SI scientific prefixes — each step below is 1,000× the previous
Once you know these, every scientific size becomes readable. (Note: full SI also includes hecto, kilo, centi, deci — but these six are the ones that matter for physics and biology.)
femto (f)
10⁻¹⁵ m
0.000000000000001 m. Proton territory.
pico (p)
10⁻¹² m
Smallest atom diameters (e.g. helium ~60 pm).
nano (n)
10⁻⁹ m
DNA, molecules, chip transistors.
micro (µ)
10⁻⁶ m
Bacteria, red blood cells, fine pollen grains.
milli (m)
10⁻³ m
1 mm — thickness of a credit card, grain of sand.
All 20 official SI prefixes — the complete table
The five above (femto → milli) are the workhorses of physics and biology. But the full system goes further in both directions — and the large-scale ones appear in energy, data storage, and astronomy.
Larger than 1 (×10ⁿ)
deca (da)
10¹
10 — rarely used alone.
hecto (h)
10²
100 — hectare, hectopascal (hPa, weather).
kilo (k)
10³
1,000 — km, kg, kWh.
mega (M)
10⁶
1 million — MHz, MW, megapixel.
giga (G)
10⁹
1 billion — GHz, GB, GW.
tera (T)
10¹²
1 trillion — TB storage, TW power grids.
peta (P)
10¹⁵
PB (petabyte) — global internet traffic scale.
exa (E)
10¹⁸
EB — total data stored globally is ~100 EB.
zetta (Z)
10²¹
ZB — annual global data creation now ~100 ZB.
yotta (Y)
10²⁴
YB — the largest named SI prefix until 2022.
ronna (R)
10²⁷
Added 2022 — Earth's mass ≈ 6 Rkg.
quetta (Q)
10³⁰
Added 2022 — the Sun's mass ≈ 2 Qkg.
Smaller than 1 (×10⁻ⁿ)
deci (d)
10⁻¹
0.1 — decilitre (dL), used in medicine.
centi (c)
10⁻²
0.01 — cm, the everyday measurement unit.
milli (m)
10⁻³
0.001 — mm, mg, mL.
micro (µ)
10⁻⁶
One millionth — µm, µg, µs.
nano (n)
10⁻⁹
One billionth — nm, ns, nanomaterial.
pico (p)
10⁻¹²
One trillionth — pF (capacitors), ps (laser pulses).
femto (f)
10⁻¹⁵
Proton scale — femtosecond laser pulses.
atto (a)
10⁻¹⁸
Attosecond (as) — timescale of electron motion.
zepto (z)
10⁻²¹
Approaching quark scale in particle physics.
yocto (y)
10⁻²⁴
Smallest named SI prefix until 2022.
ronto (r)
10⁻²⁷
Added 2022 — sub-atomic particle mass range.
quecto (q)
10⁻³⁰
Added 2022 — electron mass ≈ 910 quectograms.
Trivia · The metre and its physical incarnation
The metre was originally defined in 1793 as one ten-millionth of the distance from the North Pole to the equator along the Paris meridian — a definition meant to ground measurement in the physical world rather than the whim of a king. From that definition, a platinum bar was forged and became France's primary length standard. Today, the Conservatoire National des Arts et Métiers in Paris houses the original platinum metre bar that served as France's primary standard from 1799 to 1889. In 1889 it was superseded by the international prototype metre — a platinum–iridium bar kept in Sèvres — which remained the world standard until 1960. Since 1983, the metre has been defined by the speed of light: the distance light travels in vacuum in exactly 1/299,792,458 of a second. A king's foot gave way to a mountain survey, which gave way to a metal bar, which gave way to a fundamental constant of the universe.
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.
2–3 nm
Cutting-edge chip transistor (2024–25)
TSMC's N3 node packs ~170 million transistors per mm². Billions fit in your thumbnail-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.
~3 cm
Large coin · grape · golf ball (4.3 cm)
The scale of things that fit in a closed fist. A standard AA battery is 1.4 cm wide, 5 cm tall.
~10 cm
Hand span · orange · smartphone width
The scale of everyday objects you grip one-handed. Also: adult human heart (~12 cm long).
~30 cm
Ruler · shoe · house cat body
One foot (30.48 cm) — still the dominant non-metric length reference in the US. A newborn baby is ~50 cm.
1 m
Door handle height · child's shoulder
The base unit of the SI system. Originally defined as 1/10,000,000 of the Paris-to-North-Pole distance. Now defined by the speed of light.
1.7 m
Average human height
Our intuitive reference point. Everything else in this module is relative to this. Range: ~1.45 m (5th percentile woman) to ~1.9 m (95th percentile man).
~10 m
3-storey building · large tree · blue whale (30 m)
The tallest humans ever recorded barely reached 2.7 m. A blue whale at 30 m is ~17× a human height.
~100 m
Football pitch · Statue of Liberty (93 m)
The world's tallest buildings pass 800 m. 100 m is ~59 human heights stacked.
~1 km
12-minute walk · airport runway (~3 km)
The human walking scale. Central Park (NYC) is ~4 km long. The Channel Tunnel is 50 km.
~100 km
Kármán line — edge of space
The internationally recognised boundary of outer space. London to Oxford (~90 km). Space begins closer than most cities are to each other.
~400 km
International Space Station orbit · London–Edinburgh
The ISS orbits at ~400 km altitude — less than the London–Paris distance (340 km straight line). Yet it's in space.
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.
384,400 km
Earth–Moon distance
Light takes 1.3 seconds. You could fit ~30 Earths between here and the Moon. Apollo took 3 days.
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 (by specific tensile strength — the comparison is weight-for-weight, not absolute load) and tougher than Kevlar. A single strand of spider silk can stretch up to 40% of its length before breaking, something steel cannot do at all. One full orb web weighs less than 0.5 mg, about the weight of a grain of fine sand. The reason you can walk through a spiderweb and barely feel it is not that it's weak — it's that the total mass is so tiny.
Part F · the full span — 42 orders of magnitude at a glance
From a proton to the observable universe — every zone in one view
Each row below is one order of magnitude (10×). The coloured zones group scales by what lives there.
Part G · build your own comparison — pick any two objects
Select two objects to see the size ratio and what it means
Object A (smaller or equal)
Object B (larger or equal)
—
—
Select two objects above to compare their sizes.
Part H · the emptiness of matter — why solid things are almost nothing
The nucleus of a hydrogen atom is a proton: about 1 femtometre (10⁻¹⁵ m) across. The atom itself — nucleus plus electron cloud — is about 0.1 nanometres (10⁻¹⁰ m): 100,000× larger. In terms of volume, the nucleus occupies roughly one trillionth of the atom. The rest is empty space — technically the electron probability cloud, but nothing solid.
The diagram below is to scale on one axis. If the nucleus (blue dot) is 1 pixel wide, the atom boundary is 100,000 pixels away — well off any screen. What you see is the largest nucleus that fits.
How 2 metres of DNA fits in a 10 µm cell — the compaction chain
Each stage below folds the DNA tighter. The total compaction is ~50,000-fold.
Raw DNA strand
2 m uncoiled
Wound on histones
~11 nm fibre
30 nm chromatin fibre
~30 nm coil
Looped scaffold domains
~300 nm loops
Condensed chromosome
~700 nm
Inside cell nucleus
10 µm
All 46 chromosomes of your genome — 2 m of DNA — compact into a sphere you cannot see without a microscope.
Your body has ~37 trillion cells, each with ~2 m of DNA. Total DNA: ~74 trillion metres — enough to reach from Earth to Pluto and back roughly 17 times. Pluto's average distance from Earth is ~5.9 billion km. All of it coiled into structures you cannot see with a light microscope.
Part I · order-of-magnitude calculator — how many fit?
Enter any two sizes to find the ratio and what it means
Use scientific notation (e.g. 1e-9 for 1 nm) or plain numbers (e.g. 0.000000001). Units must match — enter both in metres.
Smaller size (metres)
Larger size (metres)
Part J · estimation game — which is bigger?
10 questions. Each asks you to pick the larger, or estimate a ratio. See how your size intuition holds up.
Press Start to begin.
Score: 0 / 0
Part K · 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 ~2–3 nm. How many transistors fit across the width of one hair?
Roughly 25,000–35,000 transistors. At 2 nm: 70,000 nm ÷ 2 nm = 35,000. At 3 nm: ≈23,000. 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.
6. The Sun contains 99.86% of all the mass in the solar system. Yet it is considered an average-sized star. How big are the largest known stars relative to the Sun?
The largest known stars (hypergiant candidates like Stephenson 2-18, R136a1, and others) are estimated at roughly 1,500–2,000 solar radii — meaning if placed at the Sun's position, their surface would extend past Jupiter or even Saturn's orbit. The Sun's radius is ~696,000 km; a 2,000-radius star would be ~1.4 billion km across. Our Sun looks average because it sits in the mid-range of the main sequence; smaller red dwarfs are far more common, while giants are rare. Size in stars does not correlate with age in a simple way — some of the biggest are also the youngest and shortest-lived.
7. Earth's oceans average ~3,688 metres deep. If Earth were perfectly smooth (no mountains, no ocean trenches), would the oceans completely cover it?
Yes, and by a significant margin. Earth's surface area is ~510 million km². The total volume of ocean water is ~1.335 billion km³. Spread uniformly over a smooth Earth, water would stand about 2.7 km deep everywhere. But more instructively: the height difference between the deepest oceanic trench (Mariana, ~11 km) and the highest mountain (Everest, ~8.8 km) is only ~20 km total — against Earth's diameter of 12,742 km, that's a variation of less than 0.16%. A billiard ball is smoother than Earth by regulation, but only barely. Earth is more spherical and smooth (proportionally) than a billiard ball, which has bumps of ~0.03% of its diameter — Earth's surface roughness is ~0.17%.
8. A photon of visible light has a wavelength of ~500 nm. A transistor gate is ~2 nm. How many times smaller is the transistor than the wavelength of light — and why does this matter for manufacturing?
250 times smaller. 500 nm ÷ 2 nm = 250. This matters enormously: you cannot use ordinary visible light to print or etch features smaller than its own wavelength (the diffraction limit). Modern chip lithography uses extreme ultraviolet (EUV) light at ~13.5 nm wavelength — still larger than the 2 nm features, which is why manufacturers use computational tricks (multiple patterning, phase-shift masks) and the "2 nm" label refers to a process generation rather than a literal physical dimension. It's a naming convention, not a direct measurement of the gate width.