I'm very new to Ham radio and would like to know in simple terms how to calculate antenna the length of an antenna required for a 477 MHz uhf radio and or half wave or 1/4 wave whatever is better. I would like to add an external aerial on the end of coax. Thanks
Antenna length is generally very simple.
You first have to calculate the wavelenght, which is given by the formula : L=C/F
With C = speed of light 3x10^8
F = 447x10^6
You have obtained the wavelenght, divide this by 4 to obtain a quarter wavelength antenna. There are lots of online calculator which will give the result to you even corrected for some factors. You should definitely use them.
You ask whether a half-wave ($\lambda/2$) or quarter-wave ($\lambda/4$) antenna is better.
It depends on where the antenna is mounted and what you are trying to achieve.
The most common use case in your band is repeater communication. You might also look into a $5/8\lambda$ antenna as well, which provides a little extra gain. There are tons of these available cheaply from various manufacturers, usually supporting dual-band operation.