Math Playground
Measurement

Lengths small to large

From an atom to the universe — every length, on a log scale.

Lengths in the universe span 60 orders of magnitude — from 10⁻¹⁵ m (proton) to 10⁴⁵ m (observable universe).

Try this
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what's about 10ⁿ metres across? = 10^0 m ~ 1 metre — a small child

Powers of ten

Each step on the slider multiplies length by 10. Going from a person (10⁰ m) to a galaxy (≈10²¹ m) is 21 such steps — and to a proton (≈10⁻¹⁵ m) is 15 steps the other way. Writing sizes as 10ⁿ (scientific notation) is the only sane way to compare them.

Some landmarks

  • 10⁻¹⁰ m — an atom (1 ångström)
  • 10⁻³ m — a millimetre
  • 10⁰ m — about your height
  • ~10⁷ m — Earth's diameter (≈12,700 km)
  • ~10¹⁶ m — about one light-year
  • ~10²⁶ m — the observable universe

From the smallest meaningful length (≈10⁻³⁵ m, the Planck length) to the observable universe (≈10²⁷ m) is roughly 60 orders of magnitude — a 1 followed by 60 zeros.