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Physics: Back Of The Envelope

Here's a memory exercise to help you make calculations, approximately, without looking up those pesky constants on your phone. Enter answers in MKS units to one-digit precision following these examples:
  • enter 2.3*1045 as 2p45
  • enter 6.7*10-89 as 7n89
Quiz by
eutaxy
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Last updated: December 30, 2025
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First submittedDecember 30, 2025
Times taken19
Average score38.5%
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Constant
Expression
Value
Notes
Percent Error
Avogadro
NA
6p23
conversion from protons to grams
-0
speed of light
c
3p8
 
+0
gravitational
G
7n11
the coefficient is closer to a simple fraction
+5
reduced Planck
ℏ
1n34
 
-5
Boltzmann
k
1.4n23
just one digit is too sloppy
+1
Coulomb
1/4πε0
9p9
 
+0
Biot-Savart
μ0/4π
1n7
1/ε0μ0 = c2
+0
eV per Joule or electrons per Coulomb
 
6p18
convenient conversion from atomic to macroscopic scale
-4
Joules per (small-c) calorie
 
4
 
-4
reciprocal of fine structure
1/α
137
 
-0
reduced Compton wavelength
ƛ = ℏ/mec
4n13
the Bohr radius is ƛ/α and the classical electron radius is ƛα
+4
Bohr magneton
eℏ/2me
9n24
 
-3
electron masses per nucleon
 
2p3
 
+9
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