Last Updated on May 17, 2026 by John Berry
If we are to understand how to assemble our EME station, we need a good figure for EME path loss for use in the path budget. We know that the transmitted power incident on the Moon is captured and re-radiated. That’s the Huygens-Fresnel principle dating from 1818. The Moon’s ability to reflect energy in this way is defined by its cross sectional area or echo area. In the radar world, this is termed the radar cross section.
Empirically, we know that the round trip path loss is about 252dBi at 144MHz, 261dBi at 432MHz, and 271dBi at 1296MHz.
Path loss model
There are four parts to the loss:
Free space path loss up to the Moon;
A reflection factor recognising that the Moon is spherical and rough;
A factor for the coefficient of reflection of rock itself; and
Free space path loss back from the Moon.
The two free space components vary as the distance: 398,000km at apogee, 350,000km at perigee (surface to surface). They are calculated using the free space loss equation. The model below illustrates the gains and losses in simple spatial terms.
Working left to right, the TX power is increased by the TX antenna gain. It is then attenuated by the Free Space Loss to the Moon. The Moon is a big reflector and increases the signal by the passive reflector gain (called target gain factor in the radar world). But the Moon as a lump of rock is an inefficient reflector, and so the signal must be reduced by the Moon’s reflection coefficient. It’s then attenuated again by the FSL on the return leg. It’s finally increased by the RX antenna gain to give the RX input power.
As the budget suggests, if the RX input power is bigger than the receiver threshold (hence having a positive margin), communications will be possible.
There are two approaches to calculation. We could use the microwave engineer’s approach and use the billboard equation. Or we could use the radar engineer’s approach and use the bistatic radar equation. Here’s both.
Billboard approach
The billboard approach uses the idea that we can calculate the effective gain of the Moon as a reflector using the equation:
Billboard gain=42.9 + 40log f + 20log Ae
Coefficient f is the frequency in GHz, and Ae is the billboard (or Moon in this case) cross sectional area in square kilometres.
This approach is neat, but the Moon is a sphere and does not reflect energy coherently back to Earth. Like a disco ball, much of the reflection is lost to space. With contribution from the Moon’s roughness, only the central area of the sphere could be considered a coherent reflector.
Also, in the billboard model, the 40log f term in the gain exactly cancels the 20log f from the uplink path loss and the 20log f from the downlink path loss. This predicts that total path loss is independent of frequency. We know that this is not true.
To account for the aperture reduction with frequency for the Moon as a rough sphere a correction is needed.
Bistatic radar approach
The radar equation balls the whole lot into a single equation. That’s less helpful for understanding but not wrong. It’s bistatic or two-location since the two EME stations are in different places on the surface of the Earth. It comes from radar theory.
The radar equation gives loss as:
Where R is the range or distance to the Moon in metres, lambda is the wavelength in metres, and sigma is the Radar Cross Section (RCS).
In the radar equation, the empirical RCS performs this same role as the wavelength corrected reflective area above. While there are first-principles methods, for a body as complex as the Moon, the empirical formula is often used:
RCS = ρ . π . R2
Reflection coefficient rho is the same rho used in the billboard approach, typically assumed to be 0.07 or 12dB. The RCS (sigma) is in units of dBsm (decibels relative to one square meter). For the Moon it is about 118dBsm.
Since RCS is a unit independent of frequency, the EME path loss correctly increases with frequency.
Separating the terms and expressing the loss in dBi gives us:
L=103.44 + 40log10R + 20log10f – RCS
Here frequency f is in MHz. Distance R in kilometres contributes a fourth power loss (R4 or 40LogR) capturing the loss of the go and return free space contributions as discussed above. RCS is in units of dBsm.
Conclusion
The billboard approach to calculating the EME path loss is easier to understand. But it does need an empirical correction to account for the reflection from a rough sphere.
The bistatic radar equation is an all-in-one calculation that incorporates all the correction needed. More importantly, radio amateurs more often use this.
To help you understand the equations, I’ve had Google Gemini AI build calculators based on the two methods. You can input a more exact distance in both calculators, though not a different distance for each station.
Calculators
For the billboard calculator, use a radius correction of 45% for 144MHz, 25% for 432MHz, and 15% for 1296MHz. I’ve not included other effects that apply outwith the VHF/UHF frequency range.