How to Calculate the Volume of an Irregular Object
Make sure the object is waterproof before you begin., Find a container that can comfortably fit the object you are measuring., Fill it partway with water., Mark the water level., Drop the object into the water and see if it absorbs water., Learn...
Step-by-Step Guide
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Step 1: Make sure the object is waterproof before you begin.
This method involves submerging the object in water.
If the object is hollow and not watertight, you cannot get an accurate measure of volume using this method.
If the object absorbs water, make sure water will not damage it, and read the instructions carefully to see how to adjust the process.
Never drop an electric or electronic item in water, as this could cause a dangerous electrical shock and/or damage the object beyond repair.
If you have access to a vacuum sealer, you may be able to seal a small object in a watertight plastic coating with minimal air inside.
This will allow you to get a good estimate of volume, since the volume of the plastic used is likely to be relatively small compared to the volume of the object. -
Step 2: Find a container that can comfortably fit the object you are measuring.
If you are measuring a small object, you could use a graduated cylinder or measuring cup, which have volume measurements printed on the side.
Otherwise, find a watertight container with a volume that is simple to calculate, such as a cylinder or rectangular box.
A bowl will not be as accurate, but you can treat it as a cylinder and get an approximate answer, especially if the object is very small compared to the bowl.
It's a good idea to locate a dry towel as well, since the object will be dripping water when removed from the container. , Add enough water to submerge the object, but leave plenty of space between the water and the top of the container.
If the object has an irregularly shaped base, such as rounded bottom corners, fill it up enough that the water level reaches a more regular portion, such as straight rectangular walls. , If the container is transparent, mark the top of the water level on the outside with a wet-erase marker or other easily cleaned writing device.
Otherwise, mark the water level on the inside using a piece of colored tape or other mark that will not be washed off by the water.
If you are using a graduated cylinder or measuring cup with volume measurements on the side, you do not need to make a mark.
Just look for the volume measurement at the water's surface, and write this number down. , Sink the object you want to measure completely in the water.
If the object absorbs water, wait at least thirty seconds for it to absorb the water, then remove the object.
The water level should have dropped, since some of the water is in the object.
Remove your old mark or piece of colored tape, and replace it with a new one at the new water level.
You may then drop the object into the water a second time and leave it there. , If the object floats, attach a dense, heavy item to it and continue on to measure the volume of both combined.
After you write down that result, repeat this method with the heavy item alone to find its volume.
Take the combined volume of both items (your first result), then subtract the heavy item's volume.
The answer is the volume of the original object.
When you take the volume of the heavy item alone, include anything you used to attach it to the original object, such as safety pins or tape. , If you are using a graduated cylinder or measuring cup, you can write down the volume measurement at the new water height instead.
Once you have done this, you can remove your object.
You may not wish to leave the object underwater for more than a couple minutes, since even some "waterproof" objects can be affected if left underwater for too long. , Since you know the water rose from one level to a higher level when the object was submerged, the volume of space between those two levels is the volume of the object.
This is called the displacement method, and works because an object submerged in water always "displaces" an amount of water exactly equal to its volume.
Depending on what type of container you used, there are different ways to calculate the volume of this displaced water, which is the same as your object's volume.
Finish the problem by continuing on to the step that matches your container's description. , If you used a graduated cylinder, measuring cup, or any other container that has volume measurements printed on the side, you already wrote down the two volumes you need to calculate the answer.
Take the volume you wrote down when the object was submerged (the larger volume) and subtract the original volume of the water level (the smaller volume).
The answer is the volume of the object. , If you used a rectangular container, look at the space in the box between the first water mark and second water mark you made.
This space forms a "rectangular prism"
or box shape, that was filled with the displaced water.
Find the volume of this space by measuring the height between the two water marks, then the length and width between the container's inside surfaces.
As explained here, you can find the volume of this box-shaped space by multiplying its length, width, and height together (length x width x height).
The answer to this multiplication problem is the volume of the object.
Do not measure the height of the entire container, just the height from one water mark to another.
Use this online calculator or search for another "rectangular prism calculator" that can multiply these numbers for you. , If you used a cylindrical container, look at the space between the first water mark and the second water mark.
This cylindrical space was once filled with the displaced water, and so its volume is equal to the object's volume.
To find the volume of this cylindrical space, you'll need to measure two distances: its height and its diameter.
First, measure the height between the two water marks, and write this down.
Next, find the diameter of the cylinder by measuring the distance from the inside edge of the cylinder to the opposite side, through the center.
Then divide the diameter by two to find the radius, which is the distance from the center of the circle to the edge.
Write the radius down, then use your measurements to finish the calculations:
Calculate πr2, or π x the radius x the radius, to find the area of a circle across the cylinder.
If you don't have a calculator with a π button, find one online or estimate by replacing it with
3.14.
Multiple your answer by the height between the water marks (which you measured at the beginning of this step) to find the volume of space the water took up.
This answer is also the volume of your object.
You can get a more precise answer, or save yourself some math, if you enter your measurements on an online cylinder volume calculator. -
Step 3: Fill it partway with water.
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Step 4: Mark the water level.
-
Step 5: Drop the object into the water and see if it absorbs water.
-
Step 6: Learn what to do if the object floats.
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Step 7: Make a second mark where the new water level is.
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Step 8: Understand why this method works.
-
Step 9: Find the volume using your container's printed measurements.
-
Step 10: Find the volume using a rectangular container.
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Step 11: Find the volume using a cylindrical container.
Detailed Guide
This method involves submerging the object in water.
If the object is hollow and not watertight, you cannot get an accurate measure of volume using this method.
If the object absorbs water, make sure water will not damage it, and read the instructions carefully to see how to adjust the process.
Never drop an electric or electronic item in water, as this could cause a dangerous electrical shock and/or damage the object beyond repair.
If you have access to a vacuum sealer, you may be able to seal a small object in a watertight plastic coating with minimal air inside.
This will allow you to get a good estimate of volume, since the volume of the plastic used is likely to be relatively small compared to the volume of the object.
If you are measuring a small object, you could use a graduated cylinder or measuring cup, which have volume measurements printed on the side.
Otherwise, find a watertight container with a volume that is simple to calculate, such as a cylinder or rectangular box.
A bowl will not be as accurate, but you can treat it as a cylinder and get an approximate answer, especially if the object is very small compared to the bowl.
It's a good idea to locate a dry towel as well, since the object will be dripping water when removed from the container. , Add enough water to submerge the object, but leave plenty of space between the water and the top of the container.
If the object has an irregularly shaped base, such as rounded bottom corners, fill it up enough that the water level reaches a more regular portion, such as straight rectangular walls. , If the container is transparent, mark the top of the water level on the outside with a wet-erase marker or other easily cleaned writing device.
Otherwise, mark the water level on the inside using a piece of colored tape or other mark that will not be washed off by the water.
If you are using a graduated cylinder or measuring cup with volume measurements on the side, you do not need to make a mark.
Just look for the volume measurement at the water's surface, and write this number down. , Sink the object you want to measure completely in the water.
If the object absorbs water, wait at least thirty seconds for it to absorb the water, then remove the object.
The water level should have dropped, since some of the water is in the object.
Remove your old mark or piece of colored tape, and replace it with a new one at the new water level.
You may then drop the object into the water a second time and leave it there. , If the object floats, attach a dense, heavy item to it and continue on to measure the volume of both combined.
After you write down that result, repeat this method with the heavy item alone to find its volume.
Take the combined volume of both items (your first result), then subtract the heavy item's volume.
The answer is the volume of the original object.
When you take the volume of the heavy item alone, include anything you used to attach it to the original object, such as safety pins or tape. , If you are using a graduated cylinder or measuring cup, you can write down the volume measurement at the new water height instead.
Once you have done this, you can remove your object.
You may not wish to leave the object underwater for more than a couple minutes, since even some "waterproof" objects can be affected if left underwater for too long. , Since you know the water rose from one level to a higher level when the object was submerged, the volume of space between those two levels is the volume of the object.
This is called the displacement method, and works because an object submerged in water always "displaces" an amount of water exactly equal to its volume.
Depending on what type of container you used, there are different ways to calculate the volume of this displaced water, which is the same as your object's volume.
Finish the problem by continuing on to the step that matches your container's description. , If you used a graduated cylinder, measuring cup, or any other container that has volume measurements printed on the side, you already wrote down the two volumes you need to calculate the answer.
Take the volume you wrote down when the object was submerged (the larger volume) and subtract the original volume of the water level (the smaller volume).
The answer is the volume of the object. , If you used a rectangular container, look at the space in the box between the first water mark and second water mark you made.
This space forms a "rectangular prism"
or box shape, that was filled with the displaced water.
Find the volume of this space by measuring the height between the two water marks, then the length and width between the container's inside surfaces.
As explained here, you can find the volume of this box-shaped space by multiplying its length, width, and height together (length x width x height).
The answer to this multiplication problem is the volume of the object.
Do not measure the height of the entire container, just the height from one water mark to another.
Use this online calculator or search for another "rectangular prism calculator" that can multiply these numbers for you. , If you used a cylindrical container, look at the space between the first water mark and the second water mark.
This cylindrical space was once filled with the displaced water, and so its volume is equal to the object's volume.
To find the volume of this cylindrical space, you'll need to measure two distances: its height and its diameter.
First, measure the height between the two water marks, and write this down.
Next, find the diameter of the cylinder by measuring the distance from the inside edge of the cylinder to the opposite side, through the center.
Then divide the diameter by two to find the radius, which is the distance from the center of the circle to the edge.
Write the radius down, then use your measurements to finish the calculations:
Calculate πr2, or π x the radius x the radius, to find the area of a circle across the cylinder.
If you don't have a calculator with a π button, find one online or estimate by replacing it with
3.14.
Multiple your answer by the height between the water marks (which you measured at the beginning of this step) to find the volume of space the water took up.
This answer is also the volume of your object.
You can get a more precise answer, or save yourself some math, if you enter your measurements on an online cylinder volume calculator.
About the Author
Lauren Harris
Professional writer focused on creating easy-to-follow lifestyle tutorials.
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