1,000,000 cm³.
Conversion table of the most popular volume units
The table below helps you quickly understand the proportions between volume units:
| Output unit | in centimeters cubic (cm³) / ml | in cubic decimeters (dm³) / liters | in cubic meters (m³) / cubic |
|---|---|---|---|
| 1 cm³ (1 ml) | 1 | 0.001 | 0.000001 |
| 1 dm³ (1 letter) | 1,000 | 1 | 0.001 |
| 1 m³ (1 cubic) | 1,000,000 | 1,000 | 1 |
Examples of calculating the volume of a cuboid step by step
Example 1: Calculating the capacity of an aquarium in liters
Let's assume that you bought an aquarium with dimensions: length 80 cm, width 40 cm and height 50 cm. You want to know how many liters of water will fit inside.
1. All dimensions are in centimeters, so we can multiply them: V = 80 cm * 40 cm * 50 cm = 160,000 cm³.
2. We know that 1 liter is 1000 cm³. We divide the result by 1000: V = 160,000 / 1000 = 160 letters.
The aquarium has a maximum capacity of 160 liters (remember that in practice slightly less water is poured due to the substrate and the margin from the top edge).
Example 2: Calculation of the volume of concrete in the foundation excavation (cubic meters)
The project assumes pouring a foundation footing 12 m long, 50 cm (0.5 m) wide and 40 cm (0.4 m) deep.
1. We reduce the dimensions to a common unit (meters): length = 12 m, width = 0.5 m, depth = 0.4 m.
2. Multiply the values: V = 12 m * 0.5 m * 0.4 m = 2.4 m³.
You will need exactly 2.4 cubic meters (cubic meters) of concrete to fill this trench.
Frequently asked questions (FAQ)
What is the simplest formula for the volume of a cuboid?
The simplest formula is V = a * b * c, where a, b, c are the lengths of three edges touching at one vertex of the solid. Optionally, it is written as V = Pp * h, where Pp is the area of the base (a * b) and h is the height of the cuboid.
How to convert cubic centimeters (cm³) to liters?
To convert cm³ to liters, divide the number of cubic centimeters by 1000. For example, a volume of 5000 cm³ corresponds to exactly 5 liters (5000 / 1000 = 5).
What is the difference between a cube and a cuboid?
A cube is a special case of a cuboid. In a cube, all faces are identical squares, which means that all its edges are exactly the same length (a = b = c). The formula for the volume of a cube then shortens to V = a³.
How to calculate the capacity of a cuboid in liters, given its dimensions in decimeters?
Since 1 cubic decimeter (dm³) is exactly 1 letters, simply multiply the dimensions given in decimeters. For example, a box with dimensions of 3 dm x 4 dm x 5 dm has the volume: V = 3 * 4 * 5 = 60 dm³, which means a capacity of exactly 60 letters.
How to calculate the volume of a room for the selection of an air conditioner?
To select an air conditioner or heater power, the cubic capacity of the room (i.e. its volume) is crucial. Measure the length and width of the room at floor level, then the height from floor to ceiling. Multiply these three values by each other. For example, a room measuring 4 m by 5 m and 2.5 m high has a volume of V = 4 * 5 * 2.5 = 50 m³ (cubic).