Atmospheric Pressure with Altitude
Lesson notes
Overview
Pressure halves roughly every 5.5 km of altitude. This topic is rated beginner and is number 62 of 98 in Earth & Space. Core ideas and first intuitions. No prior knowledge needed.
What you are seeing
The panel above shows a graph of the function. Each slider changes one parameter, so you can see exactly how the curve bends, shifts or stretches. The animation is drawn live from the model, so everything you see responds to the sliders. Press Space to pause, use Restart to replay from the start, and change the speed to slow down quick events.
In depth
Air pressure falls roughly exponentially with height, P = P₀e^(−h/H), where the scale height H is about 8 km. In practical terms pressure halves roughly every 5.5 km, so at the summit of Everest, 8.8 km, it is about a third of the sea-level value, and the air contains only a third of the oxygen per breath. Aircraft cabins are pressurised to the equivalent of about 2,000 m for comfort.
Reading the relationship
The expression "P = P₀e^(−h/H)" is a compact summary of the idea. It uses the symbols P, P₀e, h, H; name what each one stands for before you start. Notice that it contains a ratio, so increasing the denominator makes the result smaller, and an exponential, which changes by the same factor for every equal step. Then use the sliders to see how changing one quantity changes the others.
A guided exploration
1. Set every slider to its middle value and note the shape of the curve. 2. Move one slider at a time and describe whether the curve shifts, stretches or turns. 3. Find the value where the behaviour changes sharply, then connect it to the formula.
Try this
Start by only moving one slider at a time. Say aloud what you expect, then check.
Common pitfalls
Earth and space systems work on very different scales of time and distance. Check which scale a number refers to before comparing it with another.
How it connects
It builds on “Geothermal Gradient”, the topic before it in Earth & Space. Once you are comfortable, continue with “Temperature Lapse Rate”.
Why it matters
Earth and space science helps us understand our planet, its climate and the wider universe.
Where you might use it
- Revising “Atmospheric Pressure with Altitude” before a class, exam or certification
- Forecasting weather and understanding climate records and their uncertainty
- Planning for earthquakes, floods and other natural hazards in cities
- Interpreting satellite images, space missions and the age of rocks and stars
Frequently asked questions
What is Atmospheric Pressure with Altitude?
Pressure halves roughly every 5.5 km of altitude. It is a beginner topic in Earth & Space.
How do I use the Atmospheric Pressure with Altitude simulation?
The panel at the top shows a graph of the function. Each slider changes one parameter, so you can see exactly how the curve bends, shifts or stretches. Move the sliders one at a time, then press Space to pause the animation and look closer.
What does the formula mean?
The expression P = P₀e^(−h/H) packs the idea into symbols. Name each symbol first, then change one quantity with the sliders and see which others respond.
Who is this topic for?
Core ideas and first intuitions. No prior knowledge needed. If the quiz feels hard, reread the lesson notes and try the previous topic first.
What should I learn before this?
Start with “Geothermal Gradient”, the previous topic in Earth & Space. Each topic in a subject builds on the ones before it.
How do I track my progress?
Press “Mark as learned” on this page. Progress is stored only in this browser and is never sent anywhere. The Browse page can show topics you have learned or still need to learn.