what is the relationship between antenna gain and range?

Im trying to expand the range of my wifi network, and Im not sure exactly what to expect from a +27 dbi antenna. As I understand it, this will cause the power density to increase by a factor of 2^9. Does that mean the range will increase by a factor of sqrt(2^9) from an inverse square law? If anyone knows the math behind this stuff, Id really appreciate any help. Thanks.

ok, let me preface this by warning you all: I havent taken a math or physics class in over a decade. So I apologize in advance for any logical or notational inconsistancies.

w = power density
G = initial gain
G' = final gain
P = power
r = initial distance from antenna
r' = final distance
k = proportionality constant

from this equation:
w=G*P*k / 4*pi*r^2

so if P, k, and W are constant...

G*p*k / 4*pi*r^2 = G'*p*k/4*pi*r'^2

therefore:

G'/ G = r'^2 / r^2

and

r * sqrt(G'/ G) = r'

so, as I understand it, after a gain increase of +27 dbi, and a distance increase by a factor of sqrt(2^9), there would be an equivalent power density. Is this math correct? Does this mean that the range of my wifi network will also increase by sqrt(2^9)?

put down the calculator and back away from the chalkboard. you're just going to hurt yourself.

Support :: Calculations :: System Operating Margin :: Terabeam Wireless

Your asking three questions.

Q. How does antenna gain change affect distance?
A. For every 6 dB increase or decrease, you double or half your distance. This is simple inverse square law.

Q. How much will a 27 dBi antenna increase your range?
A. If your current antenna is 21 dBi, then a 27 dBi will double your range.

Q. Where does power come into the picture.
A. It doesn't if you're simple asking about antenna gain.

This is a great WiFi range calculator for iPhone and iPad

WiFi range calculator for iPhone and iPad

you can plug in all the antenna gain and power settings you like and see the results.