Height Gain

Last Updated on July 13, 2026 by John Berry

There are two approaches to predicting radio path performance: estimation using empirical models, and calculation using numerical methods. Estimation of path loss using empirical methods needs a height gain correction.

Estimation does not take account of path specifics at the stations like antenna height. Its computational method is based on a small number of variables. The loss needs to be corrected to account for effective antenna height. This is ground height above surrounding terrain plus antenna height on the mast.

By defining all aspects of the path, the numerical methods approach accounts for antenna height, hence no height correction is needed.

I’ve illustrated here an approach to antenna height correction that works with the page on path prediction using empirical formulae or nomograms. I’ve used methods from Recommendation ITU-R P.526-15. See the bibliography for a full reference.

Height correction

The notion of height gain is simple enough. Given a long-distance path (of say 300km) where the Earth’s bulge intrudes into and significantly obstructs the line of sight, path loss is estimated using a calculator or nomogram. These tools assume a terrain and land use on top of the Earth with standard station antenna heights. The result is a standard form of path with the Earth bulge dominating estimates of loss. Effectively then, there’s only one variable – path distance.

If there is indeed a significant antenna height above ground at either or both stations (such as might exist at National Field Day stations), some correction is appropriate. One or both stations may peek above local obstructions, thereby reducing the diffraction loss.

Calculating height gain

The path loss between two stations is given by four terms:

Loss = F(FSL) + F(X) + G(Y1) + G(Y2) dB

FSL is the Free Space Loss as discussed elsewhere on this site. X is a term including primarily the distance but also the type of ground and polarisation. Y1 and Y2 are antenna height gain terms. Here, I’m specifically interested in the terms Y1 and Y2, the height gain at site 1 or TX and site 2 or RX.

The term Y, the height gain, is given by:

Where:
d is the path length in km;
a_e is the effective Earth radius in km;
h is the effective antenna height; and
F is the frequency in MHz.

Height gain is given in decibels. The value for each station must then be used with the corresponding excess path loss over Free Space using the same values for each variable.

For horizontal polarisation at all frequencies, β may be taken as equal to 1.

The antenna height is the effective height over the surrounding terrain, so mast height plus ground height above surroundings.

Nomographs for height gain

Recommendation ITU-R P.526-15 also gives a method using a nomogram. The nomogram for horizontal polarisation over land is given below.

This illustrates, for example, a height gain of around 20dB at 144MHz for a station able to boast an effective antenna height of about 300m above surrounding terrain. This is commensurate with a high broadcast site like Ashkirk, UK, or a contest site from an equivalent commanding hilltop (with a more modest antenna mast).

Height gains effectively add to the system value to give a total available loss value for the path.

Nomogram correction for differing k

Note that because the Earth radius factor, k, modifies the ability of the elevated site to peek over the Earth bulge, the antenna gain must be corrected for variations in k. For the state for 50% of time, use the k=4/3 scale. Otherwise, for small percentages of time modify the frequency using: f_eff = f√k. Then use f_eff on the k = 1 scale. For example, for k=3 to emulate k exceeded for about 5% of time, use a frequency of about 100MHz at 144MHz.