SI prefixes — each step is exactly 1,000× the previous
Once you know these, every scientific size becomes readable.
femto (f)
10⁻¹⁵ m
0.000000000000001 m. Proton territory.
pico (p)
10⁻¹² m
Atom size range.
nano (n)
10⁻⁹ m
DNA, molecules, chip transistors.
micro (µ)
10⁻⁶ m
Bacteria, human hair width, cell size.
milli (m)
10⁻³ m
1 mm — thickness of a credit card, grain of sand.
Part B · the interactive zoom — drag to travel the full scale
Drag the slider from the smallest known things to the largest
ProtonUniverse
Part C · key anchors at every scale — the ones to memorize
10⁻¹⁵ m
Proton — 1 femtometre
The nucleus of a hydrogen atom. 100,000× smaller than the atom itself.
10⁻¹⁰ m
Hydrogen atom — 0.1 nanometres (1 Ångström)
The smallest atom. A row of 10 hydrogen atoms = 1 nanometre.
0.3 nm
Water molecule (H₂O)
3× bigger than a hydrogen atom. 3 million water molecules fit across 1 mm.
2 nm
DNA double helix width
The most information-dense structure known. Your total DNA uncoiled = ~2 metres per cell.
7 nm
Cutting-edge chip transistor (2024)
Modern chips pack billions of these in your fingernail-sized processor.
~100 nm
Virus (e.g. coronavirus is ~120 nm)
700× smaller than a human hair. Too small to see with a light microscope.
~1 µm
Bacterium (e.g. E. coli ≈ 2 µm long)
Just visible with the best light microscopes. 1,000× bigger than a virus.
~7 µm
Red blood cell
5,000 fit side by side across 1 cm. So thin it has no nucleus — optimised for oxygen.
~70 µm
Human hair width
The universal "thin" reference. A spider silk thread is ~3 µm — 20× thinner.
~0.1 mm
Grain of fine sand · human egg cell
The human egg is the largest single cell in the body — just barely visible to the naked eye.
1 mm
Credit card thickness · ant width
The threshold of comfortable naked-eye visibility.
1 cm
Fingernail width · large ant
10,000 bacteria fit in 1 cm. 10,000,000 viruses fit in 1 cm.
1.7 m
Average human height
Our intuitive reference point. Everything else in this module is relative to this.
12,742 km
Earth's diameter
A human is 1/7,500,000th of Earth's diameter. Earth is 1/109th of the Sun's diameter.
150M km
Earth–Sun distance (1 AU)
Light takes 8 minutes. A car at 120 km/h would take 142 years.
9.46T km
1 light-year
The distance light travels in one year. Nearest star: 4.2 light-years away.
100,000 ly
Milky Way diameter
Our galaxy. Light takes 100,000 years to cross it. ~200–400 billion stars inside.
93B ly
Observable universe diameter
The furthest light that has had time to reach us. Beyond this: unknown, possibly infinite.
Part D · the ratio shockers — comparing across scales
Atom → human hair
1,000,000×
A hydrogen atom (0.1 nm) fits one million times across a single hair width (70 µm). 1 million = a medium city's population.
Virus → human hair
700×
A coronavirus (~120 nm) is 700× narrower than a hair. Yet it can shut down the world.
Human → Earth
1 : 7,500,000
If Earth were the size of a basketball (24 cm), a human would be 32 nanometres — smaller than a virus.
Earth → Sun
1 : 109
1.3 million Earths fit inside the Sun. Yet the Sun is a perfectly average-sized star.
Sun → Milky Way
1 : 10⁹
If the Sun were a grain of sand, the Milky Way would be wider than Europe.
Proton → observable universe
10⁴² ×
42 orders of magnitude separate the smallest known structure from the largest. The full range of physical reality.
Part E · spider silk — the most remarkable thin thing
Spider silk is ~3–8 µm in diameter — about 10–20× thinner than a human hair, and invisible to the naked eye unless light catches it. Yet it is, weight for weight, 5× stronger than steel and tougher than Kevlar. A single thread of spider silk weighing 300 grams (thicker than real silk, but same material) could theoretically encircle the entire Earth. The reason you can walk through a spiderweb and barely feel it is not that it's weak — it's that the mass is so tiny. One full orb web weighs less than 0.5 mg, about the weight of a grain of fine sand.
Part F · test yourself
1. A virus is ~100 nm. A bacterium is ~1,000 nm (1 µm). How many times bigger is the bacterium?
10 times bigger. 1,000 nm ÷ 100 nm = 10. This is why bacteria can be seen under a standard light microscope but viruses cannot — they're below the ~200 nm resolution limit of visible light. To see viruses you need an electron microscope. Important consequence: antibiotics can target bacteria (large enough to have complex internal machinery to disrupt) but don't work on viruses (too simple, too small — antiviral drugs work on completely different principles).
2. Your DNA is 2 nm wide and about 2 metres long when uncoiled. How does 2 metres of DNA fit in a cell that is only 10 µm across?
Extreme folding and compaction. The 2 metres are wound around protein spools (histones), then coiled, then super-coiled, then organised into chromosomes — compacting the DNA about 50,000-fold. If you took all the DNA from all your ~37 trillion cells and laid it end to end, it would reach from Earth to Pluto and back — about 17 times. All of that coiled up into structures you cannot see without a microscope.
3. The nearest star (Proxima Centauri) is 4.2 light-years away. The Milky Way is 100,000 light-years across. How many "nearest star distances" fit across our galaxy?
About 24,000. 100,000 ÷ 4.2 ≈ 23,800. So even if we could travel to the nearest star, we'd still need to make that same journey 24,000 more times to cross our galaxy — and our galaxy is just one of an estimated 2 trillion galaxies in the observable universe. Interstellar travel, let alone intergalactic travel, is not just a technology problem. It's a scale problem that dwarfs anything else in this course.
4. A human hair is 70 µm wide. A transistor on a modern chip is ~7 nm. How many transistors fit across the width of one hair?
10,000 transistors. 70,000 nm ÷ 7 nm = 10,000. And modern chips pack billions of these transistors into a surface the size of your thumbnail. An Apple M-series chip contains around 20 billion transistors in roughly 120 mm². That's ~167 million transistors per square millimetre — a density so extreme it requires manufacturing tolerances measured in atoms.
5. If you scaled the observable universe (93 billion light-years) down so that 1 metre = 1 light-year, how big would a human be at that scale?
About 180 femtometres — roughly the size of a proton. A 1.7 m human, scaled down by 9.46 × 10¹⁵ (metres per light-year), becomes 1.7 ÷ 9.46×10¹⁵ ≈ 1.8 × 10⁻¹⁶ metres = 0.18 femtometres. Smaller than a proton (which is ~1 fm). At cosmic scale, a human isn't just invisible — we don't even register as subatomic. And yet, as far as we know, we are the only part of the universe that is aware of its own scale.