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Updated 2 Mar 2026
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Understanding Density: Definition and Calculation
1 / 6
What is Density?
Think of density as how tightly packed the "stuff" is in any object. If you've got two blocks the same size, the heavier one is more dense. A lead block feels much heavier than a wooden block of the same size because lead packs way more matter into the same space.
Density is basically mass per unit volume - it tells you how much matter is crammed into a given space. The symbol for density is ρ (rho), which looks like a curvy 'p'.
The key formula you need to master is: ρ = m/V . This simple equation is your ticket to solving loads of physics problems.
Quick Tip: Remember that mass (measured in grams or kilograms) isn't the same as weight. Mass stays constant wherever you go, even on the moon!
The Formula Triangle and Units
Here's a brilliant trick to remember the density formula and rearrange it easily. Draw a triangle with mass (m) at the top, and density (ρ) and volume (V) at the bottom.
To use it, just cover what you want to find. Cover ρ to get density: m ÷ V. Cover m to get mass: ρ × V. Cover V to get volume: m ÷ ρ.
Units for density depend on what you use for mass and volume. The two most common are grams per cubic centimetre and kilograms per cubic metre . Always check your units match before calculating!
Remember: 1 millilitre equals 1 cubic centimetre . This conversion pops up constantly in exams.
Measuring Mass and Volume
Measuring mass is straightforward - just use digital scales or a balance. Always zero the balance first for accurate readings.
Volume measurement depends on your object's shape. For regular solids like cubes, measure length, width, and height with a ruler, then multiply them together. Make sure all measurements use the same units!
For liquids, pour into a measuring cylinder and read from the bottom of the meniscus (that curved surface). For irregular solids like stones, use the displacement method. Fill a measuring cylinder with water, record the starting volume (V₁), add your object, then record the new volume (V₂). The object's volume is V₂ - V₁.
Common Mistake: Don't just write down the final water level - you need the difference between final and initial volumes!
Worked Examples
Let's tackle a density calculation with an aluminium block. It has a mass of 540g and measures 10cm × 5cm × 4cm.
First, calculate the volume: 10 × 5 × 4 = 200 cm³. Then use the formula: ρ = 540g ÷ 200cm³ = 2.7 g/cm³.
Here's another example: 50 cm³ of unknown liquid has a mass of 40g. Using ρ = m/V: 40g ÷ 50cm³ = 0.8 g/cm³. Since water has a density of 1 g/cm³, this liquid is less dense than water and will float.
The key to success is working systematically - identify what you know, calculate what you need, then apply the formula carefully.
Exam Tip: Always include units in your final answer. You'll lose marks without them, even if your calculation is perfect!
Floating, Sinking, and Exam Success
Understanding density helps predict floating and sinking. Objects less dense than a fluid will float; denser objects will sink. If densities match exactly, the object hovers suspended in the middle.
For exam success, remember these crucial points: units are absolutely essential, keep mass and volume units consistent, and don't confuse mass (kg) with weight (N). Density always uses mass, not weight.
Water's density is approximately 1 g/cm³ - memorise this because it's your reference point for comparing other substances. Oil floats on water because it's less dense, while rocks sink because they're denser.
Quick Check: If you're using the displacement method, always subtract the initial water volume from the final volume. This catches out loads of students!
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Where can I download the Knowunity app?
You can download the app in the Google Play Store and in the Apple App Store.
Is Knowunity really free of charge?
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The app is very easy to use and well designed. I have found everything I was looking for so far and have been able to learn a lot from the presentations! I will definitely use the app for a class assignment! And of course it also helps a lot as an inspiration.
Stefan S
iOS user
This app is really great. There are so many study notes and help [...]. My problem subject is French, for example, and the app has so many options for help. Thanks to this app, I have improved my French. I would recommend it to anyone.
Samantha Klich
Android user
Wow, I am really amazed. I just tried the app because I've seen it advertised many times and was absolutely stunned. This app is THE HELP you want for school and above all, it offers so many things, such as workouts and fact sheets, which have been VERY helpful to me personally.
Anna
iOS user
I think it’s very much worth it and you’ll end up using it a lot once you get the hang of it and even after looking at others notes you can still ask your Artificial intelligence buddy the question and ask to simplify it if you still don’t get it!!! In the end I think it’s worth it 😊👍 ⚠️Also DID I MENTION ITS FREEE YOU DON’T HAVE TO PAY FOR ANYTHING AND STILL GET YOUR GRADES IN PERFECTLY❗️❗️⚠️
Thomas R
iOS user
Knowunity is the BEST app I’ve used in a minute. This is not an ai review or anything this is genuinely coming from a 7th grade student (I know 2011 im young) but dude this app is a 10/10 i have maintained a 3.8 gpa and have plenty of time for gaming. I love it and my mom is just happy I got good grades
Brad T
Android user
Not only did it help me find the answer but it also showed me alternative ways to solve it. I was horrible in math and science but now I have an a in both subjects. Thanks for the help🤍🤍
David K
iOS user
The app's just great! All I have to do is enter the topic in the search bar and I get the response real fast. I don't have to watch 10 YouTube videos to understand something, so I'm saving my time. Highly recommended!
Sudenaz Ocak
Android user
In school I was really bad at maths but thanks to the app, I am doing better now. I am so grateful that you made the app.
Greenlight Bonnie
Android user
I found this app a couple years ago and it has only gotten better since then. I really love it because it can help with written questions and photo questions. Also, it can find study guides that other people have made as well as flashcard sets and practice tests. The free version is also amazing for students who might not be able to afford it. Would 100% recommend
Aubrey
iOS user
Best app if you're in Highschool or Junior high. I have been using this app for 2 school years and it's the best, it's good if you don't have anyone to help you with school work.😋🩷🎀
Marco B
iOS user
THE QUIZES AND FLASHCARDS ARE SO USEFUL AND I LOVE Knowunity AI. IT ALSO IS LITREALLY LIKE CHATGPT BUT SMARTER!! HELPED ME WITH MY MASCARA PROBLEMS TOO!! AS WELL AS MY REAL SUBJECTS ! DUHHH 😍😁😲🤑💗✨🎀😮
Elisha
iOS user
This app is phenomenal down to the correct info and the various topics you can study! I greatly recommend it for people who struggle with procrastination and those who need homework help. It has been perfectly accurate for world 1 history as far as I’ve seen! Geometry too!
Paul T
iOS user
The app is very easy to use and well designed. I have found everything I was looking for so far and have been able to learn a lot from the presentations! I will definitely use the app for a class assignment! And of course it also helps a lot as an inspiration.
Stefan S
iOS user
This app is really great. There are so many study notes and help [...]. My problem subject is French, for example, and the app has so many options for help. Thanks to this app, I have improved my French. I would recommend it to anyone.
Samantha Klich
Android user
Wow, I am really amazed. I just tried the app because I've seen it advertised many times and was absolutely stunned. This app is THE HELP you want for school and above all, it offers so many things, such as workouts and fact sheets, which have been VERY helpful to me personally.
Anna
iOS user
I think it’s very much worth it and you’ll end up using it a lot once you get the hang of it and even after looking at others notes you can still ask your Artificial intelligence buddy the question and ask to simplify it if you still don’t get it!!! In the end I think it’s worth it 😊👍 ⚠️Also DID I MENTION ITS FREEE YOU DON’T HAVE TO PAY FOR ANYTHING AND STILL GET YOUR GRADES IN PERFECTLY❗️❗️⚠️
Thomas R
iOS user
Knowunity is the BEST app I’ve used in a minute. This is not an ai review or anything this is genuinely coming from a 7th grade student (I know 2011 im young) but dude this app is a 10/10 i have maintained a 3.8 gpa and have plenty of time for gaming. I love it and my mom is just happy I got good grades
Brad T
Android user
Not only did it help me find the answer but it also showed me alternative ways to solve it. I was horrible in math and science but now I have an a in both subjects. Thanks for the help🤍🤍
David K
iOS user
The app's just great! All I have to do is enter the topic in the search bar and I get the response real fast. I don't have to watch 10 YouTube videos to understand something, so I'm saving my time. Highly recommended!
Sudenaz Ocak
Android user
In school I was really bad at maths but thanks to the app, I am doing better now. I am so grateful that you made the app.
Greenlight Bonnie
Android user
I found this app a couple years ago and it has only gotten better since then. I really love it because it can help with written questions and photo questions. Also, it can find study guides that other people have made as well as flashcard sets and practice tests. The free version is also amazing for students who might not be able to afford it. Would 100% recommend
Aubrey
iOS user
Best app if you're in Highschool or Junior high. I have been using this app for 2 school years and it's the best, it's good if you don't have anyone to help you with school work.😋🩷🎀
Marco B
iOS user
THE QUIZES AND FLASHCARDS ARE SO USEFUL AND I LOVE Knowunity AI. IT ALSO IS LITREALLY LIKE CHATGPT BUT SMARTER!! HELPED ME WITH MY MASCARA PROBLEMS TOO!! AS WELL AS MY REAL SUBJECTS ! DUHHH 😍😁😲🤑💗✨🎀😮
Elisha
iOS user
This app is phenomenal down to the correct info and the various topics you can study! I greatly recommend it for people who struggle with procrastination and those who need homework help. It has been perfectly accurate for world 1 history as far as I’ve seen! Geometry too!
Paul T
iOS user
Understanding Density: Definition and Calculation
Ever wondered why oil floats on water or why a tiny piece of gold feels so heavy? It's all about density - one of the most practical physics concepts you'll use. Understanding density helps explain everything from why ships float... Show more
What is Density?
Think of density as how tightly packed the "stuff" is in any object. If you've got two blocks the same size, the heavier one is more dense. A lead block feels much heavier than a wooden block of the same size because lead packs way more matter into the same space.
Density is basically mass per unit volume - it tells you how much matter is crammed into a given space. The symbol for density is ρ (rho), which looks like a curvy 'p'.
The key formula you need to master is: ρ = m/V . This simple equation is your ticket to solving loads of physics problems.
Quick Tip: Remember that mass (measured in grams or kilograms) isn't the same as weight. Mass stays constant wherever you go, even on the moon!
Sign up to see the contentIt's free!
Access to all documents
Improve your grades
Join milions of students
By signing up you accept Terms of Service and Privacy Policy
The Formula Triangle and Units
Here's a brilliant trick to remember the density formula and rearrange it easily. Draw a triangle with mass (m) at the top, and density (ρ) and volume (V) at the bottom.
To use it, just cover what you want to find. Cover ρ to get density: m ÷ V. Cover m to get mass: ρ × V. Cover V to get volume: m ÷ ρ.
Units for density depend on what you use for mass and volume. The two most common are grams per cubic centimetre and kilograms per cubic metre . Always check your units match before calculating!
Remember: 1 millilitre equals 1 cubic centimetre . This conversion pops up constantly in exams.
Sign up to see the contentIt's free!
Access to all documents
Improve your grades
Join milions of students
By signing up you accept Terms of Service and Privacy Policy
Measuring Mass and Volume
Measuring mass is straightforward - just use digital scales or a balance. Always zero the balance first for accurate readings.
Volume measurement depends on your object's shape. For regular solids like cubes, measure length, width, and height with a ruler, then multiply them together. Make sure all measurements use the same units!
For liquids, pour into a measuring cylinder and read from the bottom of the meniscus (that curved surface). For irregular solids like stones, use the displacement method. Fill a measuring cylinder with water, record the starting volume (V₁), add your object, then record the new volume (V₂). The object's volume is V₂ - V₁.
Common Mistake: Don't just write down the final water level - you need the difference between final and initial volumes!
Sign up to see the contentIt's free!
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Improve your grades
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Worked Examples
Let's tackle a density calculation with an aluminium block. It has a mass of 540g and measures 10cm × 5cm × 4cm.
First, calculate the volume: 10 × 5 × 4 = 200 cm³. Then use the formula: ρ = 540g ÷ 200cm³ = 2.7 g/cm³.
Here's another example: 50 cm³ of unknown liquid has a mass of 40g. Using ρ = m/V: 40g ÷ 50cm³ = 0.8 g/cm³. Since water has a density of 1 g/cm³, this liquid is less dense than water and will float.
The key to success is working systematically - identify what you know, calculate what you need, then apply the formula carefully.
Exam Tip: Always include units in your final answer. You'll lose marks without them, even if your calculation is perfect!
Sign up to see the contentIt's free!
Access to all documents
Improve your grades
Join milions of students
By signing up you accept Terms of Service and Privacy Policy
Floating, Sinking, and Exam Success
Understanding density helps predict floating and sinking. Objects less dense than a fluid will float; denser objects will sink. If densities match exactly, the object hovers suspended in the middle.
For exam success, remember these crucial points: units are absolutely essential, keep mass and volume units consistent, and don't confuse mass (kg) with weight (N). Density always uses mass, not weight.
Water's density is approximately 1 g/cm³ - memorise this because it's your reference point for comparing other substances. Oil floats on water because it's less dense, while rocks sink because they're denser.
Quick Check: If you're using the displacement method, always subtract the initial water volume from the final volume. This catches out loads of students!
Sign up to see the contentIt's free!
Access to all documents
Improve your grades
Join milions of students
By signing up you accept Terms of Service and Privacy Policy
We thought you’d never ask...
What is the Knowunity AI companion?
Our AI companion is specifically built for the needs of students. Based on the millions of content pieces we have on the platform we can provide truly meaningful and relevant answers to students. But its not only about answers, the companion is even more about guiding students through their daily learning challenges, with personalised study plans, quizzes or content pieces in the chat and 100% personalisation based on the students skills and developments.
Where can I download the Knowunity app?
You can download the app in the Google Play Store and in the Apple App Store.
Is Knowunity really free of charge?
That's right! Enjoy free access to study content, connect with fellow students, and get instant help – all at your fingertips.
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The app is very easy to use and well designed. I have found everything I was looking for so far and have been able to learn a lot from the presentations! I will definitely use the app for a class assignment! And of course it also helps a lot as an inspiration.
Stefan S
iOS user
This app is really great. There are so many study notes and help [...]. My problem subject is French, for example, and the app has so many options for help. Thanks to this app, I have improved my French. I would recommend it to anyone.
Samantha Klich
Android user
Wow, I am really amazed. I just tried the app because I've seen it advertised many times and was absolutely stunned. This app is THE HELP you want for school and above all, it offers so many things, such as workouts and fact sheets, which have been VERY helpful to me personally.
Anna
iOS user
I think it’s very much worth it and you’ll end up using it a lot once you get the hang of it and even after looking at others notes you can still ask your Artificial intelligence buddy the question and ask to simplify it if you still don’t get it!!! In the end I think it’s worth it 😊👍 ⚠️Also DID I MENTION ITS FREEE YOU DON’T HAVE TO PAY FOR ANYTHING AND STILL GET YOUR GRADES IN PERFECTLY❗️❗️⚠️
Thomas R
iOS user
Knowunity is the BEST app I’ve used in a minute. This is not an ai review or anything this is genuinely coming from a 7th grade student (I know 2011 im young) but dude this app is a 10/10 i have maintained a 3.8 gpa and have plenty of time for gaming. I love it and my mom is just happy I got good grades
Brad T
Android user
Not only did it help me find the answer but it also showed me alternative ways to solve it. I was horrible in math and science but now I have an a in both subjects. Thanks for the help🤍🤍
David K
iOS user
The app's just great! All I have to do is enter the topic in the search bar and I get the response real fast. I don't have to watch 10 YouTube videos to understand something, so I'm saving my time. Highly recommended!
Sudenaz Ocak
Android user
In school I was really bad at maths but thanks to the app, I am doing better now. I am so grateful that you made the app.
Greenlight Bonnie
Android user
I found this app a couple years ago and it has only gotten better since then. I really love it because it can help with written questions and photo questions. Also, it can find study guides that other people have made as well as flashcard sets and practice tests. The free version is also amazing for students who might not be able to afford it. Would 100% recommend
Aubrey
iOS user
Best app if you're in Highschool or Junior high. I have been using this app for 2 school years and it's the best, it's good if you don't have anyone to help you with school work.😋🩷🎀
Marco B
iOS user
THE QUIZES AND FLASHCARDS ARE SO USEFUL AND I LOVE Knowunity AI. IT ALSO IS LITREALLY LIKE CHATGPT BUT SMARTER!! HELPED ME WITH MY MASCARA PROBLEMS TOO!! AS WELL AS MY REAL SUBJECTS ! DUHHH 😍😁😲🤑💗✨🎀😮
Elisha
iOS user
This app is phenomenal down to the correct info and the various topics you can study! I greatly recommend it for people who struggle with procrastination and those who need homework help. It has been perfectly accurate for world 1 history as far as I’ve seen! Geometry too!
Paul T
iOS user
The app is very easy to use and well designed. I have found everything I was looking for so far and have been able to learn a lot from the presentations! I will definitely use the app for a class assignment! And of course it also helps a lot as an inspiration.
Stefan S
iOS user
This app is really great. There are so many study notes and help [...]. My problem subject is French, for example, and the app has so many options for help. Thanks to this app, I have improved my French. I would recommend it to anyone.
Samantha Klich
Android user
Wow, I am really amazed. I just tried the app because I've seen it advertised many times and was absolutely stunned. This app is THE HELP you want for school and above all, it offers so many things, such as workouts and fact sheets, which have been VERY helpful to me personally.
Anna
iOS user
I think it’s very much worth it and you’ll end up using it a lot once you get the hang of it and even after looking at others notes you can still ask your Artificial intelligence buddy the question and ask to simplify it if you still don’t get it!!! In the end I think it’s worth it 😊👍 ⚠️Also DID I MENTION ITS FREEE YOU DON’T HAVE TO PAY FOR ANYTHING AND STILL GET YOUR GRADES IN PERFECTLY❗️❗️⚠️
Thomas R
iOS user
Knowunity is the BEST app I’ve used in a minute. This is not an ai review or anything this is genuinely coming from a 7th grade student (I know 2011 im young) but dude this app is a 10/10 i have maintained a 3.8 gpa and have plenty of time for gaming. I love it and my mom is just happy I got good grades
Brad T
Android user
Not only did it help me find the answer but it also showed me alternative ways to solve it. I was horrible in math and science but now I have an a in both subjects. Thanks for the help🤍🤍
David K
iOS user
The app's just great! All I have to do is enter the topic in the search bar and I get the response real fast. I don't have to watch 10 YouTube videos to understand something, so I'm saving my time. Highly recommended!
Sudenaz Ocak
Android user
In school I was really bad at maths but thanks to the app, I am doing better now. I am so grateful that you made the app.
Greenlight Bonnie
Android user
I found this app a couple years ago and it has only gotten better since then. I really love it because it can help with written questions and photo questions. Also, it can find study guides that other people have made as well as flashcard sets and practice tests. The free version is also amazing for students who might not be able to afford it. Would 100% recommend
Aubrey
iOS user
Best app if you're in Highschool or Junior high. I have been using this app for 2 school years and it's the best, it's good if you don't have anyone to help you with school work.😋🩷🎀
Marco B
iOS user
THE QUIZES AND FLASHCARDS ARE SO USEFUL AND I LOVE Knowunity AI. IT ALSO IS LITREALLY LIKE CHATGPT BUT SMARTER!! HELPED ME WITH MY MASCARA PROBLEMS TOO!! AS WELL AS MY REAL SUBJECTS ! DUHHH 😍😁😲🤑💗✨🎀😮
Elisha
iOS user
This app is phenomenal down to the correct info and the various topics you can study! I greatly recommend it for people who struggle with procrastination and those who need homework help. It has been perfectly accurate for world 1 history as far as I’ve seen! Geometry too!
Paul T
iOS user