ITU-R P.838-3 rain attenuation coefficients

Specific attenuation follows γ = k·R^α. These are the coefficients, computed from the recommendation’s own fitting functions rather than interpolated from a sparse table.

Coefficients by frequency

f (GHz)	k_H	α_H	k_V	α_V
1	0.00002589	0.9691	0.0000308	0.8592
2	0.00008469	1.0664	0.00009977	0.9490
3	0.000139	1.2322	0.0001942	1.0688
4	0.0001071	1.6009	0.0002461	1.2475
5	0.0002162	1.6969	0.0002428	1.5317
6	0.0007056	1.5900	0.0004878	1.5728
7	0.001915	1.4810	0.001425	1.4745
8	0.004115	1.3905	0.00345	1.3797
9	0.007535	1.3155	0.006691	1.2895
10	0.01217	1.2571	0.01129	1.2156
11	0.01772	1.2140	0.01731	1.1617
12	0.02386	1.1825	0.02455	1.1216
13	0.03041	1.1586	0.03266	1.0901
14	0.03738	1.1396	0.04126	1.0646
15	0.04481	1.1233	0.05008	1.0440
16	0.05282	1.1086	0.05899	1.0273
17	0.06146	1.0949	0.06797	1.0137
18	0.07078	1.0818	0.07708	1.0025
19	0.08084	1.0691	0.08642	0.9930
20	0.09164	1.0568	0.09611	0.9847
22	0.1155	1.0329	0.117	0.9700
23	0.1286	1.0214	0.1284	0.9630
24	0.1425	1.0101	0.1404	0.9561
25	0.1571	0.9991	0.1533	0.9491
26	0.1724	0.9884	0.1669	0.9421
28	0.2051	0.9679	0.1964	0.9277
30	0.2403	0.9485	0.2291	0.9129
32	0.2778	0.9302	0.2646	0.8981
35	0.3374	0.9047	0.3224	0.8761
38	0.4001	0.8816	0.3844	0.8552
40	0.4431	0.8673	0.4274	0.8421
42	0.4865	0.8539	0.4712	0.8296
45	0.5521	0.8355	0.5375	0.8123
48	0.6172	0.8187	0.6037	0.7967
50	0.66	0.8084	0.6472	0.7871
55	0.7635	0.7853	0.7527	0.7661
60	0.8606	0.7656	0.8515	0.7486
70	1.031	0.7345	1.025	0.7215
80	1.17	0.7115	1.167	0.7021
90	1.281	0.6944	1.279	0.6876
100	1.367	0.6815	1.368	0.6765

How these were produced

ITU-R P.838-3 gives k and α not as a table but as log-logistic fitting functions, defined continuously from 1 to 1000 GHz:

log₁₀ k = Σ a_j · exp[ −((log₁₀ f − b_j) / c_j)² ] + m_k log₁₀ f + c_k

The table above is those functions evaluated at each frequency. Reproducing the recommendation's own published values this way agrees to within 0.03 % across all 44 tabulated entries from 1 to 48 GHz, which is the rounding in the printed table. The advantage over copying the table is that any frequency works, not just the tabulated ones.

Polarisation

Horizontal polarisation fades worse than vertical, because raindrops flatten as they fall and present a wider target to a horizontally polarised wave. At 18 GHz in 50 mm/h the difference is around 20 %, which is free margin for choosing vertical when nothing else constrains you.

For a tilt angle τ and path elevation θ, the recommendation combines the two:

k = [ k_H + k_V + ( k_H − k_V ) cos²θ cos2τ ] / 2

Circular polarisation is τ = 45°, which puts it midway between the two.

Related tool: Microwave link budget and availability, which applies these with the ITU-R P.530 effective path length and time percentage conversion.