Minimum sample size n for for estimating the proportion within E percentage points. Of given C.L.=1-α

For proportion: given estimate p̂ (and thus q̂=1-p̂) or else 0.5 for both

p̂:
desired E: (0..1)
C.L.=1-α
90% Zc=1.645 95% Zc=1.96 98% Zc=2.326 99% Zc=2.576

n= Zc2 p̂q̂ / E2:round up
Population size N is irrelevant!

Exs. 

PROPORTION
If want 95% CL that E within .03 (3%) of p.  p̂=.79
If want 95% CL that E within .03 (3%) of p.  p̂ unknown thus .5

If want 99% CL that E within .03 (3%) of p.  p̂=.79
If want 99% CL that E within .03 (3%) of p.  p̂ unknown thus .5
  CL     E     p̂     n  
  95%     3%     .4  
  95%     3%     .5  
  95%     3%     .6  
  99%     3%     .4  
  99%     3%     .5  
  99%     3%     .6  
  95%     2%     .4  
  95%     2%     .5  
  95%     2%     .6  
  99%     2%     .4  
  99%     2%     .5  
  99%     2%     .6