- What is volume? Volume definition
- Volume units, conversion table
- How to calculate volume? Volume formulas
- Volume calculator and tools dedicated to specific shapes
- Volume calculator - how to use
- Measuring the volume of solids, liquids and gases
- How to find the volume of a rectangle vs volume of a box
- Real-life applications
The volume calculator will calculate the volume of some of the most common three-dimensional solids. Before you go into how to calculate volume, you must know the definition of volume. Volume differs from the area, which is the amount of space taken up in a two-dimensional figure. Therefore you might be confused as to how to find the volume of a rectangle versus how to find the volume of a box. The calculator will assist in calculating the volume of a sphere, cylinder, cube, cone, and rectangular solids.
What is volume? Volume definition
Volume is the amount of space that an object or substance occupies. Generally, the volume of a container is understood as its capacity - not amount of space the container itself displaces. Cubic meter is an SI unit for volume.
However, the term volume may also refer to many other things, such as
Volume units, conversion table
Popular units of volume are:
- Metric volume units
- cubic centimeters (cm³)
- cubic meters (m³)
- liters (l, L)
- milliliters (ml, mL)
- US Standard, UK
- fluid ounce (fl oz)
- cubic inch (cu in)
- cubic foot (cu ft)
- pints (pt)
- quarts (qt)
- gallons (gal)
If you need to convert the units of volume, you can use our great volume converter. Other useful tool is a grams to cups calculator which can help if you want to use a food recipe from different country. Note that it's not a simple conversion, but change from weight (grams) to volume unit (cups) - that's why you need to know the ingredient type (or more specifically, its density).
Also, you can have a look at this neat volume unit conversion table to find out the conversion factor in a blink of an eye:
|cubic inches||cubic feet||cubic yards||us liquid gallons||us dry gallons||imp liquid gallons||barrels (oil)||cups||fluid ounces (UK)||fluid ounces (US)||pints (UK)|
|cubic metre||6.1 104||35.3||1.308||264.2||227||220||6.29||4227||3.52 104||3.38 104||1760|
|cubic decimetre||61.02||0.035||1.3 10-3||0.264||0.227||0.22||0.006||4.23||35.2||33.8||1.76|
|cubic centimetre||0.061||3.5 10-5||1.3 10-6||2.64 10-4||2.27 10-4||2.2 10-4||6.29 10-6||4.2 10-3||3.5 10-2||3.34 10-2||1.76 103|
|cubic millimetre||6.1 10-5||3.5 10-8||1.31 10-9||2.64 10-7||2.27 10-7||2.2 10-7||6.3 10-9||4.2 10-6||3.5 10-5||3.4 10-5||1.76 10-6|
|hectoliters||6.1 103||3.53||0.13||26.4||22.7||22||0.63||423||3.5 103||3381||176|
|liters||61||3.5 10-2||1.3 10-3||0.26||0.23||0.22||6.3 10-3||4.2||35.2||33.8||1.76|
|centiliters||0.61||3.5 10-4||1.3 10-5||2.6 10-3||2.3 10-3||2.2 10-3||6.3 10-5||4.2 10-2||0.35||0.338||1.76 10-2|
|milliliters||6.1 10-2||3.5 10-5||1.3 10-6||2.6 10-4||2.3 10-4||2.2 10-4||6.3 10-6||4.2 10-3||3.5 10-2||3.4 10-2||1.76 10-3|
|cubic inches||1||5.79 10-4||2.1 10-5||4.3 10-3||3.7 10-3||3.6 10-3||10-4||6.9 10-2||0.58||0.55||2.9 10-2|
|cubic yards||4.7 104||27||1||202||173.6||168.2||4.8||3232||2.69 104||2.59 104||1345|
|us liquid gallons||231||0.134||4.95 10-3||1||0.86||0.83||0.024||16||133.2||128||6.7|
|us dry gallons||268.8||0.156||5.76 10-3||1.16||1||0.97||0.028||18.62||155||148.9||7.75|
|imp liquid gallons||277.4||0.16||5.9 10-3||1.2||1.03||1||0.029||19.2||160||153.7||8|
|cups||14.4||8.4 10-3||3.1 10-4||6.2 10-2||5.4 10-2||5.2 10-2||1.5 10-3||1||8.3||8||0.4|
|fluid ounces (UK)||1.73||10-3||3.7 10-5||7.5 10-3||6.45 10-3||6.25 10-3||1.79 10-4||0.12||1||0.96||5 10-2|
|fluid ounces (US)||1.8||10-3||3.87 10-5||7.8 10-3||6.7 10-3||6.5 10-3||1.89 10-4||0.13||1.04||1||0.052|
|pints (UK)||34.7||0.02||7.4 10-4||0.15||0.129||0.125||3.57 103||2.4||20||19.2||1|
How to calculate volume? Volume formulas
There is no simple answer to this question, as it depends on the type of geometric solid. Here are the formulas for some of the most common figures:
s³, where s is the length of the side.
(4/3)πr³, where r is the radius.
πr²h, where r is the radius and h is the height.
(1/3)πr²h, where r is the radius and h is the height.
Rectangular solid (volume of a box) =
lwh, where l is the length, w is the width and h is the height (a simple pool may serve as an example of such shape).
(1/3)Ahwhere A is a base area and h is the height. For a pyramid with a regular base, other equation may be used as well: Pyramid =
(n/12) * h * side_length² * cot(π/n), where n is a number of sides of the base for a regular polygon.
πAh, where A is a base area and h is the height. For a right triangular prism, the equation can be easily derived, as well as for a right rectangular prism, which is apparently the same shape as a box.
|Cube||V = s³|
|Right Rectangular Prism (cuboid, box)||V = lwh|
|Prism or Cylinder||V = Ah|
|Pyramid or Cone||V = Ah/3|
|Sphere||V = 4πr³/3|
Volume calculator and tools dedicated to specific shapes
We've decided to make this volume calculator - one simple tool which covers five basic most popular 3D shapes. However, not every volume equation and shape type may be implemented here as it will make the calculator overloaded and unintuitive. So if you're looking for a specific shape, check out the calculators dedicated to volumes of chosen shapes:
Volume calculator - how to use
Let's look at the example of how to use this volume calculator:
Select the 3D shape type. If you can't find the shape you want to calculate the volume of, choose other special dedicated calculators (you'll find the links above). In this example, let's assume you want to calculate the volume of a cylinder.
Choose the right section of the volume calculator. In our case, it's the part titled Cylinder volume.
Type given data into proper boxes. Our cylinder has a radius of 1 ft and a height of 3 ft. You can change the units by a simple click on the unit name.
Here you go! The volume of a chosen shape is displayed. In our case, it's 9.42478 cu ft.
If you want to check how much is that in US barrels unit, just click on the unit name and choose barrels from a drop-down list. Our cylinder has a capacity of ~2.24 oil barrels.
Measuring the volume of solids, liquids and gases
How to find the volume of an object in different states of matter?
So, if you want to measure an irregular object's volume, just follow Archimedes footsteps (though you can omit the naked race part):
Take a container bigger than the object you want to measure the volume of. It may be e.g. a bucket, a measuring cup, a beaker, or a graduated cylinder. It should have a scale.
Pour water into the container and read the volume measurement.
Put the object inside. It should be totally submerged to measure the object whole volume. Read the volume value. This method won't work if your object dissolves in water.
The difference between the measurements is the volume of our object.
The measurements done are the essentials for calculating the buoyancy force which can be found basing on Archimedes' principle.
Usually, it's also easy to measure the volume of a liquid - all you need to have is a graduated measuring vessel of some kind. Choose the one that fits your needs: the amount of liquid and degree of accuracy are the parameters to consider. Other container will be used for cake recipe (check out awesome calculator for a pancake recipe), different in chemistry (e.g. in molar concentration calculations) and another for medical purposes (like dose of a medication).
We have to use more elaborate methods to measure the volume of a gas. You need to remember that the volume of gas is influenced by temperature and pressure, and that gases expand to fill any container in which they're placed. You can try to measure it:
Inflate a balloon with the gas you want to measure (e.g., with helium, to lift you up in the air). Then you can use the Archimedes method - put the balloon into the bucket with water and check the volume difference. You'll find detailed instructions here.
Check out the measures connected to your lung capacity by using a device called spirometer.
In chemistry, gas syringe is used to insert or withdraw a volume of a gas from a closed system. This laboratory glassware can also be used to measure the volume of gas evolved from a chemical reaction.
Find the volume of the gas, given its density and mass. Use simple
V = m / dvolume equation.
Calculate the volume of a compressed gas in a cylinder applying ideal gas equation.
How to find the volume of a rectangle vs volume of a box
You can't calculate a volume of a rectangle, a volume of a circle or a volume of a square, because they are 2-dimensional geometric figures. As such, a rectangle does not have a volume (but it does have an area). What you're probably looking for is the volume of a rectangular cuboid (or, in more common terms, you want to find the volume of a box), which is a 3-dimensional figure.
To find the volume of a box, simply multiply length, width, and height - and you're good to go! For example, if a box is 5x7x2 cm, then the volume of a box is 70 cubic centimeters. For dimensions that are relatively small whole numbers, calculating volume by hand is easy. For larger or decimal valued numbers, the use of the volume calculator is very efficient.
There are many applications in real life where the volume calculator is useful. One such instance is in road or pavement construction where slabs of concrete must be built. Generally, concrete slabs are rectangular solids, so the concrete calculator - which is an application of the volume calculator - can be used.
Also, the volume formulas may be helpful if you are a keen gardener or just a happy owner of a house with a yard. Check out our awesome tools such as:
mulch calculator to find the amount of mulch needed for you garden project
gravel calculator which can help in planning a gravel driveway construction
Moreover, you can meet volume in your kitchen or bathroom: any liquid we drink (e.g. bottled water), as well as beauty products or a toothpaste have a volume written on the product packaging (either in milliliters/liters or fluid ounces/gallons).
Another related application, although slightly different, is the concept of surface area. Suppose the entire exterior of a building must be painted. To know how much paint must be purchased, the surface area of the building must be calculated. The convenient to use surface area calculator will calculate this for you.