Free space path loss
A radio signal spreads out as it travels, so its power density falls with the square of the distance. Free space path loss measures that spreading between two isotropic antennas, and because a receiving antenna's effective area shrinks at higher frequencies, it also rises with frequency:
Doubling the distance adds 6 dB, as does doubling the frequency. On 2m at 50 km the loss is about 110 dB. Real paths add more: hills, buildings and trees can add tens of dB, while tropospheric ducting can occasionally make signals far stronger than free space predicts.
Building a link budget
The margin is how far the received signal is above the receiver's sensitivity. Aim for 10 to 20 dB on a fixed path to ride out fading. A typical FM handheld needs about 0.25 µV (−119 dBm) for a usable signal, while SSB and CW receivers can work with signals 10 dB or more weaker, and FT8 decodes well below the noise.
dBi and dBd
Antenna gain is quoted against two different references. dBi compares with an imaginary isotropic antenna that radiates equally in every direction. dBd compares with a half-wave dipole, which itself has 2.15 dBi of gain. A figure in dBi is always 2.15 higher than the same gain in dBd, which is worth remembering when comparing adverts. ERP is measured against a dipole and EIRP against an isotropic antenna, so EIRP is 2.15 dB higher than ERP for the same station.
What an S-unit means
IARU Region 1 Technical Recommendation R.1 sets S9 at −73 dBm (50 µV into 50 Ω) below 30 MHz and −93 dBm (5 µV) above, with 6 dB per S-unit. Many radios aren't calibrated this closely, especially at the low end of the scale, so treat S-meter readings as rough. Above S9, readings are given as dB over S9.
Radio horizon
VHF and UHF signals normally travel by line of sight, but the atmosphere bends them slightly, so the radio horizon is about 15% further than the optical one. With heights in metres:
Two stations with antennas 10 m up can expect to reach about 26 km over flat ground. Height matters more than power for VHF and UHF range. Hilltops, of course, help enormously.
Questions
What is the free space path loss at 145 MHz over 50 km?
About 109.7 dB, between isotropic antennas.
How do I convert dBd to dBi?
Add 2.15. A 6 dBd Yagi has a gain of 8.15 dBi.
What is S9 in dBm?
−73 dBm (50 µV into 50 Ω) on HF and −93 dBm (5 µV) on VHF and above, under the IARU Region 1 standard. Each S-unit is 6 dB.
How far can I talk on 2m?
Between two stations with antennas 10 m up, the radio horizon is about 26 km over flat ground. Higher antennas, hills and favourable conditions extend that a lot.