A percentage is not a separate sum but the same ratio table, with a hundred in the left column. Put what belongs together in the same column, and the products of what stands diagonally opposite are equal. That cross multiplication gives the answer, and the units that cancel out are your check.
There are also subtitles in English and Türkçe. Choose your language under the gear icon in the player, at Subtitles.
A ratio and a percentage are two different sums. Is that right, yes or no? Most people say yes, and that is exactly why percentages keep feeling harder than they are.
In just over three minutes: how you lay two measurements side by side in a table of two columns, what you measure on the photo on the left and what it is in reality on the right. The products of what stands diagonally opposite are equal, and that cross multiplication gives the answer. A percentage then turns out to be that same table with a hundred in the left column, so you need no separate trick for it. And the units that cancel out are your check on whether you filled the columns in correctly.
For upper secondary physics.
In this video
The full explanation, in writing
One table or two separate sums?
0:00Ratios and percentages are two different sums. Is that right, yes or no? Most people say yes. It is one sum, and you use it the rest of your life.
Laying two measurements side by side
0:15One more tool, and you use it for the rest of your life. Say you see a photo of a basket with someone beside it. You know the height of a basket: the ring hangs at three point zero five metres. How tall is that person? You measure on the photo: the ring is four point six centimetres above the ground, the person is two point seven centimetres.
0:40Those four point six on the photo belong with three point zero five metres in reality. Then you put them under each other, with what belongs together in the same column. On the left what you measure on the photo, on the right what it is in reality.
1:00Products of the numbers standing diagonally opposite are equal, and that we call cross multiplication. So: two point seven times three point zero five, divided by four point six. One point eight metres. And watch what happens to the units: the centimetres cancel out and metres are left.
1:24That is exactly the check on whether you did it right.
A percentage is a ratio too
1:29But a percentage is nothing but such a ratio, with a hundred in the left column. Eight percent of a hundred and fifty means: a hundred goes with a hundred and fifty, and eight goes with how much? Cross multiplication, and twelve comes out. So for percentages you need no separate trick.
1:48They are the same two rows under each other. Two things to remember. One: put what belongs together in the same column. On the left what you measure on the photo, on the right what it is in reality. The products of what stands diagonally opposite are equal.
2:07Two: a percentage is that table, with a hundred in the left column. No separate trick. Two questions to take with you. One: on that same photo he stretches his arm up, and his hand is three point four centimetres above the ground. How high does he reach in reality?
2:28And two: sixteen percent of fifty. How much is that? One: three point four times three point zero five, divided by four point six. Two point three metres. If you get five point one, you have swapped the two numbers. And you can see that: he would then reach higher than the ring hangs.
2:54And two: sixteen times fifty, divided by a hundred. Eight. If you get eight hundred, you have forgotten the hundred in the left column. One table, two rows. That same table returns as soon as you calculate with density.
Frequently asked questions
What is cross multiplication?
If you write two ratios as a table of two columns, the products of the numbers standing diagonally opposite are equal. From that equality follows what you are looking for: multiply the two numbers you have and divide by the third.
How do you work out a percentage with a ratio table?
Put a hundred in the left column and the whole beside it. 8 percent of 150 becomes: a hundred goes with a hundred and fifty, and eight goes with how much? Cross multiplication: eight times a hundred and fifty divided by a hundred is twelve. You need no separate trick for percentages.
How do you work out someone's height from a photo?
With a measure you already know. In a photo with a basketball ring you know the ring hangs at 3.05 m. If you measure 4.6 cm to the ring on the photo and 2.7 cm for the person, that person is 2.7 times 3.05 divided by 4.6, which is 1.8 m.
How do I know whether I filled the table in correctly?
Look at the units. In a correct table the centimetres from the photo cancel out and metres are left. If a unit comes out that makes no sense, two things are in the same column that do not belong together.
How much is 16 percent of 50?
Eight. A hundred goes with fifty, and sixteen goes with the answer, so sixteen times fifty divided by a hundred. If you get eight hundred, you have forgotten to divide by the hundred in the left column.
Physics with Thomas makes physics explainers for upper secondary school. No words on screen, so what you see works in any language.
In this series
Quantities and unitswhy 20,000 is not more than 10,0007:30
Ratios and percentagesone table for both3:15
Scientific notationpowers of ten and order of magnitude5:22
Calculating with powers of tenthe four rules3:18
Pythagoras and trigonometrywhich side with which angle3:19
Deriving units from a formulaconverting to base units7:47
Significant figureshow many figures do you write6:24
Line of best fitthe line touches no point5:07
Relationships and the constantbraking twice as fast5:20
Linearising a graphyour measurements never change4:41
About me
My name is Thomas Schuurmans, and I have a passion for physics and for understanding why things work the way they do. What I want is to get young people asking “why is that?” and “how does that work?” more often, and to hand them the tools of physics in a way that is simple and that you can see.
I graduated in applied physics at Delft University of Technology in 2003. After that I spent more than twenty years outside education: first at TNO, the Dutch applied research institute, then at a design agency, and eventually founding Proportion Global, through which I work on innovation questions in Africa, Latin America and South Asia. That work resembles physics more than you would expect: don't start from a solution, first understand what is going on, try something, be wrong, and look again.
Since 2026 I have been teaching physics to both lower and upper secondary classes, and I started a master's at the University of Amsterdam for my full teaching qualification. That is where I learned that a secondary school pupil's real attention for new material lasts about seven minutes. And my own weakness happens to be telling too many side stories.
That is where the idea came from: videos that explain one topic sharply and visually, inside those seven minutes. I make them for my own pupils. Then I publish them, because good explanation should be within reach of anyone who needs it, wherever you live and whatever language you think and speak in.