Orders of Magnitude
Compare any two physical objects side-by-side and see how dramatic a factor of 10 really is.
Key Notes
A Fermi estimate uses only powers of 10 to get an answer accurate to within a factor of 10.
log₁₀(A/B) gives the orders of magnitude between A and B.
Use rounding to nearest power of 10 — 2 becomes 10⁰, 5 becomes 10¹, etc.
Formulas
Ratio in orders
Number of orders of magnitude between A and B.
Important Points
A Fermi question (like 'how many piano tuners in Chicago?') is answered by multiplying a few orders of magnitude together.
If you're off by 2 orders of magnitude, your answer is 100× too big or too small.
Orders of Magnitude notes from sciphylab (also known as SciPhy, SciPhy Lab, SciPhy Labs, Physics Lab). Class 11 physics revision for JEE Mains, JEE Advanced, NEET UG, AP Physics 1/2/C, SAT, and CUET-UG.