The value and what it means
The Planck length is about 1.616×10⁻³⁵ m (CODATA recommended value 1.616255×10⁻³⁵ m). It is built from just three constants — the gravitational constant, the speed of light and Planck’s constant — which is why it is called a “natural” unit of length. You write 34 zeros after the decimal point before the first 1 appears.
Atom and proton comparison
| Object | Rough size | Planck lengths across |
|---|---|---|
| Proton (diameter) | ~1.7×10⁻¹⁵ m | ~10²⁰ |
| Atom (diameter) | ~10⁻¹⁰ m | ~6×10²⁴ (about 10²⁵) |
| Human hair (thickness) | ~7×10⁻⁵ m | ~4×10³⁰ |
| A person | ~1.7 m | ~10³⁵ |
It is one division: 10⁻¹⁰ m ÷ 1.6×10⁻³⁵ m ≈ 6×10²⁴. That is a gap of 25 digits.
Scale it up to the universe
Take one atom (10⁻¹⁰ m across) and inflate it to the size of the observable universe (about 8.8×10²⁶ m across). The magnification is 8.8×10³⁶. Apply the same factor to the Planck length: 1.6×10⁻³⁵ × 8.8×10³⁶ ≈ 140 m (460 ft). Even with an atom blown up to the whole observable universe, the Planck length is only as tall as a skyscraper.
| Scale this up to the universe | and the Planck length becomes |
|---|---|
| An atom (10⁻¹⁰ m) | ~140 m (a tall building) |
| A proton (1.7×10⁻¹⁵ m) | ~8,400 km (about Earth’s radius) |
The “smallest unit” myth
- “Space is made of Planck-length pixels” is not an established fact. The usual reading is that it marks the scale where our current theories (quantum mechanics and general relativity) can no longer be used together.
- A well-known thought experiment says that probing such a tiny distance would need so much energy that it would create a black hole. In that sense it is closer to “unmeasurable” than “smallest”.
- Experiments are still far from that scale. For quarks we only have an upper limit: smaller than about 10⁻¹⁸ m.
In the game
A universe that starts at the Planck length
In Infinite Universe your universe starts as a Planck-length point. Every tap adds energy, and as energy grows the radius grows exponentially, passing the quark, proton and atom stages. A line on screen compares the current diameter with a real object, such as “Neptune’s orbit x 2.3”.
Fact cards and deep dives
Reaching a stage unlocks its card in the Facts tab. Tap Open deep dive on the Planck length card for the black-hole thought experiment. Every card also has a true-or-false quiz.
FAQ
Is there nothing smaller than the Planck length?
Mathematically you can always write a smaller number. What we lack is a tested theory of what happens at distances below it.
How is it related to Planck time?
Planck time (about 5.4×10⁻⁴⁴ s) is how long light takes to cross one Planck length.
Infinite Universe: Idle Space Clicker
No sign-up, start playing right away, and every record stays on your device. Free on Android.