The volume calculator will certainly calculate the volume of some of the most typical three-dimensional solids. Prior to we enter how to calculation volume, friend must recognize the definition of volume. Volume different from the area, i beg your pardon is the quantity of room taken up in a two-dimensional figure. For this reason you can be confused regarding how to find the volume that a rectangle versus how to uncover the volume that a box. The calculator will help in calculating the volume of a sphere, cylinder, cube, cone, and also rectangular solids.

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What is volume? — Volume definition

Volume is the quantity of an are that an item or problem occupies. Generally, the volume of a container is interpreted as its volume — no the quantity of an are the container itself displaces. Cubic meter (m3) is one SI unit for volume.

However, the hatchet volume may likewise refer to countless other things, together as

the number or lot of other (usually large quantity)formal word because that a book or one in a set of related books.

Volume units and conversion table

Popular devices of volume are:

Metric volume unitsCubic centimeters (cm³)Cubic meters (m³)Liters (l, L)Milliliters (ml, mL)US Standard, UKFluid oz (fl oz)Cubic customs (cu in)Cubic foot (cu ft)CupsPints (pt)Quarts (qt)Gallons (gal)

If you require to convert the devices of volume, you can use our great volume converter. An additional useful tool is ours grams to cup calculator, i beg your pardon can assist if you want to use a food recipe from a various country. Note that it's not a straightforward conversion, but readjust from load (grams) come volume unit (cups) — that's why you require to know the ingredient kind (or much more specifically, that density).

Also, you deserve to have a look in ~ this practiced volume unit switch table to find out the conversion aspect in a blink of an eye:

cubic customs cubic feet cubic yards united state liquid gallons us dry gallons imp fluid gallons barrels (oil) cups fluid ounces (UK) liquid ounces (US) pints (UK)
cubic meter 6.1 104 35.3 1.308 264.2 227 220 6.29 4227 3.52 104 3.38 104 1760
cubic decimeter 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 centimeter 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 millimeter 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 feet 1728 1 0.037 7.48 6.43 6.23 0.18 119.7 997 958 49.8
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 fluid gallons 277.4 0.16 5.9 10-3 1.2 1.03 1 0.029 19.2 160 153.7 8
barrels (oil) 9702 5.61 0.21 42 36.1 35 1 672 5596 5376 279.8
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 an easy answer come this question, as it relies on the form of the object in question. Right here are the recipe for some of the most common shapes:

Cube = s³, wherein s is the length of the side.

Sphere = (4/3)πr³, wherein r is the radius.

Cylinder = πr²h, where r is the radius and h is the height.

Cone = (1/3)πr²h, where r is the radius and h is the height.

Pyramid = (1/3)Ah where A is a base area and also h is the height. Because that a pyramid with a constant base, other equation may be used as well: Pyramid = (n/12) * h * side_length² * cot(π/n), where n is a number of sides the the base because that a constant polygon.

Prism = πAh, where A is a basic area and h is the height. For a right triangular prism, the equation deserve to be quickly derived, as well as for a right rectangular prism, which is apparently the same shape together a box.

form Name Formula


Cube V = s³


Right rectangle-shaped Prism (cuboid, box) V = lwh


Prism or Cylinder V = Ah


Pyramid or Cone V = Ah/3


Sphere V = 4πr³/3

Volume calculator and tools committed to certain shapes

We've chose to do this volume calculator a simple tool which covers the five most well-known 3D shapes. However, not every volume equation and also shape kind may be enforced here, as it will make the calculator overloaded and also unintuitive. For this reason if you're trying to find a certain shape, examine out the calculators specialized to quantities of chosen shapes:

How execute I usage the volume calculator?

Let's look at the example of exactly how to usage this volume calculator:

Select the 3D form type. If you can't uncover the form you desire to calculate the volume of, choose other special devoted calculators (you'll uncover the links above). In this example, let's assume you want to calculation the volume that a cylinder.

Choose the best section the the volume calculator. In our case, it's the component titled Cylinder volume.

Type given data into appropriate boxes. Our cylinder has actually a radius the 1 ft and a elevation of 3 ft. Girlfriend can change the devices by a straightforward click on the unit name.

Here friend go! The volume that a liked shape is displayed. In our case, it's 9.42478 cu ft.

If you want to check how lot that is in us barrels unit, just click the unit name and choose barrels from the drop-down list. Ours cylinder has a volume of ~2.24 oil barrels.

Measuring the volume that solids, liquids and also gases

How to find the volume the objects with different states of matter?

1. Solid

For continual three-dimensional objects, friend can quickly calculate the volume by taking measurements of the dimensions and also applying the appropriate volume equation. If it's an rarely often rare shape, girlfriend can shot to perform the very thing that led to Archimedes to shout the famed word *Eureka*! more than likely you heard that story - Archimedes to be asked to discover out if the Hiero's crown is do from pure gold or just gold-plated - however without bending or destroying it. The idea concerned him once he was acquisition a bath - stepping into a bathtub, the noticed that the water level rose. From this observation, he deduced the volume that water displaced must be same to the volume of the part of his human body he had submerged. Discovering the irregular object volume and also its weight, he can calculate the density and compare it with the density of pure gold. Legend claims that Archimedes was so excited around this exploration that that popped the end of his tub and ran naked v the roadways of Syracuse.

So, if you want to measure an irregular object's volume, just follow Archimedes footsteps (though you can omit the naked gyeongju part):


Take a container bigger 보다 the object you want to measure up the volume of. It may be a bucket, a measure up cup, a beaker, or a i graduated cylinder. It should have a scale.

Pour water right into the container and read the volume measurement.

Put the thing inside. It must be completely submerged to measure up the objects entirety volume. Check out off the volume. This an approach won't work if her object disappear in water.

The difference in between the dimensions is the volume of our object.

These dimensions are necessary in calculating the buoyancy pressure which are based upon Archimedes' principle.

2. Liquid


Usually, it's fairly easy to measure the volume of a liquid - all you require to have actually is a graduated measuring vessel of some kind. Pick the one the fits your needs: the quantity of liquid and degree the accuracy space the parameters come consider. The containers supplied in baking a cake (check the end awesome calculator because that a pancake recipe) will be various to those provided in chemistry (e.g. In molar concentration calculations) will certainly be different to ones used for medical purposes (like sheep of a medication).


3. Gas

We need to use an ext elaborate approaches to measure the volume of a gas. You need to remember that the volume that gas is affected by temperature and also pressure, and that gases broaden to fill any type of container in i m sorry they're placed. You can shot to measure it:

In chemistry, a gas syringe is supplied to insert or retract a volume that a gas indigenous a closeup of the door system. This laboratory glassware can also be supplied to measure up the volume of gas evolved from a chemical reaction.

Or calculate:

Find the volume of the gas, given the density and also mass. Use simple V = m / d volume equation.

How to uncover the volume of a rectangle vs volume of a box

You can't calculate a volume that a rectangle, a volume the a circle or a volume the a square due to the fact that they room 2-dimensional geometric figures. Together such, a rectangle walk not have actually a volume (but the does have an area). What you're probably trying to find is the volume of a rectangle-shaped cuboid (or, in much more common terms, you desire to discover the volume that a box), i beg your pardon is a 3-dimensional object.

To uncover the volume of a box, merely multiply length, width, and also height — and you're good to go! because that example, if a box is 5×7×2 cm, then the volume of a crate is 70 cubic centimeters.For dimensions the are reasonably small entirety numbers, calculating volume by hand is easy. For bigger or decimal valued numbers, the usage of the volume calculator is an extremely efficient.

Real-life applications

There are plenty of applications in real life wherein the volume calculator is useful. One such circumstances is in road or pavement construction, whereby slabs that concrete should be built. Generally, concrete slabs are rectangular solids, therefore the concrete calculator — i beg your pardon is an application of the volume calculator — have the right to be used.

Also, the volume formulas might be beneficial if you are a crawl gardener or just a happy owner that a home with a yard. Examine out ours awesome tools such as:

Moreover, girlfriend can satisfy volume in your kitchen or bathroom: any liquid we drink (e.g. Bottled water), as well as beauty assets or a toothpaste have a volume composed on the product packaging (either in milliliters/liters or liquid ounces/gallons).

Another associated application, although slightly different, is the principle of surface area. Mean the whole exterior that a building must it is in painted. To know how much paint need to be purchased, the surface ar area that the building must be calculated. The convenient to use surface ar area calculator will certainly calculate this for you.

How to find volume?

The volume formula depends ~ above the form of the object. Among the most popular shapes is a rectangular prism, additionally known together a box, wherein you can simply multiply length times broad times height to find its volume. An additional common shape is a cylinder — to find its volume, main point the height of the cylinder through the area of its basic (π × r2). For various other 3D shapes, inspect Omni's Volume Calculator.

How execute I measure volume?

Measuring the volume depends on her object's state the matter. For liquids, you have the right to use a i graduated cylinder or burette for the chemistry laboratory measurements, or a measuring cup & spoon for day-to-day life purposes. For gases, to approximately measure the volume, you have the right to inflate a balloon and also use it come displace the water in a graduate cylinder. A similar method works because that solids — placed the object into a graduated container and also measure the readjust in reading.

Is volume squared or cubed?

Volume is "cubed", as it's a three-dimensional measure. Area is a "squared" value, together the area the a shape covers 2 dimensions. You deserve to remember the volume is a cubed worth by recalling a few volume unit names, such together cubic meters, cubic feet or cubic yards.

How carry out I calculate volume?

Depending on her object shape, you can use various formulas to calculation volume:

Cube volume = side3Cuboid (rectangular box) volume = length × width × heightSphere volume = (4/3) × π × radius3Cylinder volume = π × radius2 × heightCone volume = (1/3) × π × radius2 × heightPyramid volume = (1/3) × base area × height

What is volume measure in?

A cubic meter is the SI volume unit. However, together it's fairly impractical, most frequently you will encounter volume expressed in:

Cubic centimetersCubic inchesMillilitersLitersGallons

How to find volume of a liquid?

Graduated cylinders and also Erlenmeyer flasks will work if you require to roughly measure the volume the a liquid. For much more precise measurements, you should use a volumetric pipette and also burette. However, if you're baking a cake or prepare a delicious dish and the recipe provides volume units, you can simply use a measure cup, glass or spoon.

What is the SI unit for volume?

The cubic meter (m3) is the SI unit the volume. That is derived from the basic SI unit of size — the meter. Return the cubic meter is the basic SI unit, other units room used an ext often: for the metric system milliliters, liters, or cubic centimeters are well-known choices, while because that the royal system friend can discover volume expressed in pints, gallons, cubic inches, cubic feet or cubic yards.

Is volume intensive or extensive?

Volume is an extensive property, the same as the amount of substance, mass, energy, or entropy. An extensive property is a measure the depends top top the amount of matter. Examine out this example: a glass, a barrel, and also a pool full of water have different volumes & masses (extensive properties), yet water in these three containers will have the exact same density, refractive table of contents & viscosity (intensive properties).

What is the difference in between surface area and also volume?

A volume is a 3D measure, when surface area is two-dimensional. The volume speak us around the cubic space that things occupies, and the surface ar area is the sum of all areas forming the 3D shape. Take the cardboard box as instance 📦:

Volume is the lot of an are taken increase by the box — simply, it's the space easily accessible inside the box.Surface area is the space inhabited by the box's sides, calculated as soon as painting the sides or wrapping the box in paper.

How to uncover the volume of an irregular-shaped object?

You can use the liquid displacement method because that the irregular shaped solid objects:

Fill the container through water and also mark the water level.Drop her object inside and also mark the level again. Make certain your object isn't dissolve in water.For scaled containers, you can just subtract the original volume native the brand-new volume. And that's it, congrats!

But if your original container doesn't have actually a scale:

Take out the object.Fill her container with water to the 2nd mark, pour the water right into a i graduated cylinder/another measure up vessel.Repeat step 6 for another marked level and subtract the volumes.Pat yourself on the back — you uncovered the volume of an irregular-shaped object!

What does volume measure?

The volume actions the amount of an are taken increase by an item in three dimensions. Another closely associated term is capacity, which is the volume of the interior of the object. In other words, the capacity describes how lot the container deserve to hold (water, gas, etc.).

See more: Approximately How Many Mp3 Fit On 32Gb, How Much Music Does A 32Gb Sd Card Hold

What is the volume the the Earth?

The volume that the earth is about equal to 1.08321×1012 km3 (1.08 quadrillion cubic kilometers), or 2.59876×1011 cu mi (259 sunshine cubic miles). Friend can get this an outcome using the sphere volume formula (4/3) × π × radius3 and also assuming that the Earth's median radius is 6,371 kilometers (3,958.76 mi).

How do I calculate surface ar area come volume ratio?

To calculation the surface ar area to volume ratio SA:V, you merely divide the surface area by volume. Because that some liked shapes:

SA:V proportion for cube = (6 × side2) / (side3) = 6 / sideSA:V proportion for sphere = (4 × π × radius2) / ((4/3) × π × radius3)= 3 / radiusSA:V ratio for cylinder = (2 × π × radius2 + 2 × π × radius × height) / (π × radius2 × height) = 2 × (radius + height) / (radius × height)