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Pascal's law sits in the physics syllabus for both JEE Main 2026 and NEET-UG 2026, and the binomial coefficients you meet in Class 11 maths sit in "Pascal's triangle". Both come from one person who died at 39. This post covers what Blaise Pascal actually did in pressure and probability, how his mountain experiment was designed, and what you can borrow from the way he worked.
Who was Blaise Pascal?
Pascal was born in Clermont, France, on 19 June 1623 and died in Paris on 19 August 1662, according to the MacTutor biography from the University of St Andrews. His father taught him at home. MacTutor records that at 16 he presented a sheet of projective geometry theorems to Mersenne's circle in Paris, and that between 1642 and 1645 he built a mechanical calculator, the Pascaline, to help his father with tax accounts.
From about 1646 he began experiments on air pressure and the vacuum. That put him in a live argument: many scholars, including Descartes, did not accept that a vacuum could exist.
What was the Puy de Dôme experiment?
In Italy, Evangelista Torricelli had found that mercury in an inverted glass tube stops at a height of roughly 30 inches, and he suggested that the weight of the air outside holds it up. Pascal saw a way to test that idea. If air pressure holds the mercury up, then at the top of a mountain, with less air above, the column should be shorter.
There are no mountains in Paris, so in 1647 he wrote to his brother-in-law Florin Périer, who lived near the Puy de Dôme in central France. The Linda Hall Library's account describes what happened on 19 September 1648:
Périer set up two identical tubes at a convent in Clermont and checked that they read the same.
He left one there, with a monk to watch it through the day. That tube was the control.
He carried the other about 3,000 feet higher, to the summit. The mercury there stood about three inches lower.
He took readings at several points on the summit and on the way down, and found the column rising again as he descended.
Pascal printed Périer's letter, with his own commentary, in his *Récit de la grande expérience de l'équilibre des liqueurs* the same year.
Does three inches make sense? A quick check
You can test the result with the physics you already know. The pressure difference across a height h of fluid is ρgh.
Take the height gained as about 3,000 feet, or roughly 914 m.
Take air density as about 1.2 kg/m³. It actually falls with height, so this slightly overestimates.
Pressure drop ≈ 1.2 × 9.8 × 914 ≈ 10,700 Pa.
One millimetre of mercury is 133.3 Pa (NIST conversion factors), so the column should fall by about 10,700 ÷ 133.3 ≈ 80 mm.
That is about 3.2 inches. Périer's three inches is the right size, which is a nice sign that the explanation holds.
What is Pascal's law?
From 1653 Pascal wrote his *Treatise on the Equilibrium of Liquids*, which MacTutor describes as the first complete outline of hydrostatics. Its central idea, now called Pascal's law, is that pressure applied to an enclosed fluid is passed on undiminished to every part of the fluid.
The hydraulic press follows directly. Push with force F₁ on a small piston of area A₁, and the pressure F₁/A₁ reaches a large piston of area A₂, which then pushes with F₂ = F₁ × A₂/A₁. With A₁ = 10 cm², A₂ = 500 cm² and F₁ = 200 N, the output is F₂ = 200 × 50 = 10,000 N. The catch is that the big piston moves 50 times less far, so the work in and out is the same.
The SI unit of pressure, one newton per square metre, is named the pascal (Pa) in his honour (NIST SP 811 lists it among the SI derived units). For the mistakes students make with these ideas, see our guide to pressure, buoyancy and Bernoulli's equation.
How did Pascal help start probability theory?
In the summer of 1654 Pascal exchanged five letters with Pierre de Fermat, MacTutor records. One question was the "problem of points": if a game of chance stops early, how should the stakes be split fairly?
Here is a modern example of the kind of problem they solved. Two players each put 32 coins into a pot of 64. The first to win three rounds takes it all, and each round is a fair 50:50. The game stops when A leads 2 rounds to 1.
B can only win the pot by winning the next two rounds: probability ½ × ½ = ¼.
So A's chance is ¾, and a fair split gives A ¾ × 64 = 48 coins and B 16.
The key move is to count the futures that remain, not the rounds already played. That idea, expected value, is still the core of the probability chapter. Our post on common probability mistakes works through more.
What can you learn from how Pascal worked?
Turn an argument into a prediction. The vacuum debate had gone on for centuries. Pascal asked what each side predicted at the top of a mountain, and got an answer.
Build in a control. The tube left behind in Clermont is why the result convinced people.
Check your answer with a rough calculation. The ρgh estimate above takes two minutes and tells you whether a number is believable.
If pressure in fluids is still easier to state than to picture, the Fermi Simulation Lab has interactive simulations for ideas that are easier to see than to read, so you can change a depth or a piston area and watch what happens.
Try it now: redo the three-inch check for a hill or building near you, using its height in metres.
